NEETS, MODULE 09--INTRODUCTION TO WAVE-GENERATION AND WAVE-SHAPING CIRCUITS

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

1-1 UNCLASSIFIED 1 TUNED CIRCUITS LEARNING OBJECTIVES After you finish this chapter, you should be able to do the following: 1. State the applications of a resonant circuit. 2. Identify the conditions that exist in a resonant circuit. 3. State and apply the formula for resonant frequency of an a.c. circuit. 4. State the effect of changes in inductance (L) and capacitance (C) on resonant frequency (fr). 5. Identify the characteristics peculiar to a series resonant circuit. 6. Identify the characteristics peculiar to a parallel resonant circuit. 7. State and apply the formula for Q. 8. State what is meant by the bandwidth of a resonant circuit and compute the bandwidth for a given circuit. 9. Identify the four general types of filters. 10. Identify how the series- and parallel-resonant circuit can be used as a bandpass or a band-reject filter.

1.1 INTRODUCTION When your radio or television set is turned on, many events take place within the "receiver" before you hear the sound or see the picture being sent by the transmitting station.

Many different signals reach the antenna of a radio receiver at the same time. To select a station, the listener adjusts the tuning dial on the radio receiver until the desired station is heard. Within the radio or TV receiver, the actual "selecting" of the desired signal and the rejecting of the unwanted signals are accomplished by what is called a TUNED CIRCUIT. A tuned circuit consists of a coil and a capacitor connected in series or parallel. Later in this chapter you will see the application and advantages of both series- and parallel-tuned circuits. Whenever the characteristics of inductance and capacitance are found in a tuned circuit, the phenomenon as RESONANCE takes place.

You learned earlier in the Navy Electricity and Electronics Training Series, Module 2, chapter 4, that inductive reactance (X L) and capacitive reactance (XC) have opposite effects on circuit impedance (Z).

You also learned that if the frequency applied to an LCR circuit causes X L and XC to be equal, the circuit is RESONANT.

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

1-2 UNCLASSIFIED If you realize that XL and XC can be equal ONLY at ONE FREQUENCY (the resonant frequency), then you will have learned the most important single fact about resonant circuits. This fact is the principle that enables tuned circuits in the radio receiver to select one particular frequency and reject all others. This is the reason why so much emphasis is placed on XL and XC in the discussions that follow.

Examine figure 1-1. Notice that a basic tuned circuit consists of a coil and a capacitor, connected either in series, view (A), or in parallel, view (B). The resistance (R) in the circuit is usually limited to the inherent resistance of the components (particularly the resistance of the coil). For our purposes we are going to disregard this small resistance in future diagrams and explanations.

Figure 1-1A. — Basic tuned circuits. SERIES TUNED CIRCUIT

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You have already learned how a coil and a capacitor in an a.c. circuit perform. This action will be the basis of the following discussion about tuned circuits.

Why should you study tuned circuits? Because the tuned circuit that has been described above is used in just about every electronic device, from remote-controlled model airplanes to the most sophisticated space satellite.

You can assume, if you are going to be involved in electricity or electronics, that you will need to have a good working knowledge of tuned circuits and how they are used in electronic and electrical circuits.

1.2 REVIEW OF SERIES/PARALLEL A.C. CIRCUITS First we will review the effects of frequency on a circuit which contains resistance, inductance, and capacitance. This review recaps what you previously learned in the Inductive and Capacitive Reactance chapter in module 2 of the NEETS.

1.2.1 Frequency Effects on RLC Circuits Perhaps the most often used control of a radio or television set is the station or channel selector. Of course, the volume, tone, and picture quality controls are adjusted to suit the individual's taste, but very often they are not adjusted when the station is changed. What goes on behind this station selecting? In this chapter, you will learn the basic principles that account for the ability of circuits to "tune" to the desired station.

Figure 1-1B.— Basic tuned circuits. PARALLEL TUNED CIRCUIT

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

1-4 UNCLASSIFIED 1.2.1.1 Effect of Frequency on Inductive Reactance In an a.c. circuit, an inductor produces inductive reactance which causes the current to lag the voltage by 90 degrees. Because the inductor "reacts" to a changing current, it is known as a reactive component. The opposition that an inductor presents to a.c. is called inductive reactance (XL). This opposition is caused by the inductor "reacting" to the changing current of the a.c. source. Both the inductance and the frequency determine the magnitude of this reactance. This relationship is stated by the formula:

As shown in the equation, any increase in frequency, or "f," will cause a corresponding increase of inductive reactance, or "X L." Therefore, the INDUCTIVE REACTANCE VARIES DIRECTLY WITH THE FREQUENCY. As you can see, the higher the frequency, the greater the inductive reactance; the lower the frequency, the less the inductive reactance for a given inductor. This relationship is illustrated in figure 1-2. Increasing values of XL are plotted in terms of increasing frequency. Starting at the lower left corner with zero frequency, the inductive reactance is zero. As the frequency is increased (reading to the right), the inductive reactance is shown to increase in direct proportion.

Figure 1-2 Effect of frequency on inductive reactance

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

1-5 UNCLASSIFIED 1.2.1.2 Effect of Frequency on Capacitive Reactance In an a.c. circuit, a capacitor produces a reactance which causes the current to lead the voltage by 90 degrees. Because the capacitor "reacts" to a changing voltage, it is known as a reactive component. The opposition a capacitor presents to a.c. is called capacitive reactance (X C). The opposition is caused by the capacitor "reacting" to the changing voltage of the a.c. source. The formula for capacitive reactance is:

In contrast to the inductive reactance, this equation indicates that the CAPACITIVE REACTANCE VARIES INVERSELY WITH THE FREQUENCY. When f = 0, X C is infinite (∞) and decreases as frequency increases. That is, the lower the frequency, the greater the capacitive reactance; the higher the frequency, the less the reactance for a given capacitor.

As shown in figure 1-3, the effect of capacitance is opposite to that of inductance. Remember, capacitance causes the current to lead the voltage by 90 degrees, while inductance causes the current to lag the voltage by 90 degrees.

Figure 1-3 Effect of frequency on capacitive reactance

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1-6 UNCLASSIFIED 1.2.1.3 Effect of Frequency on Resistance In the expression for inductive reactance, XL = 2 fL, and in the expression for capacitive reactance,

both contain "f" (frequency). Any change of frequency changes the reactance of the circuit components as already explained. So far, nothing has been said about the effect of frequency on resistance. In an Ohm's law relationship, such as R = E/I no "f" is involved. Thus, for all practical purposes, a change of frequency does not affect the resistance of the circuit. If a 60-hertz a.c. voltage causes 20 milliamperes of current in a resistive circuit, then the same voltage at 2000 hertz, for example, would still cause 20 milliamperes to flow.

NOTE: Remember that the total opposition to a.c. is called impedance (Z). Impedance is the combination of inductive reactance (X L), capacitive reactance (XC), and resistance (R). When dealing with a.c. circuits, the impedance is the factor with which you will ultimately be concerned. But, as you have just been shown, the resistance (R) is not affected by frequency. Therefore, the remainder of the discussion of a.c. circuits will only be concerned with the reactance of inductors and capacitors and will ignore resistance.

1.2.1.4 A.c. Circuits Containing both Inductive and Capacitive Reactances A.c. circuits that contain both an inductor and a capacitor have interesting characteristics because of the opposing effects of L and C. X L and XC may be treated as reactors which are 180 degrees out of phase. As shown in figure 1-2, the vector for XL should be plotted above the baseline; vector for XC, figure 1-3, should be plotted below the baseline. In a series circuit, the effective reactance, or what is termed the RESULTANT REACTANCE, is the difference between the individual reactances. As an equation, the resultant reactance is:

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1-7 UNCLASSIFIED Suppose an a.c. circuit contains an XL of 300 ohms and an XC of 250 ohms. The resultant reactance is:

In some cases, the X C may be larger than the X L. If XL = 1200 ohms and X C = 4000 ohms, the difference is: X = XL − XC = 1200 − 4000 = −2800 ohms (capacitive). The total carries the sign (+ or −) of the greater number (factor).

Q-1. What is the relationship between frequency and the values of (a) X L, (b) XC, and (c) R? Q-2. In an a.c. circuit that contains both an inductor and a capacitor, what term is used for the difference between the individual reactances? 1.3 RESONANCE For every combination of L and C, there is only ONE frequency (in both series and parallel circuits) that causes X L to exactly equal XC; this frequency is known as the RESONANT FREQUENCY. When the resonant frequency is fed to a series or parallel circuit, X L becomes equal to XC, and the circuit is said to be RESONANT to that frequency. The circuit is now called a RESONANT CIRCUIT; resonant circuits are tuned circuits. The circuit condition wherein XL becomes equal to XC is known as RESONANCE.

Each LCR circuit responds to resonant frequency differently than it does to any other frequency. Because of this, an LCR circuit has the ability to separate frequencies. For example, suppose the TV or radio station you want to see or hear is broadcasting at the resonant frequency. The LC "tuner" in your set can divide the frequencies, picking out the resonant frequency and rejecting the other frequencies. Thus, the tuner selects the station you want and rejects all other stations. If you decide to select another station, you can change the frequency by tuning the resonant circuit to the desired frequency.

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1-8 UNCLASSIFIED 1.3.1 Resonant Frequency As stated before, the frequency at which XL equals XC (in a given circuit) is known as the resonant frequency of that circuit. Based on this, the following formula has been derived to find the exact resonant frequency when the values of circuit components are known:

There are two important points to remember about this formula. First, the resonant frequency found when using the formula will cause the reactances (X L and XC) of the L and C components to be equal. Second, any change in the value of either L or C will cause a change in the resonant frequency.

An increase in the value of either L or C, or both L and C, will lower the resonant frequency of a given circuit. A decrease in the value of L or C, or both L and C, will raise the resonant frequency of a given circuit.

The symbol for resonant frequency used in this text is f. Different texts and references may use other symbols for resonant frequency, such as f o, Fr, and fR. The symbols for many circuit parameters have been standardized while others have been left to the discretion of the writer. When you study, apply the rules given by the writer of the text or reference; by doing so, you should have no trouble with nonstandard symbols and designations.

The resonant frequency formula in this text is:

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

1-9 UNCLASSIFIED By substituting the constant .159 for the quantity

the formula can be simplified to the following:

Let's use this formula to figure the resonant frequency (f r). The circuit is shown in the practice tank circuit of figure 1-4.

Figure 1-4 Practice tank circuit

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The important point here is not the formula nor the mathematics. In fact, you may never have to compute a resonant frequency. The important point is for you to see that any given combination of L and C can be resonant at only one frequency; in this case, 205 kHz.

The universal reactance curves of figures 1-2 and 1-3 are joined in figure 1-5 to show the relative values of X L and XL at resonance, below resonance, and above resonance.

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First, note that f r, (the resonant frequency) is that frequency (or point) where the two curves cross. At this point, and ONLY this point, XL equals XC. Therefore, the frequency indicated by fr is the one and only frequency of resonance. Note the resistance symbol which indicates that at resonance all reactance is cancelled and the circuit impedance is effectively purely resistive. Remember, a.c. circuits that are resistive have no phase shift between voltage and current. Therefore, at resonance, phase shift is cancelled. The phase angle is effectively zero.

Second, look at the area of the curves to the left of f r. This area shows the relative reactances of the circuit at frequencies BELOW resonance. To these LOWER frequencies, X C will always be greater than XL. There will always be some capacitive reactance left in the circuit after all inductive reactance has been cancelled. Because the impedance has a reactive component, there will be a phase shift. We can also state that below fr the circuit will appear capacitive.

Lastly, look at the area of the curves to the right of f. This area shows the relative reactances of the circuit at frequencies ABOVE resonance. To these HIGHER frequencies, X L will always be greater than XC. There will always be some inductive reactance left in the circuit after all capacitive reactance has been cancelled. The inductor symbol shows that to these higher frequencies, the circuit will always appear to have some inductance. Because of this, there will be a phase shift.

Figure 1-5 Relationship between XL and XC as frequency increases

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1-12 UNCLASSIFIED 1.4 RESONANT CIRCUITS Resonant circuits may be designed as series resonant or parallel resonant. Each has the ability to discriminate between its resonant frequency and all other frequencies. How this is accomplished by both series- and parallel-LC circuits is the subject of the next section.

NOTE: Practical circuits are often more complex and difficult to understand than simplified versions. Simplified versions contain all of the basic features of a practical circuit, but leave out the nonessential features. For this reason, we will first look at the IDEAL SERIES-RESONANT CIRCUIT— a circuit that r eally doesn't exist except for our purposes here.

1.4.1 The Ideal Series-Resonant Circuit The ideal series-resonant circuit contains no resistance; it consists of only inductance and capacitance in series with each other and with the source voltage. In this respect, it has the same characteristics of the series circuits you have studied previously. Remember that current is the same in all parts of a series circuit because there is only one path for current.

Each LC circuit responds differently to different input frequencies. In the following paragraphs, we will analyze what happens internally in a series-LC circuit when frequencies at resonance, below resonance, and above resonance are applied. The L and C values in the circuit are those used in the problem just studied under resonant- frequency. The frequencies applied are the three inputs from figure 1-6. Note that the resonant frequency of each of these components is 205 kHz, as figured in the problem.

Figure 1-6 Output of the resonant circuit

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1-13 UNCLASSIFIED 1.4.1.1 How the Ideal Series-LC Circuit Responds to the Resonant Frequency (205 kHz)

Note: You are given the values of X L, XC, and fr but you can apply the formulas to figure them. The values given are rounded off to make it easier to analyze the circuit.

First, note that X L and XC are equal. This shows that the circuit is resonant to the applied frequency of 205 kHz. XL and XC are opposite in effect; therefore, they subtract to zero. (2580 ohms − 2580 ohms = zero.) At resonance, then, X = zero. In our theoretically perfect circuit with zero resistance and zero reactance, the total opposition to current (Z) must also be zero.

Now, apply Ohm's law for a.c. circuits:

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1-14 UNCLASSIFIED Don't be confused by this high value of current. Our perfect, but impossible, circuit has no opposition to current. Therefore, current flow will be extremely high. The important points here are that AT RESONANCE, impedance is VERY LOW, and the resulting current will be comparatively HIGH.

If we apply Ohm's law to the individual reactances, we can figure relative values of voltage across each reactance.

These are reactive voltages that you have studied previously. The voltage across each reactance will be comparatively high. A comparatively high current times 2580 ohms yields a high voltage. At any given instant, this voltage will be of opposite polarity because the reactances are opposite in effect. E L + EC = zero volts.

WARNING THE INDIVIDUAL VOLTAGES MAY REACH QUITE HIGH VALUES. ALTHOUGH LITTLE POWER IS PRESENT, THE VOLTAGE IS REAL AND CARE SHOULD BE TAKEN IN WORKING WITH IT.

Let's summarize our findings so far. In a series-LC circuit with a resonant-frequency voltage applied, the following conditions exist:

• XL and XC are equal and subtract to zero.

• Resultant reactance is zero ohms.

• Impedance (Z) is reduced to a MINIMUM value.

• With minimum Z, current is MAXIMUM for a given voltage.

• Maximum current causes maximum voltage drops across the individual reactances.

All of the above follow in sequence from the fact that XL = XC at the resonant frequency.

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1-15 UNCLASSIFIED 1.4.1.2 How the Ideal Series-LC Circuit Respond to a Frequency Below Resonance (100 kHz) Given:

First, note that X L and XC are no longer equal. XC is larger than it was at resonance; XL is smaller. By applying the formulas you have learned, you know that a lower frequency produces a higher capacitive reactance and a lower inductive reactance. The reactances subtract but do not cancel (X L − XC = 1260 − 5300 = 4040 ohms (capacitive)). At an input frequency of 100 kHz, the circuit (still resonant to 205 kHz) has a net reactance of 4040 ohms. In our theoretically perfect circuit, the total opposition (Z) is equal to X, or 4040 ohms.

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1-16 UNCLASSIFIED As before, let's apply Ohm's law to the new conditions.

The voltage drops across the reactances are as follows:

In summary, in a series-LC circuit with a source voltage that is below the resonant frequency (100 kHz in the example), the resultant reactance (X), and therefore impedance, is higher than at resonance. In addition current is lower, and the voltage drops across the reactances are lower. All of the above follow in sequence due to the fact that X C is greater than XL at any frequency lower than the resonant frequency.

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1-17 UNCLASSIFIED 1.4.1.3 How the Ideal Series-LC Circuit Responds to a Frequency Above Resonance (300 kHz)

Again, X L and XC are not equal. This time, XL is larger than XC. (If you don't know why, apply the formulas and review the past several pages.) The resultant reactance is 2000 ohms (XL − X C = 3770 − 1770 = 2000 ohms.) Therefore, the resultant reactance (X), or the impedance of our perfect circuit at 300 kHz, is 2000 ohms.

By applying Ohm's law as before:

In summary, in a series-LC circuit with a source voltage that is above the resonant frequency (300 kHz in this example), impedance is higher than at resonance, current is lower, and the voltage drops across the reactances are lower. All of the above follow in sequence from the fact that X L is greater than XC at any frequency higher than the resonant frequency.

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1-18 UNCLASSIFIED 1.4.1.4 Summary of the Response of the Ideal Series-LC Circuit to Frequencies Above, Below, and at Resonance The ideal series-resonant circuit has zero impedance. The impedance increases for frequencies higher and lower than the resonant frequency. The impedance characteristic of the ideal series-resonant circuit results because resultant reactance is zero ohms at resonance and ONLY at resonance. All other frequencies provide a resultant reactance greater than zero.

Zero impedance at resonance allows maximum current. All other frequencies have a reduced current because of the increased impedance. The voltage across the reactance is greatest at resonance because voltage drop is directly proportional to current. All discrimination between frequencies results from the fact that X L and XC completely counteract ONLY at the resonant frequency.

1.4.1.5 How the Typical Series-LC Circuit Differs From the Ideal As you learned much earlier in this series, resistance is always present in practical electrical circuits; it is impossible to eliminate. A typical series-LC circuit, then, has R as well as L and C.

If our perfect (ideal) circuit has zero resistance, and a typical circuit has "some" resistance, then a circuit with a very small resistance is closer to being perfect than one that has a large resistance. Let's list what happens in a series-resonant circuit because resistance is present. This is not new to you - just a review of what you have learned previously.

In a series-resonant circuit that is basically L and C, but that contains "some" R, the following statements are true:

• X L, XC, and R components are all present and can be shown on a vector diagram, each at right angles with the resistance vector (baseline).

• At resonance, the resultant reactance is zero ohms. Thus, at resonance, The circuit impedance equals only the resistance (R). The circuit impedance can never be less than R because the original resistance will always be present in the circuit.

• At resonance, a practical series-RLC circuit ALWAYS has MINIMUM impedance. The actual value of impedance is that of the resistance present in the circuit (Z = R).

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1-19 UNCLASSIFIED Now, if the designers do their very best (and they do) to keep the value of resistance in a practical series-RLC circuit LOW, then we can still get a fairly high current at resonance. The current is NOT "infinitely" high as in our ideal circuit, but is still higher than at any other frequency. The curve and vector relationships for the practical circuit are shown in figure 1-7.

Figure 1-7 Curves of impedance and current in an RLC series resonant circuit

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1-20 UNCLASSIFIED Note that the impedance curve does not reach zero at its minimum point. The vectors above and below resonance show that the phase shift of the circuit at these frequencies is less than 90 degrees because of the resistance.

The horizontal width of the curve is a measure of how well the circuit will pick out (discriminate) the one desired frequency. The width is called BANDWIDTH, and the ability to discriminate between frequencies is known as SELECTIVITY. Both of these characteristics are affected by resistance. Lower resistance allows narrower bandwidth, which is the same as saying the circuit has better selectivity. Resistance, then, is an unwanted quantity that cannot be eliminated but can be kept to a minimum by the circuit designers.

More on bandwidth, selectivity, and measuring the effects of resistance in resonant circuits will follow the discussion of parallel resonance.

Q-3. State the formula for resonant frequency. Q-4. If the inductor and capacitor values are increased, what happens to the resonant frequency? Q-5. In an "ideal" resonant circuit, what is the relationship between impedance and current? Q-6. In a series-RLC circuit, what is the condition of the circuit if there is high impedance, low current, and low reactance voltages?

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1-21 UNCLASSIFIED 1.4.1.6 How the Parallel-LC Circuit Stores Energy A parallel-LC circuit is often called a TANK CIRCUIT because it can store energy much as a tank stores liquid. It has the ability to take energy fed to it from a power source, store this energy alternately in the inductor and capacitor, and produce an output which is a continuous a.c. wave. You can understand how this is accomplished by carefully studying the sequence of events shown in figure 1-8. You must thoroughly understand the capacitor and inductor action in this figure before you proceed further in the study of parallel-resonant circuits.

In each view of figure 1-8, the waveform is of the charging and discharging CAPACITOR VOLTAGE. In view (A), the switch has been moved to position C. The d.c. voltage is applied across the capacitor, and the capacitor charges to the potential of the battery.

In view (B), moving the switch to the right completes the circuit from the capacitor to the inductor and places the inductor in series with the capacitor. This furnishes a path for the excess electrons on the upper plate of the capacitor to flow to the lower plate, and thus starts neutralizing the capacitor charge. As these electrons flow through the coil, a magnetic field is built up around the coil. The energy which was first stored by the electrostatic field of the capacitor is now stored in the electromagnetic field of the inductor.

Figure 1-8A. Capacitor and inductor action in a tank circuit

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View (C) shows the capacitor discharged and a maximum magnetic field around the coil. The energy originally stored in the capacitor is now stored entirely in the magnetic field of the coil.

Since the capacitor is now completely discharged, the magnetic field surrounding the coil starts to collapse. This induces a voltage in the coil which causes the current to continue flowing in the same direction and charges the capacitor again. This time the capacitor charges to the opposite polarity, view (D).

Figure 1-8B.—Capacitor and inductor action in a tank circuit Figure 1-8C.— Capacitor and inductor action in a tank circuit

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In view (E), the magnetic field has completely collapsed, and the capacitor has become charged with the opposite polarity. All of the energy is again stored in the capacitor.

In view (F), the capacitor now discharges back through the coil. This discharge current causes the magnetic field to build up again around the coil.

Figure 1-8D.—Capacitor and inductor action in a tank circuit Figure 1-8E.— Capacitor and inductor action in a tank circuit

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In view (G), the capacitor is completely discharged. The magnetic field is again at maximum.

Figure 1-8F.—Capacitor and inductor action in a tank circuit Figure 1-8G.— Capacitor and inductor action in a tank circuit

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1-25 UNCLASSIFIED In view (H), with the capacitor completely discharged, the magnetic field again starts collapsing. The induced voltage from the coil maintains current flowing toward the upper plate of the capacitor.

In view (I), by the time the magnetic field has completely collapsed, the capacitor is again charged with the same polarity as it had in view (A). The energy is again stored in the capacitor, and the cycle is ready to start again.

Figure 1-8H.— Capacitor and inductor action in a tank circuit Figure 1-8I.—Capacitor and inductor action in a tank circuit

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1-26 UNCLASSIFIED The number of times per second that these events in figure 1-8 take place is called NATURAL FREQUENCY or RESONANT FREQUENCY of the circuit. Such a circuit is said to oscillate at its resonant frequency.

It might seem that these oscillations could go on forever. You know better, however, if you apply what you have already learned about electric circuits.

This circuit, as all others, has some resistance. Even the relatively small resistance of the coil and the connecting wires cause energy to be dissipated in the form of heat (I 2R loss). The heat loss in the circuit resistance causes the charge on the capacitor to be less for each subsequent cycle. The result is a DAMPED WAVE, as shown in figure 1-9. The charging and discharging action will continue until all of the energy has been radiated or dissipated as heat.

If it were possible to have a circuit with absolutely no resistance, there would be no heat loss, and the oscillations would tend to continue indefinitely. You have already learned that tuned circuits are designed to have very little resistance. Reducing I 2R losses is still another reason for having low resistance.

A "perfect" tuned circuit would produce the continuous sine wave shown in figure 1-10. Its frequency would be that of the circuit.

Figure 1-9 Damped wave

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Because we don't have perfection, another way of causing a circuit to oscillate indefinitely would be to apply a continuous a.c. or pulsing source to the circuit. If the source is at the resonant frequency of the circuit, the circuit will oscillate as long as the source is applied.

The reasons why the circuit in figure 1-8 oscillates at the resonant frequency have to do with the characteristics of resonant circuits. The discussion of parallel resonance will not be as detailed as that for series resonance because the idea of resonance is the same for both circuits. Certain characteristics differ as a result of L and C being in parallel rather than in series. These differences will be emphasized.

Q-7. When the capacitor is completely discharged, where is the energy of the tank circuit stored? Q-8. When the magnetic field of the inductor is completely collapsed, where is the energy of the tank circuit stored?

Figure 1-10 Sine wave-resonant frequency

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1-28 UNCLASSIFIED 1.4.2 Parallel Resonance Much of what you have learned about resonance and series-LC circuits can be applied directly to parallel-LC circuits. The purpose of the two circuits is the same — to select a specific frequency and reject all others. XL still equals XC at resonance. Because the inductor and capacitor are in parallel, however, the circuit has the basic characteristics of an a.c. parallel circuit. The parallel hookup causes frequency selection to be accomplished in a different manner. It gives the circuit different characteristics. The first of these characteristics is the ability to store energy.

1.4.2.1 The Characteristics of a Typical Parallel-Resonant Circuit Look at figure 1-11. In this circuit, as in other parallel circuits, the voltage is the same across the inductor and capacitor. The currents through the components vary inversely with their reactances in accordance with Ohm's law. The total current drawn by the circuit is the vector sum of the two individual component currents. Finally, these two currents, IL and IC, are 180 degrees out of phase because the effects of L and C are opposite. There is not a single fact new to you in the above. It is all based on what you have learned previously about parallel a.c. circuits that contain L and C.

Figure 1-11 Curves of impedance and current in an RLC parallel- resonant circuit

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1-29 UNCLASSIFIED Now, at resonance, XL is still equal to X C. Therefore, IL must equal IC. Remember, the voltage is the same; the reactances are equal; therefore, according to Ohm's law, the currents must be equal. But, don't forget, even though the currents are equal, they are still opposites. That is, if the current is flowing "up" in the capacitor, it is flowing "down" in the coil, and vice versa. In effect, while the one component draws current, the other returns it to the source. The net effect of this "give and take action" is that zero current is drawn from the source at resonance. The two currents yield a total current of zero amperes because they are exactly equal and opposite at resonance.

A circuit that is completed and has a voltage applied, but has zero current, must have an INFINITE IMPEDANCE (apply Ohm's law — any voltage divided by zero yields infinity).

By now you know that we have just ignored our old friend resistance from previous discussions. In an actual circuit, at resonance, the currents will not quite counteract each other because each component will have different resistance. This resistance is kept extremely low, but it is still there. The result is that a relatively small current flows from the source at resonance instead of zero current. Therefore, a basic characteristic of a practical parallel-LC circuit is that, at resonance, the circuit has MAXIMUM impedance which results in MINIMUM current from the source. This current is often called line current. This is shown by the peak of the waveform for impedance and the valley for the line current, both occurring at f r the frequency of resonance in figure 1-11.

There is little difference between the circuit pulsed by the battery in figure 1-8 that oscillated at its resonant (or natural) frequency, and the circuit we have just discussed. The equal and opposite currents in the two components are the same as the currents that charged and discharged the capacitor through the coil.

For a given source voltage, the current oscillating between the reactive parts will be stronger at the resonant frequency of the circuit than at any other frequency. At frequencies below resonance, capacitive current will decrease; above the resonant frequency, inductive current will decrease. Therefore, the oscillating current (or circulating current, as it is sometimes called), being the lesser of the two reactive currents, will be maximum at resonance.

If you remember, the basic resonant circuit produced a "damped" wave. A steady amplitude wave was produced by giving the circuit energy that would keep it going. To do this, the energy had to be at the same frequency as the resonant frequency of the circuit.

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1-30 UNCLASSIFIED So, if the resonant frequency is "timed" right, then all other frequencies are "out of time" and produce waves that tend to buck each other. Such frequencies cannot produce strong oscillating currents.

In our typical parallel-resonant (LC) circuit, the line current is minimum (because the impedance is maximum). At the same time, the internal oscillating current in the tank is maximum. Oscillating current may be several hundred times as great as line current at resonance.

In any case, this circuit reacts differently to the resonant frequency than it does to all other frequencies. This makes it an effective frequency selector.

1.4.2.2 Summary of Resonance Both series- and parallel-LC circuits discriminate between the resonant frequency and all other frequencies by balancing an inductive reactance against an equal capacitive reactance.

In series, these reactances create a very low impedance. In parallel, they create a very high impedance. These characteristics govern how and where designers use resonant circuits. A low impedance requirement would require a series-resonant circuit. A high- impedance requirement would require the designer to use a parallel-resonant circuit.

1.4.2.3 Tuning a Band of Frequencies Our resonant circuits so far have been tuned to a single frequency - the resonant frequency. This is fine if only one frequency is required. However, there are hundreds of stations on many different frequencies.

Therefore, if we go back to our original application, that of tuning to different radio stations, our resonant circuits are not practical. The reason is because a tuner for each frequency would be required and this is not practical.

What is a practical solution to this problem? The answer is simple. Make either the capacitor or the inductor variable. Remember, changing either L or C changes the resonant frequency.

Now you know what has been happening all of these years when you "pushed" the button or "turned" the dial. You have been changing the L or C in the tuned circuits by the amount necessary to adjust the tuner to resonate at the desired frequency. No matter how complex a unit, if it has LC tuners, the tuners obey these basic laws.

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1-31 UNCLASSIFIED Q-9. What is the term for the number of times per second that tank circuit energy is either stored in the inductor or capacitor? Q-10. In a parallel-resonant circuit, what is the relationship between impedance and current? Q-11. When is line current minimum in a parallel-LC circuit? 1.5 RESONANT CIRCUITS AS FILTER CIRCUITS The principle of series- or parallel-resonant circuits have many applications in radio, television, communications, and the various other electronic fields throughout the Navy. As you have seen, by making the capacitance or inductance variable, the frequency at which a circuit will resonate can be controlled.

In addition to station selecting or tuning, resonant circuits can separate currents of certain frequencies from those of other frequencies.

Circuits in which resonant circuits are used to do this are called FILTER CIRCUITS.

If we can select the proper values of resistors, inductors, or capacitors, a FILTER NETWORK, or "frequency selector," can be produced which offers little opposition to one frequency, while BLOCKING or ATTENUATING other frequencies. A filter network can also be designed that will "pass" a band of frequencies and "reject" all other frequencies. Most electronic circuits require the use of filters in one form or another.

One example of a filter being applied is in a rectifier circuit. As you know, an alternating voltage is changed by the rectifier to a direct current. However, the d.c. voltage is not pure; it is still pulsating and fluctuating. In other words, the signal still has an a.c. component in addition to the d.c. voltage. By feeding the signal through simple filter networks, the a.c. component is reduced. The remaining d.c. is as pure as the designers require.

Bypass capacitors, which you have already studied, are part of filter networks that, in effect, bypass, or shunt, unwanted a.c. components to ground.

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1-32 UNCLASSIFIED 1.5.1 The Idea of "Q" Several times in this chapter, we have discussed "ideal" or theoretically perfect circuits. In each case, you found that resistance kept our circuits from being perfect. You also found that low resistance in tuners was better than high resistance. Now you will learn about a factor that, in effect, measures just how close to perfect a tuner or tuner component can be. This same factor affects BANDWIDTH and SELECTIVITY. It can be used in figuring voltage across a coil or capacitor in a series-resonant circuit and the amount of circulating (tank) current in a parallel-resonant circuit. This factor is very important and useful to designers. Technicians should have some knowledge of the factor because it affects so many things. The factor is known as Q. Some say it stands for quality (or merit). The higher the Q, the better the circuit; the lower the losses (I2R), the closer the circuit is to being perfect.

Having studied the first part of this chapter, you should not be surprised to learn that resistance (R) has a great effect on this figure of merit or quality.

1.5.1.1 Q is a Ratio Q is really very simple to understand if you think back to the tuned-circuit principles just covered. Inductance and capacitance are in all tuners. Resistance is an impurity that causes losses. Therefore, components that provide the reactance with a minimum of resistance are "purer" (more perfect) than those with higher resistance. The actual measure of this purity, merit, or quality must include the two basic quantities, X and R.

The ratio

does the job for us. Let's take a look at it and see just why it measures quality.

First, if a perfect circuit has zero resistance, then our ratio should give a very high value of Q to reflect the high quality of the circuit. Does it?

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1-33 UNCLASSIFIED Assume any value for X and a zero value for R.

Then:

Remember, any value divided by zero equals infinity. Thus, our ratio is infinitely high for a theoretically perfect circuit.

With components of higher resistance, the Q is reduced. Dividing by a larger number always yields a smaller quantity. Thus, lower quality components produce a lower Q. Q, then, is a direct and accurate measure of the quality of an LC circuit.

Q is just a ratio. It is always just a number — no units. The higher the number, the "better" the circuit. Later as you get into more practical circuits, you may find that low Q may be desirable to provide certain characteristics. For now, consider that higher is better.

Because capacitors have much, much less resistance in them than inductors, the Q of a circuit is very often expressed as the Q of the coil or:

The answer you get from using this formula is very near correct for most purposes. Basically, the Q of a capacitor is so high that it does not limit the Q of the circuit in any practical way. For that reason, the technician may ignore it.

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1-34 UNCLASSIFIED 1.5.1.2 The Q of a Coil Q is a feature that is designed into a coil. When the coil is used within the frequency range for which it is designed, Q is relatively constant. In this sense, it is a physical characteristic.

Inductance is a result of the physical makeup of a coil - number of turns, core, type of winding, etc. Inductance governs reactance at a given frequency. Resistance is inherent in the length, size, and material of the wire. Therefore, the Q of a coil is mostly dependent on physical characteristics.

Values of Q that are in the hundreds are very practical and often found in typical equipment.

1.5.1.3 Application of Q For the most part, Q is the concern of designers, not technicians. Therefore, the chances of you having to figure the Q of a coil are remote. However, it is important for you to know some circuit relationships that are affected by Q.

1.5.1.4 Q Relationships in Series Circuits Q can be used to determine the "gain" of series-resonant circuits. Gain refers to the fact that at resonance, the voltage drop across the reactances are greater than the applied voltage. Remember, when we applied Ohm's law in a series-resonant circuit, it gave us the following characteristics:

• Low impedance, high current.

• High current; high voltage across the comparatively high reactances.

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1-35 UNCLASSIFIED This high voltage is usable where little power is required, such as in driving the grid of a vacuum tube or the gate of a field effect transistor (F.E.T.). The gain of a properly designed series-resonant circuit may be as great or greater than the amplification within the amplifier itself. The gain is a function of Q, as shown in the following example:

If the Q of the coil were 100, then the gain would be 100; that is, the voltage of the coil would be 100 times that of the input voltage to the series circuit.

Resistance affects the resonance curve of a series circuit in two ways — the lower the resistance, the higher the current; also, the lower the resistance, the sharper the curve. Because low resistance causes high Q, these two facts are usually expressed as functions of Q. That is, the higher the Q, the higher and sharper the curve and the more selective the circuit.

The lower the Q (because of higher resistance), the lower the current curve; therefore, the broader the curve, the less selective the circuit. A summary of the major characteristics of series RLC-circuits at resonance is given in table 1-1.

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1.5.1.5 Q Relationships in a Parallel-Resonant Circuit There is no voltage gain in a parallel-resonant circuit because voltage is the same across all parts of a parallel circuit. However, Q helps give us a measure of the current that circulates in the tank.

Table 1-1 Major Characteristics of Series RLC Circuits at Resonance

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1-37 UNCLASSIFIED Given:

Again, if the Q were 100, the circulating current would be 100 times the value of the line current. This may help explain why some of the wire sizes are very large in high-power amplifying circuits.

The impedance curve of a parallel-resonant circuit is also affected by the Q of the circuit in a manner similar to the current curve of a series circuit. The Q of the circuit determines how much the impedance is increased across the parallel-LC circuit. (Z = Q ⋅ X L)

The higher the Q, the greater the impedance at resonance and the sharper the curve. The lower the Q, the lower impedance at resonance; therefore, the broader the curve, the less selective the circuit. The major characteristics of parallel-RLC circuits at resonance are given in table 1-2.

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Table 1-2 Major Characteristics of Parallel RLC Circuits at Resonance

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1-39 UNCLASSIFIED 1.5.1.6 Summary of Q The ratio that is called Q is a measure of the quality of resonant circuits and circuit components. Basically, the value of Q is an inverse function of electrical power dissipated through circuit resistance. Q is the ratio of the power stored in the reactive components to the power dissipated in the resistance. That is, high power loss is low Q; low power loss is high Q.

Circuit designers provide the proper Q. As a technician, you should know what can change Q and what quantities in a circuit are affected by such a change.

1.6 BANDWIDTH If circuit Q is low, the gain of the circuit at resonance is relatively small. The circuit does not discriminate sharply (reject the unwanted frequencies) between the resonant frequency and the frequencies on either side of resonance, as shown by the curve in figure 1-12, view (A). The range of frequencies included between the two frequencies (426.4 kHz and 483.6 kHz in this example) at which the current drops to 70 percent of its maximum value at resonance is called the BANDWIDTH of the circuit.

Figure 1-12A. Bandwidth for high- and low-Q series circuit. LOW Q CURRENT CURVE

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It is often necessary to state the band of frequencies that a circuit will pass. The following standard has been set up: the limiting frequencies are those at either side of resonance at which the curve falls to a point of .707 (approximately 70 percent) of the maximum value. This point is called the HALF-POWER point. Note that in figure 1-12, the series- resonant circuit has two half-power points, one above and one below the resonant frequency point. The two points are designated upper frequency cutoff (f co) and lower frequency cutoff (fco) or simply f1 and f2. The range of frequencies between these two points comprises the bandwidth. Views (A) and (B) of figure 1-12 illustrate the bandwidths for low- and high-Q resonant circuits. The bandwidth may be determined by use of the following formulas:

Figure 1-12B.— Bandwidth for high- and low-Q series circuit. HIGH Q CURRENT CURVE

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For example, by applying the formula we can determine the bandwidth for the curve shown in figure 1-12, view (A).

If the Q of the circuit represented by the curve in figure 1-12, view (B), is 45.5, what would be the bandwidth?

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If Q equals 7.95 for the low-Q circuit as in view (A) of figure 1-12, we can check our original calculation of the bandwidth.

The Q of the circuit can be determined by transposing the formula for bandwidth to:

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1-43 UNCLASSIFIED To find the Q of the circuit using the information found in the last example problem:

Q-12. What is the relationship of the coil to the resistance of a circuit with high "Q"? Q-13. What is the band of frequencies called that is included between the two points at which current falls to 70 percent of its maximum value in a resonant circuit?

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1-44 UNCLASSIFIED 1.7 FILTERS In many practical applications of complex circuits, various combinations of direct, low- frequency, audio-frequency, and radio-frequency currents may exist. It is frequently necessary to have a means for separating these component currents at any desired point. An electrical device for accomplishing this separation is called a FILTER.

A filter circuit consists of inductance, capacitance, and resistance used singularly or in combination, depending upon the purpose. It may be designed so that it will separate alternating current from direct current, or so that it will separate alternating current of one frequency (or a band of frequencies) from other alternating currents of different frequencies.

The use of resistance by itself in filter circuits does not provide any filtering action, because it opposes the flow of any current regardless of its frequency. What it does, when connected in series or parallel with an inductor or capacitor, is to decrease the "sharpness," or selectivity, of the filter. Hence, in some particular application, resistance might be used in conjunction with inductance or capacitance to provide filtering action over a wider band of frequencies.

Filter circuits may be divided into four general types: LOW-PASS, HIGH-PASS, BANDPASS, AND BAND-REJECT filters.

Electronic circuits often have currents of different frequencies. The reason is that a source produces current with the same frequency as the applied voltage. As an example, the a.c. signal input to an audio amplifier can have high- and low-audio frequencies; the input to an rf amplifier can have a wide range of radio frequencies.

In such applications where the current has different frequency components, it is usually necessary for the filter either to accept or reject one frequency or a group of frequencies. The electronic filter that can pass on the higher-frequency components to a load or to the next circuit is known as a HIGH-PASS filter. A LOW-PASS filter can be used to pass on lower-frequency components.

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1-45 UNCLASSIFIED Before discussing filters further, we will review and apply some basic principles of the frequency response characteristics of the capacitor and the inductor. Recall the basic formula for capacitive reactance and inductive reactance:

Assume any given value of L and C. If we increase the applied frequency, X C decreases and XL increases. If we increase the frequency enough, the capacitor acts as a short and the inductor acts as an open. Of course, the opposite is also true. Decreasing frequency causes XC to increase and XL to decrease. Here again, if we make a large enough change, XC acts as an open and XL acts as a short. Figure 1-13 gives a pictorial representation of these two basic components and how they respond to low and high frequencies.

If we apply these same principles to simple circuits, such as the ones in figure 1-14, they affect input signals as shown. For example, in view (A) of the figure, a low frequency is blocked by the capacitor which acts as an open and at a high frequency the capacitor acts as a short. By studying the figure, it is easy to see how the various components will react in different configurations with a change in frequency.

Figure 1-13 Effect of frequency on capacitive and inductive reactance

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As mentioned before, high-pass and low-pass filters pass the specific frequencies for which circuits are designed.

There can be a great deal of confusion when talking about high-pass, low-pass, discrimination, attenuation, and frequency cutoff, unless the terms are clearly understood. Since these terms are used widely throughout electronics texts and references, you should have a clear understanding before proceeding further.

• HIGH-PASS FILTER. A high-pass filter passes on a majority of the high frequencies to the next circuit and rejects or attenuates the lower frequencies. Sometimes it is called a low-frequency discriminator or low-frequency attenuator.

Figure 1-14 Reaction to circuit by change in frequency

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1-47 UNCLASSIFIED • LOW-PASS FILTER. A low-pass filter passes on a majority of the low frequencies to the next circuit and rejects or attenuates the higher frequencies. Sometimes it is called a high-frequency discriminator or high-frequency attenuator.

• DISCRIMINATION. The ability of the filter circuit to distinguish between high and low frequencies and to eliminate or reject the unwanted frequencies.

• ATTENUATION. The ability of the filter circuit to reduce the amplitude of the unwanted frequencies below the level of the desired output frequency.

• FREQUENCY CUTOFF (f co). The frequency at which the filter circuit changes from the point of rejecting the unwanted frequencies to the point of passing the desired frequency; OR the point at which the filter circuit changes from the point of passing the desired frequency to the point of rejecting the undesired frequencies.

1.7.1 Low-Pass Filter A low-pass filter passes all currents having a frequency below a specified frequency, while opposing all currents having a frequency above this specified frequency. This action is illustrated in its ideal form in view (A) of figure 1-15. At frequency cutoff, known as fc the current decreases from maximum to zero. At all frequencies above fc the filter presents infinite opposition and there is no current. However, this sharp division between no opposition and full opposition is impossible to attain. A more practical graph of the current is shown in view (B), where the filter gradually builds up opposition as the cutoff frequency (f) is approached. Notice that the filter cannot completely block current above the cutoff frequency.

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Figure 1-15A. Low-pass filter Figure 1-15B.— Low-pass filter

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1-49 UNCLASSIFIED View (A) of figure 1-16 shows the electrical construction of a low-pass filter with an inductor inserted in series with one side of a line carrying both low and high frequencies. The opposition offered by the reactance will be small at the lower frequencies and great at the higher frequencies. In order to divert the undesired high frequencies back to the source, a capacitor must be added across the line to bypass the higher frequencies around the load, as shown in view (B).

Figure 1-16A. Components of a simple low- pass filter Figure 1-16B.— Components of a simple low- pass filter

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The capacitance of the capacitor must be such that its reactance will offer little opposition to frequencies above a definite value, and great opposition to frequencies below this value. By combining the series inductance and bypass capacitance, as shown in view (C), the simplest type of low-pass filter is obtained. At point P, a much higher opposition is offered to the low frequencies by the capacitor than by the inductor, and most of the low- frequency current takes the path of least opposition. On the other hand, the least amount of opposition is offered to the high frequencies by the capacitor, and most of the high frequency energy returns to the source through the capacitor.

1.7.2 High-Pass Filter A high-pass filter circuit passes all currents having a frequency higher than a specified frequency, while opposing all currents having a frequency lower than its specified frequency. This is illustrated in figure 1-17. A capacitor that is used in series with the source of both high and low frequencies, as shown in view (A) of figure 1-18, will respond differently to high-frequency, low-frequency, and direct currents. It will offer little opposition to the passage of high-frequency currents, great opposition to the passage of low-frequency currents, and completely block direct currents. The value of the capacitor must be chosen so that it allows the passage of all currents having frequencies above the desired value, and opposes those having frequencies below the desired value. Then, in order to shunt the undesired low-frequency currents back to the source, an inductor is used, as shown in view (B). This inductor must have a value that will allow it to pass currents having frequencies below the frequency cutoff point, and reject currents having frequencies above the frequency cutoff point, thus forcing them to pass through the capacitor. By combining inductance and capacitance, as shown in view (C), you obtain the simplest type of high-pass filter. At point P most of the high-frequency energy is passed on to the load by the capacitor, and most of the low-frequency energy is shunted back to the source through the inductor.

Figure 1-16C.— Components of a simple low-pass filter

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Figure 1-17 High-pass filter response curve Figure 1-18A. Components of a simple high-pass filter

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Figure 1-18B.—Components of a simple high- pass filter Figure 1-18C.— Components of a simple high-pass filter

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1-53 UNCLASSIFIED 1.7.3 Resonant Circuits as Filters Resonant circuits can be made to serve as filters in a manner similar to the action of individual capacitors and inductors. As you know, the series-LC circuit offers minimum opposition to currents that have frequencies at or near the resonant frequency, and maximum opposition to currents of all other frequencies.

You also know that a parallel-LC circuit offers a very high impedance to currents that have frequencies at or near the resonant frequency, and a relatively low impedance to currents of all other frequencies.

If you use these two basic concepts, the BANDPASS and BAND-REJECT filters can be constructed. The bandpass filter and the band-reject filter are two common types of filters that use resonant circuits.

1.7.3.1 Bandpass Filter A bandpass filter passes a narrow band of frequencies through a circuit and attenuates all other frequencies that are higher or lower than the desired band of frequencies. This is shown in figure 1-19 where the greatest current exists at the center frequency (f r). Frequencies below resonance (f1) and frequencies above resonance (f2) drop off rapidly and are rejected.

Figure 1-19 Bandpass filter response curve

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1-54 UNCLASSIFIED In the circuit of figure 1-20, view (A), the series-LC circuit replaces the inductor of figure 1-16, view (A), and acts as a BANDPASS filter. It passes currents having frequencies at or near its resonant frequency, and opposes the passage of all currents having frequencies outside this band.

Thus, in the circuit of figure 1-20, view (B), the parallel-LC circuit replaces the capacitor of figure 1-16, view (B). If this circuit is tuned to the same frequency as the series-LC circuit, it will provide a path for all currents having frequencies outside the limits of the frequency band passed by the series-resonant circuit. The simplest type of bandpass filter is formed by connecting the two LC circuits as shown in figure 1-20, view (C). The upper and lower frequency limits of the filter action are filter cutoff points.

Figure 1-20A. Components of a simple bandpass filter Figure 1-20B.— Components of a simple bandpass filter

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1.7.3.2 Band-Reject Filter A band-reject filter circuit is used to block the passage of current for a narrow band of frequencies, while allowing current to flow at all frequencies above or below this band. This type of filter is also known as a BAND-SUPPRESSION or BAND-STOP filter. The way it responds is shown by the response curve of figure 1-21. Since the purpose of the band-reject filter is directly opposite to that of a bandpass filter, the relative positions of the resonant circuits in the filter are interchanged. The parallel-LC circuit shown in figure 1-22, view (A), replaces the capacitor of figure 1-18, view (A). It acts as a band-reject filter, blocking the passage of currents having frequencies at or near resonant frequency and passing all currents having frequencies outside this band. The series-LC circuit shown in figure 1-22, view (B), replaces the inductor of figure 1-18, view (B). If this series circuit is tuned, to the same frequency as the parallel circuit, it acts as a bypass for the band of rejected frequencies. Then, the simplest type of band reject filter is obtained by connecting the two circuits as shown in figure 1-22, view (C).

Figure 1-20C.— Components of a simple bandpass filter

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Figure 1-21 Band-reject filter response curve Figure 1-22A. Components of a simple band-reject filter

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Q-14. What is the device called that will separate alternating current from direct current, or that will separate alternating current of one frequency from other alternating currents of different frequencies? Q-15. What are the four general types of filters?

Figure 1-22B.— Components of a simple band- reject filter Figure 1-22C.— Components of a simple band-reject filter

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1-58 UNCLASSIFIED Q-16. What is the filter called in which the low frequencies do not produce a useful voltage? Q-17. What is the filter called that passes low frequencies but rejects or attenuates high frequencies? Q-18. How does a capacitor and an inductor react to (a) low frequency and (b) high frequency? Q-19. What term is used to describe the frequency at which the filter circuit changes from the point of rejecting the unwanted frequencies to the point of passing the desired frequencies? Q-20. What type filter is used to allow a narrow band of frequencies to pass through a circuit and attenuate all other frequencies above or below the desired band? Q-21. What type filter is used to block the passage of current for a narrow band of frequencies, while allowing current to flow at all frequencies above or below this band?

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1-59 UNCLASSIFIED 1.7.4 Multisection Filters All of the various types of filters we have discussed so far have had only one section. In many cases, the use of such simple filter circuits does not provide sufficiently sharp cutoff points. But by adding a capacitor, an inductor, or a resonant circuit in series or in parallel (depending upon the type of filter action required), the ideal effect is more nearly approached. When such additional units are added to a filter circuit, the form of the resulting circuit will resemble the letter T, or the Greek letter (pi). They are, therefore, called T- or -type filters, depending upon which symbol they resemble. Two or more T- or −type filters may be connected together to produce a still sharper cutoff point.

Figure 1-23, (view A) (view B) and (view C), and figure 1-24, (view A) (view B) and (view C) depict some of the common configurations of the T- and -type filters. Further discussion about the theory of operation of these circuits is beyond the intended scope of this module.

Figure 1-23A. Formation of a T-type filter

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Figure 1-23B.— Formation of a T-type filter Figure 1-23C.— Formation of a T-type filter Figure 1-24A. Formation of a -type filter

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Figure 1-24B.— Formation of a -type filter Figure 1-24C.— Formation of a -type filter

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1-62 UNCLASSIFIED 1.8 SAFETY PRECAUTIONS When working with resonant circuits, or electrical circuits, you must be aware of the potentially high voltages. Look at figure 1-25. With the series circuit at resonance, the total impedance of the circuit is 5 ohms.

Remember, the impedance of a series-RLC circuit at resonance depends on the resistive element. At resonance, the impedance (Z) equals the resistance (R). Resistance is minimum and current is maximum. Therefore, the current at resonance is:

The voltage drops around the circuit with 2 amperes of current flow are:

Figure 1-25 Series RLC circuit at resonance

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You can see that there is a voltage gain across the reactive components at resonance.

If the frequency was such that X L and XC were equal to 1000 ohms at the resonant frequency, the reactance voltage across the inductor or capacitor would increase to 2000 volts a.c. with 10 volts a.c. applied. Be aware that potentially high voltage can exist in series-resonant circuits.

1.9 SUMMARY This chapter introduced you to the principles of tuned circuits. The following is a summary of the major subjects of this chapter.

THE EFFECT OF FREQUENCY on an INDUCTOR is such that an increase in frequency will cause an increase in inductive reactance. Remember that XL = 2 fL; therefore, XL varies directly with frequency.

THE EFFECT OF FREQUENCY on a CAPACITOR is such that an increase in frequency will cause a decrease in capacitive reactance. Therefore, the relationship between XC and frequency is that XC varies inversely with frequency.

RESULTANT REACTANCE X = (X L − X C) or X = (XC − XL). XL is usually plotted above the reference line and X C below the reference line. Inductance and capacitance have opposite effects on the current in respect to the voltage in a.c. circuits. Below resonance, XC is larger than XL, and the series circuit appears capacitive. Above resonance, XL is larger than XC, and the series circuit appears inductive. At resonance, XL = XC, and the total impedance of the circuit is resistive.

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1-64 UNCLASSIFIED A RESONANT CIRCUIT is often called a TANK CIRCUIT. It has the ability to take energy fed from a power source, store the energy alternately in the inductor and capacitor, and produce an output which is a continuous a.c. wave. The number of times this set of events occurs per second d is called the resonant frequency of the circuit.

IN A SERIES-LC CIRCUIT impedance is minimum and current is maximum. Voltage is the variable, and voltage across the inductor and capacitor will be equal but of opposite phases at resonance. Above resonance it acts inductively, and below resonance it acts capacitively.

IN A PARALLEL-LC CIRCUIT impedance is maximum and current is minimum. Current is the variable and at resonance the two currents are 180 degrees out of phase with each other. Above resonance the current acts capacitively, and below resonance the current acts inductively.

THE "Q" OR FIGURE OF MERIT of a circuit is the ratio of X L to R. Since the capacitor has negligible losses, the circuit Q becomes equivalent to the Q of the coil.

THE BANDWIDTH of a circuit is the range of frequencies between the half-power points. The limiting frequencies are those at either side of resonance at which the curve falls to .707 of the maximum value. If circuit Q is low, you will have a wide bandpass. If circuit Q is high, you will have a narrow bandpass.

A FILTER CIRCUIT consists of a combination of capacitors, inductors, and resistors connected so that the filter will either permit or prevent passage of a certain band of frequencies.

A LOW-PASS FILTER passes low frequencies and attenuates high frequencies.

A HIGH-PASS FILTER passes high frequencies and attenuates low frequencies.

A BANDPASS FILTER will permit a certain band of frequencies to be passed.

A BAND-REJECT FILTER will reject a certain band of frequencies and pass all others.

A SAFETY PRECAUTION concerning series resonance: Very high reactive voltage can appear across L and C. Care must be taken against possible shock hazard.

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1-65 UNCLASSIFIED ANSWERS TO QUESTIONS Q1. THROUGH Q21. A-1.

a. XL varies directly with frequency.

b. X C varies inversely with frequency.

c. Frequency has no affect on resistance.

A-2. Resultant reactance.

A-3.

A-4. Decreases.

A-5. Impedance low Current high.

A-6. Nonresonant (circuit is either above or below resonance).

A-7. Inductor magnetic field.

A-8. Capacitor.

A-9. Natural frequency or resonant frequency (f r).

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1-66 UNCLASSIFIED A-10. Maximum impedance, minimum current.

A-11. At the resonant frequency.

A-12.

A-13. Bandwidth of the circuit.

A-14. A filter.

A-15.

a. Low-pass. b. High-pass c. Bandpass. d. Band-reject.

A-16. High-pass filter, low-frequency discriminator, or low-frequency attenuator.

A-17. Low-pass filter, high-frequency discriminator or high-frequency attenuator.

A-18. At low-frequency, a capacitor acts as an open and an inductor acts as a short. At high-frequency, a capacitor acts as a short and an inductor acts as an open.

A-19. Frequency cutoff (fco).

A-20. Bandpass.

A-21. Band-reject.

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3-1 UNCLASSIFIED 3 WA VEFORMS AND WA VE GENERATORS LEARNING OBJECTIVES After you finish this chapter, you should be able to do the following: 1. Explain the operation of a stable, monostable, and bistable multivibrators. 2. Explain the operation of a blocking oscillator. 3. Explain the operation of a sawtooth generator. 4. Explain the operation of a trapezoidal wave generator. 5. Explain how the jump voltage is produced in a trapezoidal wave generator.

3.1 WAVEFORMS This chapter will present methods of generating waveforms. Before you begin to study how waveforms are generated, you need to know the basic characteristics of waveforms. This section will discuss basic periodic waveforms.

3.1.1 Periodic Waveforms A waveform which undergoes a pattern of changes, returns to its original pattern, and repeats the same pattern of changes is called a PERIODIC waveform. Periodic waveforms are nonsinusoidal except for the sine wave. Periodic waveforms which will be discussed are the sine wave, square wave, rectangular wave, sawtooth wave, trapezoidal wave, and trigger pulses.

3.1.1.1 Sine Wave Each completed pattern of a periodic waveform is called a CYCLE, as shown by the SINE WAVE in figure 3-1, view (A). Sine waves were presented in NEETS, Module 2, Alternating Current and Transformers, Chapter 1.

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3.1.1.2 Square Wave A SQUARE WAVE is shown in figure 3-1, view (B). As shown, it has two alternations of equal duration and a square presentation for each complete cycle. Figure 3-2 shows a breakdown of the square wave and is the figure you should view throughout the square wave discussion. The amplitude is measured vertically. The time for a complete cycle is measured between corresponding points on the wave (T0 to T2, or T1 to T3).

Figure 3-1 Periodic waveforms

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One alternation is called a PULSE. The time for one complete cycle is called the PULSE REPETITION TIME (prt). The number of times in 1 second that the cycle repeats itself is called the PULSE-REPETITION FREQUENCY (prf) or PULSE-REPETITION RATE (prr). If each alternation in figure 3-2 is 200 microseconds (μs), the prt will be 400 microseconds, and the prf will be 2,500 hertz. The following examples are provided to illustrate the mathematical relationship between prf and prt:

Figure 3-2 Square wave

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3-4 UNCLASSIFIED You should readily see that prt is just the inverse of prf. Therefore: Given:

The length of the pulse measured in time (T0 to T1) is referred to as the PULSE WIDTH (pw). The left side of the pulse is called the LEADING EDGE and the right side is called the TRAILING EDGE.

Time is required for a voltage or current to change in amplitude. The interval of time needed for the voltage to go from 0 to 100 percent (or from 100 to 0 percent) of its maximum value is called the TRANSIENT INTERVAL. The two types of transient intervals are RISE TIME and FALL TIME. Rise time is more accurately defined as the time required for the voltage to build up from 10 percent to 90 percent of the maximum amplitude point. Fall time is the time required for the voltage to drop from 90 percent to 10 percent of the maximum amplitude point.

In this text you will be presented with information in which waveforms appear to have instantaneous rise and fall times. This is done to simplify the presentation of the material. In reality these waveforms do have rise and fall times (transient intervals).

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3-5 UNCLASSIFIED 3.1.1.3 Rectangular Wave A rectangular wave is similar to the square wave. The difference is that in the rectangular waveform, the two alternations of the waveform are of unequal time duration. Figure 3-1, view (C), shows that the negative alternation (pulse) is shorter (in time) than the positive alternation. The negative alternation could be represented as the longer of the two alternations. Either way, the appearance is that of a rectangle.

3.1.1.4 Sawtooth Wave The SAWTOOTH waveform is shown in figure 3-1, view (D). A sawtooth wave resembles the teeth of a saw blade. There is a rapid vertical rise of voltage from T0 to T1, which is linear (straight). At T1 this voltage abruptly falls (essentially no time used) to its previous static value. The voltage remains at this value until T2 when it again has a linear rise. You can see this action in an oscilloscope where there are two voltage input locations, vertical and horizontal. If you apply a linear voltage to the vertical input, the electron beam will be forced to move in a vertical direction on the crt. A linear voltage applied to the horizontal input will cause the electron beam to move horizontally across the crt. The application of two linear voltages, one to the vertical input and one to the horizontal input at the same time, will cause the beam to move in both a vertical and horizontal (diagonal) direction at the same time. This then is how a sawtooth wave is made to appear on an oscilloscope. You should refer to NEETS, Module 6, Electronic Emission, Tubes, and Power Supplies, Chapter 2, for a review of oscilloscopes.

3.1.1.5 Trapezoidal Wave A TRAPEZOIDAL wave looks like a sawtooth wave on top of a square or rectangular wave, as shown in figure 3-1, view (E). The leading edge of a trapezoidal wave is called the JUMP voltage. The next portion of the wave is the linear rise or SLOPE. The trailing edge is called the FALL or DECAY. A trapezoidal wave is used to furnish deflection current in the electromagnetic cathode ray tube and is found in television and radar display systems. Electromagnetic cathode ray tubes use coils for the deflection system, and a linear rise in current is required for an accurate horizontal display. The square or rectangular wave portion provides the jump voltage for a linear rise in current through the resistance of the coil. This will be explained further in a discussion of the trapezoidal sweep generator.

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3-6 UNCLASSIFIED 3.1.1.6 Triggers A trigger is a very narrow pulse, as shown in figure 3-1, view (F). Trigger pulses are normally used to turn other circuits on or off.

3.2 WAVEFORM GENERATOR Nonsinusoidal oscillators generate complex waveforms such as those just discussed. Because the outputs of these oscillators are generally characterized by a sudden change, or relaxation, these oscillators are often called RELAXATION OSCILLATORS. The pulse repetition rate of these oscillators is usually governed by the charge and discharge timing of a capacitor in series with a resistor. However, some oscillators contain inductors that, along with circuit resistance, affect the output frequency. These RC and LC networks within oscillator circuits are used for frequency determination. Within this category of relaxation oscillators are MULTIVIBRATORS, BLOCKING OSCILLATORS, and SAWTOOTH- and TRAPEZOIDAL-WAVE GENERATORS.

Many electronic circuits are not in an "on" condition all of the time. In computers, for example, waveforms must be turned on and off for specific lengths of time. The time intervals vary from tenths of microseconds to several thousand microseconds. Square and rectangular waveforms are normally used to turn such circuits on and off because the sharp leading and trailing edges make them ideal for timing purposes.

3.2.1 Multivibrators The type of circuit most often used to generate square or rectangular waves is the multivibrator. A multivibrator, as shown in figure 3-3, is basically two amplifier circuits arranged with regenerative feedback. One of the amplifiers is conducting while the other is cut off.

Figure 3-3 Astable Multivibrator

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3-7 UNCLASSIFIED When an input signal to one amplifier is large enough, the transistor can be driven into cutoff, and its collector voltage will be almost VCC. However, when the transistor is driven into saturation, its collector voltage will be about 0 volts. A circuit that is designed to go quickly from cutoff to saturation will produce a square or rectangular wave at its output. This principle is used in multivibrators.

Multivibrators are classified according to the number of steady (stable) states of the circuit. A steady state exists when circuit operation is essentially constant; that is, one transistor remains in conduction and the other remains cut off until an external signal is applied. The three types of multivibrators are the ASTABLE, MONOSTABLE, and BISTABLE.

The astable circuit has no stable state. With no external signal applied, the transistors alternately switch from cutoff to saturation at a frequency determined by the RC time constants of the coupling circuits.

The monostable circuit has one stable state; one transistor conducts while the other is cut off. A signal must be applied to change this condition. After a period of time, determined by the internal RC components, the circuit will return to its original condition where it remains until the next signal arrives.

The bistable multivibrator has two stable states. It remains in one of the stable states until a trigger is applied. It then FLIPS to the other stable condition and remains there until another trigger is applied. The multivibrator then changes back (FLOPS) to its first stable state.

Q1. What type circuit is used to produce square or rectangular waves? Q2. What type of multivibrator does not have a stable state? Q3. What type of multivibrator has one stable state? Q4. What type of multivibrator has two stable states?

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3-8 UNCLASSIFIED 3.2.1.1 Astable Multivibrator An astable multivibrator is also known as a FREE-RUNNING MULTIVIBRATOR. It is called free running because it alternates between two different output voltage levels during the time it is on. The output remains at each voltage level for a definite period of time. If you looked at this output on an oscilloscope, you would see continuous square or rectangular waveforms. The astable multivibrator has two outputs, but NO inputs.

Let's look at the multivibrator in figure 3-3 again. This is an astable multivibrator. The astable multivibrator is said to oscillate. To understand why the astable multivibrator oscillates, assume that transistor Q1 saturates and transistor Q2 cuts off when the circuit is energized. This situation is shown in figure 3-4. We assume Q1 saturates and Q2 is in cutoff because the circuit is symmetrical; that is, R1 = R4, R2 = R3, C1 = C2, and Q1 = Q2. It is impossible to tell which transistor will actually conduct when the circuit is energized. For this reason, either of the transistors may be assumed to conduct for circuit analysis purposes.

Figure 3-4 Astable multivibrator (Q1 saturated)

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3-9 UNCLASSIFIED Essentially, all the current in the circuit flows through Q1; Q1 offers almost no resistance to current flow. Notice that capacitor C1 is charging. Since Q1 offers almost no resistance in its saturated state, the rate of charge of C1 depends only on the time constant of R2 and C1 (recall that TC = RC). Notice that the right-hand side of capacitor C1 is connected to the base of transistor Q2, which is now at cutoff.

Let's analyze what is happening. The right-hand side of capacitor C1 is becoming increasingly negative. If the base of Q2 becomes sufficiently negative, Q2 will conduct. After a certain period of time, the base of Q2 will become sufficiently negative to cause Q2 to change states from cutoff to conduction. The time necessary for Q2 to become saturated is determined by the time constant R2C1.

The next state is shown in figure 3-5. The negative voltage accumulated on the right side on capacitor C1 has caused Q2 to conduct. Now the following sequence of events takes place almost instantaneously. Q2 starts conducting and quickly saturates, and the voltage at output 2 changes from approximately −V CC to approximately 0 volts. This change in voltage is coupled through C2 to the base of Q1, forcing Q1 to cutoff. Now Q1 is in cutoff and Q2 is in saturation. This is the circuit situation shown in figure 3-6.

Figure 3-5 Astable multivibrator

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Notice that figure 3-6 is the mirror image of figure 3-4. In figure 3-6 the left side of capacitor C2 becomes more negative at a rate determined by the time constant R3C2. As the left side of C2 becomes more negative, the base of Q1 also becomes more negative. When the base of Q1 becomes negative enough to allow Q1 to conduct, Q1 will again go into saturation. The resulting change in voltage at output 1 will cause Q2 to return to the cutoff state.

Look at the output waveform from transistor Q2, as shown in figure 3-7. The output voltage (from either output of the multivibrator) alternates from approximately 0 volts to approximately −V CC, remaining in each state for a definite period of time. The time may range from a microsecond to as much as a second or two. In some applications, the time period of higher voltage (−VCC) and the time period of lower voltage (0 volts) will be equal. Other applications require differing higher- and lower-voltage times. For example, timing and gating circuits often have different pulse widths as shown in figure 3-8.

Figure 3-6 Astable multivibrator. (Q2 saturated)

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FREQUENCY STABILITY.—Some astable multivibrators must have a high degree of frequency stability. One way to obtain a high degree of frequency stability is to apply triggers. Figure 3-9, view (A), shows the diagram of a triggered, astable multivibrator. At time T0, a negative input trigger to the base of Q1 (through C1) causes Q1 to go into saturation, which drives Q2 to cutoff. The circuit will remain in this condition as long as the base voltage of Q2 is positive. The length of time the base of Q2 will remain positive is determined by C3, R3, and R6. Observe the parallel paths for C3 to discharge.

Figure 3-7 Square wave output from Q2 Figure 3-8 Rectangular waves

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View (B) of figure 3-9 shows the waveforms associated with the circuit. At time T1, Q2 comes out of cutoff and goes into saturation. Also, Q1 is caused to come out of saturation and is cut off. The base voltage waveform of Q1 shows a positive potential that is holding Q1 at cutoff. This voltage would normally hold Q1 at cutoff until a point between T2 and T3. However, at time T2 another trigger is applied to the base of Q1, causing it to begin conducting. Q1 goes into saturation and Q2 is caused to cut off. This action repeats each time a trigger (T2, T4, T6) is applied.

Figure 3-9A Triggered astable multivibrator and output Figure 3-9B.— Triggered astable multivibrator and output

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3-13 UNCLASSIFIED The prt of the input triggers must be shorter than the natural free-running prt of the astable multivibrator, or the trigger prf must be slightly higher than the free-running prf of the circuit. This is to make certain the triggers control the prt of the output.

3.2.1.2 Monostable Multivibrator The monostable multivibrator (sometimes called a ONE-SHOT MULTIVIBRATOR) is a square- or rectangular-wave generator with just one stable condition. With no input signal (quiescent condition) one amplifier conducts and the other is in cutoff. The monostable multivibrator is basically used for pulse stretching. It is used in computer logic systems and communication navigation equipment.

The operation of the monostable multivibrator is relatively simple. The input is triggered with a pulse of voltage. The output changes from one voltage level to a different voltage level. The output remains at this new voltage level for a definite period of time. Then the circuit automatically reverts to its original condition and remains that way until another trigger pulse is applied to the input. The monostable multivibrator actually takes this series of input triggers and converts them to uniform square pulses, as shown in figure 3- 10. All of the square output pulses are of the same amplitude and time duration.

The schematic for a monostable multivibrator is shown in figure 3-11. Like the astable multivibrator, one transistor conducts and the other cuts off when the circuit is energized.

Figure 3-10 Monostable multivibrator block diagram

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Recall that when the astable multivibrator was first energized, it was impossible to predict which transistor would initially go to cutoff because of circuit symmetry. The one-shot circuit is not symmetrical like the astable multivibrator. Positive voltage V BB is applied through R5 to the base of Q1. This positive voltage causes Q1 to cut off. Transistor Q2 saturates because of the negative voltage applied from −VCC to its base through R2. Therefore, Q1 is cut off and Q2 is saturated before a trigger pulse is applied, as shown in figure 3-12. The circuit is shown in its stable state.

Figure 3-11 Monostable multivibrator schematic Figure 3-12 Monostable multivibrator (stable state)

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3-15 UNCLASSIFIED Let's take a more detailed look at the circuit conditions in this stable state (refer to figure 3-12). As stated above, Q1 is cut off, so no current flows through R1, and the collector of Q1 is at −VCC. Q2 is saturated and has practically no voltage drop across it, so its collector is essentially at 0 volts. R5 and R3 form a voltage divider from VBB to the ground potential at the collector of Q2. The tie point between these two resistors will be positive. Thus, the base of Q1 is held positive, ensuring that Q1 remains cutoff. Q2 will remain saturated because the base of Q2 is very slightly negative as a result of the voltage drop across R2. If the collector of Q1 is near −V CC and the base of Q2 is near ground, C1 must be charged to nearly VCC volts with the polarity shown.

Now that all the components and voltages have been described for the stable state, let us see how the circuit operates (see figure 3-13). Assume that a negative pulse is applied at the input terminal. C2 couples this voltage change to the base of Q1 and starts Q1 conducting. Q1 quickly saturates, and its collector voltage immediately rises to ground potential. This sharp voltage increase is coupled through C1 to the base of Q2, causing Q2 to cut off; the collector voltage of Q2 immediately drops to VCC. The voltage divider formed by R5 and R3 then holds the base of Q1 negative, and Q1 is locked in saturation.

Figure 3-13 Monostable multivibrator (triggered)

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3-16 UNCLASSIFIED The one-shot multivibrator has now been turned on by applying a pulse at the input. It will turn itself off after a period of time. To see how it does this, look at figure 3-13 again. Q1 is held in saturation by the negative voltage applied through R3 to its base, so the circuit cannot be turned off here. Notice that the base of Q2 is connected to C1. The positive charge on C1 keeps Q2 cutoff. Remember that a positive voltage change (essentially a pulse) was coupled from the collector of Q1 when it began conducting to the base of Q2, placing Q2 in cutoff. When the collector of Q1 switches from -VCC volts to 0 volts, the charge on C1 acts like a battery with its negative terminal on the collector of Q1, and its positive terminal connected to the base of Q2. This voltage is what cuts off Q2. C1 will now begin to discharge through Q1 to ground, back through −V CC, through R2 to the other side of C1. The time required for C1 to discharge depends on the RC time constant of C1 and R2. Figure 3-14 is a timing diagram that shows the negative input pulse and the resultant waveforms that you would expect to see for this circuit description.

The only part of the operation not described so far is the short C1 charge time that occurs right after Q1 and Q2 return to their stable states. This is simply the time required for C1 to gain electrons on its left side. This charge time is determined by the R1C1 time constant.

Figure 3-14 Waveforms of a monostable multivibrator (triggered)

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3-17 UNCLASSIFIED Another version of the monostable multivibrator is shown in figure 3-15. View (A) is the circuit and view (B) shows the associated waveforms. In its stable condition (T0), Q1 is cut off and Q2 is conducting. The input trigger (positive pulse at T1) is applied to the collector of Q1 and coupled by C1 to the base of Q2 causing Q2 to be cut off. The collector voltage of Q2 then goes −VCC. The more negative voltage at the collector of Q2 forward biases Q1 through R4. With the forward bias, Q1 conducts, and the collector voltage of Q1 goes to about 0 volts. C1 now discharges and keeps Q2 cut off. Q2 remains cut off until C1 discharges enough to allow Q2 to conduct again (T2). When Q2 conducts again, its collector voltage goes toward 0 volts and Q1 is cut off. The circuit returns to its quiescent state and has completed a cycle. The circuit remains in this stable state until the next trigger arrives (T3).

Figure 3-15A Monostable multivibrator and waveshapes. Schematic

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Note that R3 is variable to allow adjustment of the gate width. Increasing R3 increases the discharge time for C1 which increases the cutoff time for Q2. Increasing the value of R3 widens the gate. To decrease the gate width, decrease the value of R3. Figure 3-16 shows the relationships between the trigger and the output signal. View (A) of the figure shows the input trigger; views (B) and (C) show the different gate widths made available by R3. Although the durations of the gates are different, the duration of the complete cycle remains the same as the pulse repetition time of the triggers. View (D) of the figure illustrates that the trailing edge of the positive alternation is variable.

Figure 3-15B.— Monostable multivibrator and waveshapes. Waveshapes Figure 3-16 Monostable multivibrator waveforms with a variable gate

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3-19 UNCLASSIFIED The reason the monostable multivibrator is also called a one-shot multivibrator can easily be seen. For every trigger pulse applied to the multivibrator, a complete cycle, or a positive and negative alternation of the output, is completed.

Q5. In an astable multivibrator, which components determine the pulse repetition frequency? Q6. What is another name for the monostable multivibrator? 3.2.1.3 Bistable Multivibrator As the name implies, the bistable multivibrator has two stable states. If a trigger of the correct polarity and amplitude is applied to the circuit, it will change states and remain there until triggered again. The trigger need not have a fixed prf; in fact, triggers from different sources, occurring at different times, can be used to switch this circuit.

The bistable multivibrator circuit and the associated waveforms are shown in figure 3-17, views (A) and (B), respectively. In this circuit, R1 and R7 are the collector load resistors. Voltage dividers R1, R2, and R5 provide forward bias for Q2; R7, R6, and R3 provide forward bias for Q1. These resistors also couple the collector signal from one transistor to the base of the other. Observe that this is direct coupling of feedback. This type of coupling is required because the circuit depends on input triggers for operation, not on RC time constants inside the circuit. Both transistors use common emitter resistor R4 which provides emitter coupling. C1 and C2 couple the input triggers to the transistor bases.

Figure 3-17A Bistable multivibrator and waveforms

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Notice that the circuit is symmetrical; that is, each transistor amplifier has the same component values. When power is first applied, the voltage divider networks place a negative voltage at the bases of Q1 and Q2. Both transistors have forward bias and both conduct.

Due to some slight difference between the two circuits, one transistor will conduct more than the other. Assume that Q1 conducts more than Q2. The increased conduction of Q1 causes the collector voltage of Q1 to be less negative (more voltage drop across R1). This decreases the forward bias of Q2 and decreases the conduction of Q2. When Q2 conducts less, its collector voltage becomes more negative. The negative-going change at the collector of Q2 is coupled to the base of Q1 and causes Q1 to conduct even more heavily. This regenerative action continues until Q2 is cut off and Q1 is saturated. The circuit is in a stable state and will remain there until a trigger is applied to change the state.

At T1, a negative trigger is applied to both bases through C1 and C2. The trigger does not affect Q1 since it is already conducting. The trigger overcomes cutoff bias on Q2 and causes it to conduct. As Q2 goes into conduction, its collector voltage becomes positive. The positive-going change at the Q2 collector causes a reverse bias on the base of Q1. As the conduction of Q1 decreases to the cutoff point, the collector voltage becomes negative. This switching action causes a very rapid change of state with Q2 now conducting and Q1 cut off.

Figure 3-17B.— Bistable multivibrator and waveforms

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3-21 UNCLASSIFIED At T2, a negative trigger is again applied to both bases. This time, Q1 is brought into conduction and the regenerative switching action cuts off Q2. The bistable multivibrator will continue to change states as long as triggers are applied. Notice that two input triggers are required to produce one gate; one to turn it on and the other to turn it off. The input trigger frequency is twice the output frequency.

The bistable multivibrator that most technicians know is commonly known by other names: the ECCLES-JORDAN circuit and, more commonly, the FLIP-FLOP circuit (figure 3-18). The flip-flop is a bistable multivibrator, "bi" meaning two; that is, the flip- flop has two stable states. The flip-flop (f/f) can rapidly flip from one state to the other and then flop back to its original state. If a voltmeter were connected to the output of a flip-flop, it would measure either a small positive or negative voltage, or a particularly low voltage (essentially 0 volts). No matter which voltage is measured, the flip-flop would be stable. Remember, stable means that the flip-flop will remain in a particular state indefinitely. It will not change states unless the proper type of trigger pulse is applied.

Figure 3-18 Basic flip-flop

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3-22 UNCLASSIFIED Flip-flops are used in switching-circuit applications (computer logic operations) as counters, shift registers, clock pulse generators, and in memory circuits. They are also used for relay-control functions and for a variety of similar applications in radar and communications systems.

Notice that the basic flip-flop, illustrated in figure 3-18, has two inputs and two outputs. The inputs are coupled to the bases of the transistors and the outputs are coupled from the collectors of the transistors. Think of the flip-flop as two common-emitter amplifier circuits, where the output of one amplifier is connected to the input of the other amplifier, and vice-versa. Point (D) is connected through R4 to C4 to point (A). Point (A) is the input to transistor Q1. By the same token, point (C), which is the output of Q1, is connected through R3 and C3 to the input (point (B)) of transistor Q2.

Taking a close look at the flip-flop circuit, you should be able to see how it maintains its stable condition. Typical values for the resistors and applied voltages are shown in figure 3-19. The capacitors have been removed for simplicity.

Figure 3-19 Flip-flop (capacitors removed)

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3-23 UNCLASSIFIED Two voltage-divider networks extend from -10 volts (VCC) to +6 volts (VBB). One voltage divider consisting of resistors R1, R4, and R6 supplies the bias voltage to the base of Q1. The other voltage divider consists of R2, R3, and R5 and supplies the bias voltage to the base of Q2.

Assume that Q1 (figure 3-20) is initially saturated and Q2 is cut off. Recall that the voltage drop from the base to the emitter of a saturated transistor is essentially 0 volts. In effect, this places the base of Q1 at ground potential. The voltages developed in the voltage divider, −VCC, R6, R4, R1, and +VBB, are shown in the figure.

Since no current flows through Q2, very little voltage is dropped across R6 (approximately 0.5 volt). The voltage at output 2 would measure -9.5 volts to ground (approximately −V CC).

This voltage (−9.5 volts) is considered to be a HIGH output. Figure 3-21 shows the values of the other voltage-divider network.

Figure 3-20 Flip-flop (Q1 voltage divider)

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With Q1 saturated, a large current flows through R5. The meter would measure approximately 0 volts (ground potential) at point (C). Notice that point (B) is located between point (C) (at 0 volts) and +V BB (at +6 volts). The meter would measure a positive voltage (between 0 volts and +6 volts) at the base of Q2 (point (B)).

A positive voltage on the base of a pnp transistor will cause that transistor to cut off. If one transistor is saturated, the other must be cut off. The flip-flop is stable in this state.

The capacitors that were removed from figure 3-19 must be returned to the flip-flop as shown in figure 3-22 to change the state of the flip-flop from one condition to the other. Capacitors C3 and C4 transmit almost instantaneously any changes in voltage from the collector of one transistor to the base of the other. Capacitors C1 and C2 are input coupling capacitors.

Figure 3-21 Flip-flop (Q2 voltage divider)

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As before, assume that transistor Q1 is saturated and transistor Q2 is cut off. Two methods are available to cause the flip-flop to change states. First, a positive-going pulse can be applied to input 1 to cause Q1 to change from saturation to cutoff. Second, the same result can be achieved by applying a negative-going pulse to input 2. Transistor Q2 would then change from Cutoff to saturation. Normally, a pulse is applied to the saturated transistor causing it to cut off. An input pulse which is of the correct polarity to change the state of the flip-flop is, as before, called a trigger pulse.

In figure 3-23 a positive-going trigger pulse has been applied to input 1. The flip-flop has now changed states; Q1 is cut off and Q2 is saturated. If a second positive-going trigger pulse is applied to input 1, it has no effect. This is because Q1 is already cut off; therefore, a positive pulse on its base has no effect. But if a positive-going trigger pulse were applied to input 2, the flip-flop would change back to its original state as shown in figure 3-24.

Figure 3-22 Flip-flop

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Figure 3-23 Bistable multivibrator (flip-flop) Figure 3-24 Flip-flop (original state)

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3-27 UNCLASSIFIED So far, the basic flip-flop has used only pnp transistors. It could have just as easily used npn transistors. The functional operation would not change; only the polarities required for conduction and cutoff change. As a technician, you may see either type of transistor used, npn or pnp. A symbolic block diagram is sometimes used to avoid confusion about voltage polarities.

A special kind of block diagram has been adopted as a standard symbol for the flip-flop and is shown in figures 3-25 and 3-26. The two inputs are represented by the lines on the left and the outputs by the lines on the right. INPUTS to a flip-flop are S (SET) and C (CLEAR) and OUTPUTS from a flip-flop are "1" and "0." A trigger pulse applied to the SET input causes the "1" output to be a positive or negative voltage, depending on the type of transistor. At the same time, the "0" output equals 0 volts. This condition is called the SET STATE.

If a trigger pulse is applied to the CLEAR input, a positive or negative voltage is produced at the "0" output. The "1" output goes to 0 volts. This condition is called the CLEAR STATE, as shown in figure 3-26.

Figure 3-25 Flip-flop (SET state) Figure 3-26 Flip-flop (CLEAR state)

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3-28 UNCLASSIFIED To determine what state the flip-flop is in, you can measure either the "1" or the "0" output. Measuring 0 volts at the "1" output indicates that the flip-flop is in the CLEAR state. If the "0" output is measured, a positive or negative voltage would also indicate that the flip-flop is in the CLEAR state. Either way, only one reading is necessary.

In figure 3-27, the flip-flop is in the SET state prior to T0 (negative voltage on the "1" output). Now compare the changes in output voltage at each point in time (T0, T1, T2, and T3) with the input pulse. Studying this figure should help you understand how the flip-flop works. The positive pulse at T0 on the CLEAR input shifts the f/f to the CLEAR state (negative voltage at the "0" output). At T1 a positive pulse on the SET input drives the "1" output to the SET state. At T2 a positive pulse on the CLEAR input drives the "0" output to a CLEAR state. At T3 another positive pulse is applied to the CLEAR input. This input has no effect since the f/f is already in the CLEAR state.

Some flip-flops use a third input lead, as shown in figure 3-28. This third input lead is called a TOGGLE (T) input. Every time a pulse is applied to the T input, the flip-flop will change states from whatever its state was previously. The two diodes (CR1, CR2) form a STEERING NETWORK. This steering network directs a positive input pulse to the saturated transistor, causing it to cut off. Negative pulses are blocked by the diodes. Note that if npn transistors were used, the diodes would have to be reversed and the TOGGLE signal would have to be negative. For example, assume that Q1 is saturated, Q2 is cut off, and a positive pulse is applied the at T input. The input pulse will be directed to both transistors. The positive pulse will not affect Q2 since it is already in cutoff. Q1 however, which is conducting, will cut off and will cause Q2 to become saturated. The transistors have reversed states. A block diagram which represents a multivibrator and its outputs with only a TOGGLE input signal is shown in figure 3-29. Studying this figure should help you understand how this flip-flop works. Each TOGGLE input causes the output to change states. Figure 3-30 shows what happens when triggers are applied to all three inputs of the flip-flop shown in figure 3-28. Assume that the flip-flop in figure 3-30 is in the CLEAR state ("1" output is 0 volts, "0" output is high) prior to T0. At T0 a trigger is applied to the set input and the flip-flop changes states.

Figure 3-27 Flip-flop with trigger pulse on SET and inputs

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3-29 UNCLASSIFIED Next, the CLEAR input is triggered and the flip-flop returns to the CLEAR state at T1. A TOGGLE at T2 causes the flip-flop to change state, so it is once again SET. Another TOGGLE changes the flip-flop to the CLEAR state at T3 (notice that TOGGLE triggers flip the multivibrator regardless of its previous state). Now, a SET input trigger at T4 sets the flip-flop. The CLEAR input pulse at T5 causes the circuit to CLEAR, and the CLEAR input at T6 has n o effect on the flip-flop, for it is already in the CLEAR state.

Figure 3-28 Flip-flop with three inputs Figure 3-29 Block diagram of a flip-flop with a toggle input

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Remember, a SET input will SET the flip-flop if it is in the CLEAR state, otherwise, it will not do anything; a trigger at the CLEAR input can only CLEAR the circuit if it is SET; and a trigger applied to the TOGGLE input will cause the bistable multivibrator to change states regardless of what state it is in.

Q7. In a bistable multivibrator, how many trigger pulses are needed to produce one complete cycle in the output? Q8. How many stable states are there for a flip-flop? Q9. If a voltage (positive or negative) is measured on the "1" output of a flip-flop, what state is it in? 3.2.2 Blocking Oscillator The BLOCKING OSCILLATOR is a special type of wave generator used to produce a narrow pulse, or trigger. Blocking oscillators have many uses, most of which are concerned with the timing of some other circuit. They can be used as frequency dividers or counter circuits and for switching other circuits on and off at specific times.

In a blocking oscillator the pulse width (pw), pulse repetition time (prt), and pulse repetition rate (prr) are all controlled by the size of certain capacitors and resistors and by the operating characteristics of the transformer. The transformer primary determines the duration and shape of the output. Because of their importance in the circuit, transformer action and series RL circuits will be discussed briefly. You may want to review transformer action in NEETS, Module 2, Alternating Current and Transformers before going to the next section.

Figure 3-30 Flip-flop with three inputs (block diagram)

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3-31 UNCLASSIFIED 3.2.2.1 Transformer Action Figure 3-31, view (A), shows a transformer with resistance in both the primary and secondary circuits. If S1 is closed, current will flow through R1 and L1. As the current increases in L1, it induces a voltage into L2 and causes current flow through R2. The voltage induced into L2 depends on the ratio of turns between L1 and L2 as well as the current flow through L1.

The secondary load impedance, R2, affects the primary impedance through reflection from secondary to primary. If the load on the secondary is increased (R2 decreased), the load on the primary is also increased and primary and secondary currents are increased.

T1 can be shown as an inductor and R1-R2 as a combined or equivalent series resistance (R E) since T1 has an effective inductance and any change in R1 or R2 will change the current. The equivalent circuit is shown in figure 3-31, view (B). It acts as a series RL circuit and will be discussed in those terms.

Figure 3-31A RL circuit

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3.2.2.2 Simple Series RL Circuit When S1 is closed in the series RL circuit (view (B) of figure 3-31) L acts as an open at the first instant as source voltage appears across it. As current begins to flow, E L decreases and ER and I increase, all at exponential rates. Figure 3-32, view (A), shows these exponential curves. In a time equal to 5 time constants the resistor voltage and current are maximum and EL is zero. This relationship is shown in the following formula:

Figure 3-31B.— RL circuit

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If S1 is closed, as shown in figure 3-31, view (B), the current will follow curve 1 as shown in figure 3-32, view (A). The time required for the current to reach maximum depends on the size of L and R E. If RE is small, then the RL circuit has a long time constant. If only a small portion of curve 1 (C to D of view (A)) is used, then the current increase will have maximum change in a given time period. Further, the smaller the time increment the more nearly linear is the current rise. A constant current increase through the coil is a key factor in a blocking oscillator.

3.2.2.3 Blocking Oscillator Applications A basic principle of inductance is that if the increase of current through a coil is linear; that is, the rate of current increase is constant with respect to time, then the induced voltage will be constant. This is true in both the primary and secondary of a transformer. Figure 3-32, view (B), shows the voltage waveform across the coil when the current through it increases at a constant rate. Notice that this waveform is similar in shape to the trigger pulse shown earlier in figure 3-1, view (E). By definition, a blocking oscillator is a special type of oscillator which uses inductive regenerative feedback.

Figure 3-32A Voltage across a coil

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3-34 UNCLASSIFIED The output duration and frequency of such pulses are determined by the characteristics of a transformer and its relationship to the circuit. Figure 3-33 shows a blocking oscillator. This is a simplified form used to illustrate circuit operation.

Figure 3-32B.— Voltage across a coil Figure 3-33 Blocking oscillator

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3-35 UNCLASSIFIED When power is applied to the circuit, R1 provides forward bias and transistor Q1 conducts. Current flow through Q1 and the primary of T1 induces a voltage in L2. The phasing dots on the transformer indicate a 180-degree phase shift. As the bottom side of L1 is going negative, the bottom side of L2 is going positive. The positive voltage of L2 is coupled to the base of the transistor through C1, and Q1 conducts more. This provides more collector current and more current through L1. This action is regenerative feedback. Very rapidly, sufficient voltage is applied to saturate the base of Q1. Once the base becomes saturated, it loses control over collector current. The circuit now can be compared to a small resistor (Q1) in series with a relatively large inductor (L1), or a series RL circuit.

The operation of the circuit to this point has generated a very steep leading edge for the output pulse. Figure 3-34 shows the idealized collector and base waveforms. Once the base of Q1 (figure 3-33) becomes saturated, the current increase in L1 is determined by the time constant of L1 and the total series resistance. From T0 to T1 in figure 3-34 the current increase (not shown) is approximately linear. The voltage across L1 will be a constant value as long as the current increase through L1 is linear.

Figure 3-34 Blocking oscillator idealized waveforms

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3-36 UNCLASSIFIED At time T1, L1 saturates. At this time, there is no further change in magnetic flux and no coupling from L1 to L2. C1, which has charged during time TO to T1, will now discharge through R1 and cut off Q1. This causes collector current to stop, and the voltage across L1 returns to 0.

The length of time between T0 and T1 (and T2 to T3 in the next cycle) is the pulse width, which depends mainly on the characteristics of the transformer and the point at which the transformer saturates. A transformer is chosen that will saturate at about 10 percent of the total circuit current. This ensures that the current increase is nearly linear. The transformer controls the pulse width because it controls the slope of collector current increase between points T0 and T1. Since TC = L ÷ R, the greater the L, the longer the TC. The longer the time constant, the slower the rate of current increase. When the rate of current increase is slow, the voltage across L1 is constant for a longer time. This primarily determines the pulse width.

From T1 to T2 (figure 3-34), transistor Q1 is held at cutoff by C1 discharging through R1 (figure 3-33). The transistor is now said to be "blocked." As C1 gradually loses its charge, the voltage on the base of Q1 returns to a forward-bias condition. At T2, the voltage on the base has become sufficiently positive to forward bias Q1, and the cycle is repeated.

The collector waveform may have an INDUCTIVE OVERSHOOT (PARASITIC OSCILLATIONS) at the end of the pulse. When Q1 cuts off, current through L1 ceases, and the magnetic field collapses, inducing a positive voltage at the collector of Q1. These oscillations are not desirable, so some means must be employed to reduce them. The transformer primary may be designed to have a high dc resistance resulting in a low Q; this resistance will decrease the amplitude of the oscillations. However, more damping may be necessary than such a low-Q transformer primary alone can achieve. If so, a DAMPING resistor can be placed in parallel with L1, as shown in figure 3-35.

Figure 3-35 Circuit damping

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3-37 UNCLASSIFIED When an external resistance is placed across a tank, the formula for the Q of the tank circuit is Q = R/XL, where R is the equivalent total circuit resistance in parallel with L. You should be able to see from the equation that the Q is directly proportional to the damping resistance (R). In figure 3-35, damping resistor R2 is used to adjust the Q which reduces the amplitude of overshoot parasitic oscillations. As R2 is varied from infinity toward zero, the decreasing resistance will load the transformer to the point that pulse amplitude, pulse width, and prf are affected. If reduced enough, the oscillator will cease to function. By varying R2, varying degrees of damping can be achieved, three of which are shown in figure 3-36, view (A), view (B and view (C).

Figure 3-36A Waveform damping. CRITICAL DAMPING

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Figure 3-36B.— Waveform damping. UNDER DAMPING. Figure 3-36C.— Waveform damping. OVER DAMPING

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3-39 UNCLASSIFIED CRITICAL DAMPING gives the most rapid transient response without overshoot. This is accomplished by adjusting R2 to achieve a waveform as shown in figure 3-36, view (A). The resistance of R2 depends upon the Q of the transformer. View (A) shows that oscillations, including the overshoot, are damping out.

UNDERDAMPING gives rapid transient response with overshoot caused by high or infinite resistance as shown in figure 3-36, view (B). OVERDAMPING is caused by very low resistance and gives a slow transient response. It may reduce the pulse amplitude as shown in figure 3-36, view (C).

The blocking oscillator discussed is a free-running circuit. For a fixed prf, some means of stabilizing the frequency is needed. One method is to apply external synchronization triggers (figure 3-37), view (A) and view (B). Coupling capacitor C2 feeds input synchronization (sync) triggers to the base of Q1.

Figure 3-37A Blocking oscillator (synchronized)

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If the trigger frequency is made slightly higher than the free-running frequency, the blocking oscillator will "lock in" at the higher frequency. For instance, assume the free- running frequency of this blocking oscillator is 2 kilohertz, with a prt of 500 microseconds. If sync pulses with a prt of 400 microseconds, or 2.5 kilohertz, are applied to the base, the blocking oscillator will "lock in" and run at 2.5 kilohertz. If the sync prf is too high, however, frequency division will occur. This means that if the sync prt is too short, some of the triggers occur when the base is far below cutoff. The blocking oscillator may then synchronize with every second or third sync pulse.

For example, in figure 3-37, view (A) and view (B) if trigger pulses are applied every 200 microseconds (5 kilohertz), the trigger that appears at T1 is not of sufficient amplitude to overcome the cutoff bias and turn on Q1. At T2, capacitor C1 has nearly discharged and the trigger causes Q1 to conduct. Note that with a 200-microsecond input trigger, the output prt is 400 microseconds. The output frequency is one-half the input trigger frequency and the blocking oscillator becomes a frequency divider.

Q10. What component in a blocking oscillator controls pulse width?

Figure 3-37B.— Blocking oscillator (synchronized)

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3-41 UNCLASSIFIED 3.2.3 Time-Base Generators Radar sets, oscilloscopes, and computer circuits all use sawtooth (voltage or current) waveforms. A sawtooth waveshape must have a linear rise. The sawtooth waveform is often used to produce a uniform, progressive movement of an electron beam across the face of an electrostatic cathode ray tube. This movement of the electron beam is known as a SWEEP. The voltage which causes this movement is known as SWEEP VOLTAGE and the circuit which produces this voltage is the SWEEP GENERATOR, or TIME- BASE GENERATOR. Most common types of time-base generators develop the sawtooth waveform by using some type of switching action with either the charge or discharge of an RC or RL circuit.

3.2.3.1 Sawtooth Wave A sawtooth wave can be generated by using an RC network. Possibly the simplest sawtooth generator is that which is shown in figure 3-38, view (A). Assume that at T0 (view (B)). S1 is placed in position P. At the instant the switch closes, the applied voltage (Ea) appears at R. C begins to charge to Ea through R. If S1 remains closed long enough, C will fully charge to Ea. You should remember from NEETS, Module 2, Alternating Current and Transformers, that a capacitor takes 5 time constants (5TC) to fully charge. As the capacitor charges to the applied voltage, the rate of charge follows an exponential curve. If a linear voltage is desired, the full charge time of the capacitor cannot be used because the exponential curve becomes nonlinear during the first time constant.

Figure 3-38A Series RC circuit

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3-42 UNCLASSIFIED

However, during the first 10 percent of the first time constant, the rate of voltage change across the capacitor is almost constant (linear). Suppose that S1 is placed in position P at T0, and C is allowed to charge for 0.1 time constant. This is shown as T0 to T1 in view (B). Notice that the rate of voltage change across C is nearly constant between T0 and T1. Now, assume that at T1 the switch is moved from position P to position Q. This shorts the capacitor, and it discharges very rapidly. If the switch is placed back in position P, the capacitor will start charging again.

By selecting the sizes of R and C, you can have a time constant of any value you desire. Further, by controlling the time S1 remains closed, you can generate a sawtooth of any duration. Figure 3-39 is the Universal Time Constant Chart. Notice in the chart that if 1 time constant is 1,000 microseconds, S1 (figure 3-38, view (A)) can be closed no longer than 100 microseconds to obtain a reasonable linear sawtooth. In this example, C1 will charge to nearly 10 volts in 0.1 time constant.

Figure 3-38B.—Series RC circuit

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The dimensions of the sawtooth waveform used in oscilloscopes need to be discussed before going any further. Figure 3-40 shows a sawtooth waveform with the various dimensions labeled. The duration of the rise of voltage (T0 to T1) is known as the SWEEP TIME or ELECTRICAL LENGTH. The electron beam of an oscilloscope moves across the face of the cathode ray tube during this sweep time. The amount of voltage rise per unit of time is referred to as the SLOPE of the waveform. The time from T1 to T2 is the capacitor discharge time and is known as FALL TIME or FLYBACK TIME. This discharge time is known as flyback time because during this period the electron beam returns, or "flys" back, from the end of a scanning line to begin the next line.

Figure 3-39 Universal Time Constant Chart

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The amplitude of the rise of voltage is known as the PHYSICAL LENGTH. It is called physical length because the greater the peak voltage, the greater physical distance the beam will move. For example, the amount of voltage needed to move an electron beam 4 inches is twice the amount needed to move the beam 2 inches across the face of a given crt.

The voltage rise between T0 to T1 is the LINEAR SLOPE of the wave. The linearity of the rise of voltage is determined by the amount of time the capacitor is allowed to charge. If the charge time is kept short (10 percent or less of 1TC), the linearity is reasonably good.

As stated in the discussion of time-base generators, the waveform produced from any sawtooth generator must be linear. A LINEAR SAWTOOTH is one that has an equal change in voltage for an equal change in time. Referring to the Universal Time Constant Chart in figure 3-39, you can see that the most desirable part of the charge curve is the first one-tenth (0.1) of the first TC.

Figure 3-40 Sawtooth waveform

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3-45 UNCLASSIFIED Figure 3-41, view (A), is a transistor sawtooth generator. In this figure R1 is a forward- biasing resistor for Q1, C1 is a coupling capacitor, and Q1 is serving as a switch for the RC network consisting of R2 and C2. With forward bias applied to Q1, the generator conducts at saturation, and its collector voltage (the output) is near 0 volts as indicated by the waveform in view (B). The charge felt by C1 is nearly 0. A negative gate is applied to the base of Q1 to cut off Q1 and allow C2 to charge. The length of time that the gate is negative determines how long Q1 will remain cut off and, in turn, how long C2 will be allowed to charge. The length of time that C2 is allowed to charge is referred to as the electrical length of the sawtooth that is produced.

Figure 3-41A Transistor sawtooth generator

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The amplitude of the sawtooth that is produced is limited by the value of V CC that is used in the circuit. For example, if the voltage is 30 volts, and the capacitor (C2) is allowed to charge to 10 percent of 30 volts, then the amplitude of the sawtooth will be 3 volts (see figure 3-41, view (B)). If VCC is increased to 40 volts, C2 will charge to 10 percent of 40 volts and the output will increase in amplitude to 4 volts.

Changing the value of V CC in the circuit changes the amplitude of the sawtooth waveform that is produced; amplitude determines the physical length. Since the number of time constants used in the circuit has not been changed, linearity does not change with a change in VCC.

The linear slope that is produced by the circuit is dependent on two variables; (1) the time constant of the RC circuit and (2) the gate length of the gate applied to the circuit. The circuit will produce a linear sawtooth waveshape if the components selected are such that only one-tenth of 1 TC or less is used. The GATE LENGTH is the amount of time that the gate is applied to the circuit and controls the time that the capacitor is allowed to charge. The value of R2 and C2 determines the time for 1 time constant (TC = RC). To determine the number of time constants (or the fraction of 1TC) used, divide the time for 1 time constant into the time that the capacitor is allowed to charge:

Figure 3-41B.—Transistor sawtooth generator

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3-47 UNCLASSIFIED In figure 3-41, view (B), gate length is 500 microseconds and TC is the product of R2 (5 kilohms) and C2 (1 microfarad). The number of time constants is computed as follows:

Therefore, 0.1TC is the length of time required to produce a linear rise in the sawtooth waveform.

shows that an increase in gate length increases the number of time constants. An increase in the number of time constants decreases linearity. The reason is that C2 now charges to a greater percentage of the applied voltage, and a portion of the charge curve is being used that is less linear. The waveform in figure 3-42, view (A), shows an increase in amplitude (physical length), an increase in the time that C2 is allowed to charge (electrical length), and a decrease in linearity. If a smaller percentage of V CC is used, the gate length is decreased. As shown in view (B), this decreased gate length results in an increase in linearity, a decrease in the time that C2 is allowed to charge (electrical length), and a decrease in amplitude (physical length).

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Figure 3-42A Relationship of gate to linearity Figure 3-42B.— Relationship of gate to linearity

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3-49 UNCLASSIFIED Changing the value of R and C in the circuit affects linearity since they control the time for 1 time constant. For example, if the value of C2 is increased in the circuit, as shown in figure 3-43, view (A), the time for 1 time constant increases and the number of time constants then decreases. With a decrease in the number of time constants, linearity increases. The reason is that a smaller percentage of VCC is used, and the circuit is operating in a more linear portion of the charge curve. Increasing the value of the TC (C2 or R2) decreases the amplitude of the sawtooth (physical length) because C2 now charges to a smaller percentage V CC for a given time. The electrical length remains the same because the length of time that C2 is allowed to charge has not been changed.

Figure 3-43A Relationship of R and C to linearity

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\ Decreasing the value of the TC (R2 or C2), as shown in figure 3-43, view (B), results in an increase in the number of time constants and therefore causes linearity to decrease. Anytime the number of time constants increases, the percentage of charge increases (see the Universal Time Constant Chart, figure 3-39), and amplitude (physical length) increases. Without an increase in gate length, the time that C2 is allowed to charge through R2 remains the same; therefore, electrical length remains the same. Linearity is affected by gate length, the value of R, and the value of C; but is not affected by changing the value of V CC. Increasing the gate length decreases linearity, and decreasing gate length increases linearity. Increasing R or C in the circuit increases linearity, and decreasing R or C in the circuit decreases linearity.

The entire time of the sawtooth, from the time at which the capacitor begins charging (T0 in figure 3-41, view (B)) to the time when it starts charging again (T2), is known as the prt of the wave. The pulse repetition frequency of the sawtooth wave is:

Figure 3-43B.—Relationship of R and C to linearity

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3-51 UNCLASSIFIED 3.2.3.2 Unijunction Sawtooth Generator. So far, you have learned in this chapter that a switch and an RC network can generate a sawtooth waveform. When using a unijunction transistor as the switch, a simple sawtooth generator looks like the circuit in figure 3-44, view (A); the output waveshapes are shown in view (B). You may want to review unijunction transistors in NEETS, Module 7, Solid- State Devices and Power Supplies, chapter 3, before continuing.

When the 20 volts is applied across B2 and B1, the n-type bar acts as a voltage- divider. A voltage of 12.8 volts appears at a point near the emitter. At the first instant, C1 has no voltage across it, so the output of the circuit, which is taken across the capacitor (C1), is equal to 0 volts. (The voltage across C1 is also the voltage that is applied to the emitter of the unijunction.) The unijunction is now reverse biased. After T0, C1 begins to charge toward 20 volts.

At T1, the voltage across the capacitor (the voltage on the emitter) has reached approximately 12.8 volts. This is the peak point for the unijunction, and it now becomes forward biased. With the emitter forward biased, the impedance between the emitter and B1 is just a few ohms. This is similar to placing a short across the capacitor. The capacitor discharges very rapidly through the low resistance of B1 to E.

Figure 3-44A Unijunction sawtooth generator. SCHEMATIC

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3-52 UNCLASSIFIED As C1 discharges, the voltage from the emitter to B1 also decreases. Q1 will continue to be forward biased as long as the voltage across C1 is larger than the valley point of the unijunction.

At T2 the 3-volt valley point of the unijunction has been reached. The emitter now becomes reverse biased and the impedance from the emitter to B1 returns to a high value. Immediately after T2, Q1 is reverse biased and the capacitor has a charge of approximately 3 volts. C1 now starts to charge toward 20 volts as it did originally (just after T0). This is shown from T2 to T3 in figure 3-44, view (B).

Figure 3-44B.— Unijunction sawtooth generator. EMITTER WAVEFORM

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3-53 UNCLASSIFIED The circuit operation from now on is just a continuous repetition of the actions between T2 and T4. The capacitor charges until the emitter becomes forward biased, the unijunction conducts and C1 discharges, and Q1 becomes reverse biased and C1 again starts charging.

Now, let's determine the linearity, electrical length, and amplitude of the output waveform. First, the linearity: To charge the circuit to the full 20 volts will take 5 time constants. In the circuit shown in figure 3-44, view (B), C1 is allowed to charge from T2 to T3. To find the percentage of charge, use the equation:

This works out to be about 57 percent and is far beyond the 10 percent required for a linear sweep voltage. The linearity is very poor in this example.

The electrical length (sweep time), which is measured from T2 to T3, can be found by multiplying RC times the number of time constants. Refer to the Universal Time Constant Chart (figure 3-39) again to find that 57 percent is 0.83TC. By multiplying 0.83 times R1C1, you will find that the electrical length is approximately 21 milliseconds:

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3-54 UNCLASSIFIED The physical length (amplitude) is determined by subtracting the valley point from the peak point. This is 9.8 volts in the example (12.8 volts − 3 volts).

For a sweep generator that produces a more linear output sawtooth waveform, refer to the circuit in figure 3-45, view (A). R1 and C1 form the RC time constant. Notice that the capacitor charges toward 35 volts (V E) in this circuit.

Figure 3-45A Improved unijunction sawtooth generator Figure 3-45B.— Improved unijunction sawtooth generator

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3-55 UNCLASSIFIED The output waveform is shown in figure 3-45, view (B). With a lower voltage applied from B1 to B2, the peak and valley points are closer together. Calculating the percentage of charge:

The linearity in this case is good. Using the Universal Time Constant Chart, a 10-percent charge amounts to 0.1 time constant. The electrical length is, again, RC times the number of time constants. With R1 at 300 kilohms and C1 at .005 microfarads, the time constant is 1,500 microseconds. One-tenth of a time constant is equal to 150 microseconds; so the electrical length is 150 microseconds. Prt is the electrical length plus the fall or flyback time. If C1 discharges from 5.3 volts to 2 volts in 15 microseconds, then the prt is 150 + 15, or 165 microseconds. The prf is about 6 kilohertz.

Some unijunction circuits are triggered to obtain a very stable prf. One method is to apply triggers to B2, as shown in figure 3-46. Negative triggers applied to B2 reduce the inter- base voltage enough to cause a forward bias condition in the emitter circuit. This cuts off the sweep and allows C1 to discharge through the B1-to-emitter circuit. Then, C1 recharges until the next trigger arrives and C1 discharges. Circuit operation and parameters are figured in the same manner as in the previous sawtooth circuits.

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3.2.3.3 Transistor Sawtooth Generator. The next sawtooth generator uses a conventional pnp transistor, as shown in figure 3-47, view (A). This generator also uses an RC network, and the transistor provides the switching action.

Figure 3-46 Synchronized sawtooth generator Figure 3-47A Transistor sawtooth generator (pnp)

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3-57 UNCLASSIFIED The waveforms for the circuit are shown in views (B) and (C). With no input signals, Q1 is biased near saturation by R1. The voltage across C1 is very low (-2.5 volts) because load resistor R3 drops most of the applied voltage. The transistor must be cut off to allow C1 to charge. To cut off Q1, a positive rectangular wave is used.

Figure 3-47B.—Transistor sawtooth generator (pnp) Figure 3-47C.—Transistor sawtooth generator (pnp)

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3-58 UNCLASSIFIED Since Q1 is a pnp transistor, a positive voltage must be used to drive it to cutoff. Figure 3-47, view (B), shows a rectangular wave input 500 microseconds long on the positive alternation. At T0, the positive gate applied to the base of Q1 cuts off Q1. This effectively removes the transistor from the circuit (opens the switch), and C1 charges through R3 toward 20 volts. Starting with a charge of −2.5 volts at T0, C1 charges (T0 to T1) for 500 microseconds to -4.25 volts at T1. Let's determine the percent of charge:

This allows nearly a linear rise of voltage across C1.

Increasing the value of R3 or C1 increases the time constant. The capacitor will not charge to as high a voltage in the same period of time. Decreasing the width of the gate and maintaining the same time constant also prevents the capacitor from charging as much. With less charge on the capacitor, and the same voltage applied, linearity has been improved. Decreasing R3 or C1 or increasing gate width decreases linearity. Changing the applied voltage will change the charge on the capacitor. The percentage of charge remains constant; however, it does not affect linearity.

At T1, the positive alternation of the input gate ends, and Q1 returns to a forward-bias condition. A transistor that is near saturation has very low resistance, so C1 discharges rapidly between T1 and T2, as shown in figure 3-47, view (C). The capacitor discharges in less than 200 microseconds, the length of the negative alternation of the gate. The negative gate is made longer than the discharge time of the capacitor to ensure that the circuit has returned to its original condition.

From T1 to T2, the capacitor discharges and the circuit returns to its original condition, ready for another positive gate to arrive. The next positive gate arrives at T2 and the actions repeats.

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

3-59 UNCLASSIFIED The amplitude of the output sawtooth wave is equal to 1.75 volts (4.25 volts minus 2.5 volts). The electrical length is the same as the positive alternation of the input gate, or 500 microseconds. The prt is 700 microseconds (500 + 200) and the prf is 1/prt or 1,428 hertz.

3.2.3.4 Trapezoidal Sweep Generator Normally, oscilloscopes and synchroscopes use ELECTROSTATIC DEFLECTION and, as the name implies, electrostatic fields move the electron beam. The need here is for a sawtooth voltage waveform.

Another method of electron beam deflection is ELECTROMAGNETIC DEFLECTION. Currents through a coil produce electromagnetic fields which position the beam of electrons. The electromagnetic system requires a sawtooth of current which increases at a linear rate. Because of the inherent characteristics of a coil, a sawtooth voltage does not cause a linear increase of current. A linear increase of current requires a TRAPEZOIDAL voltage waveform applied to a coil. This section discusses the generation of a trapezoidal wave.

Figure 3-48 shows a trapezoidal wave. The wave consists of a sharp, almost instantaneous jump in voltage followed by a linear rise to some peak value. The initial change in voltage at T0 is called a JUMP or STEP. The jump is followed by a linear sawtooth voltage rise. The time from the jump to the peak amplitude is the sum of the jump voltage and the sawtooth peak; where the peak value occurs is the electrical length. The peak voltage amplitude is the sum of the jump voltage and the sawtooth peak voltage. The waveshape can be considered a combination of a rectangular wave and a sawtooth wave.

Figure 3-48 Trapezoidal waveform

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

3-60 UNCLASSIFIED The inductance and resistance of a coil form a series RL circuit. The voltage drop across this inductance and resistance must be added to obtain the voltage waveform required to produce a linear rise in current. A linear rise of current produces a linear rise of voltage across the resistance of the coil and a constant voltage drop across the inductance of the coil.

Assume figure 3-49, view (A), represents deflection coils. If we apply a voltage waveshape to the circuit, which will provide a square wave across inductor L, and a sawtooth across resistor R, then a linear current rise will result.

View (B) of figure 3-49 shows the waveforms when E a is a square wave. Recall that the inductor acts as an open circuit at this first instant. Current now starts to flow and develops a voltage across the resistor. With a square wave applied, the voltage across the inductor starts to drop as soon as any voltage appears across the resistor. This is due to the fact that the voltage across the inductor and resistor must add up to the applied voltage.

Figure 3-49A Series LR circuit Figure 3-49B.—Series LR circuit

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3-61 UNCLASSIFIED With Ea being a trapezoidal voltage, as shown in figure 3-49, view (C), the instant current flows, a voltage appears across the resistor, and the applied voltage increases. With an increasing applied voltage, the inductor voltage remains constant (EL) at the jump level and circuit current (IR) rises at a linear rate from the jump voltage point. Notice that if you add the inductor voltage (EL) and resistor voltage (ER) at any point between times T0 and T1, the sum is the applied voltage (Ea). The key fact here is that a trapezoidal voltage must be applied to a sweep coil to cause a linear rise of current. The linear rise of current will cause a uniform, changing magnetic field which, in turn, will cause an electron beam to move at a constant rate across a crt.

There are many ways to generate a trapezoidal waveshape. For example, the rectangular part could be generated in one circuit, the sawtooth portion in another, and the two combined waveforms in still a third circuit. A far easier, and less complex, way is to use an RC circuit in combination with a transistor to generate the trapezoidal waveshape in one stage.

Figure 3-50, view (A), shows the schematic diagram of a trapezoidal generator. The waveshapes for the circuit are shown in view (B). R1 provides forward bias for Q1 and, without an input gate, Q1 conducts very hard (near saturation), C1 couples the input gate signal to the base of Q1. R2, R3, and C2 form the RC network which forms the trapezoidal wave. The output is taken across R3 and C2.

Figure 3-49C.— Series LR circuit

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3-62 UNCLASSIFIED

Figure 3-50A Trapezoidal waveform generator Figure 3-50B.—Trapezoidal waveform generator

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3-63 UNCLASSIFIED With Q1 conducting very hard, collector voltage is near 0 volts prior to the gate being applied. The voltage across R2 is about 50 volts. This means no current flows across R3, and C2 has no charge.

At T0, the negative alternation of the input gate is applied to the base of Q1, driving it into cutoff. At this time the transistor is effectively removed from the circuit. The circuit is now a series-RC network with 50 volts applied. At the instant Q1 cuts off, 50 volts will appear across the combination of R2 and R3 (the capacitor being a short at the first instant). The 50 volts will divide proportionally, according to the size of the two resistors. R2 then will have 49.5 volts and R3 will have 0.5 volt. The 0.5 volt across R3 (jump resistor) is the amplitude of the jump voltage. Since the output is taken across R3 and C2 in series, the output "jumps" to 0.5 volt.

Observe how a trapezoidal generator differs from a sawtooth generator. If the output were taken across the capacitor alone, the output voltage would be 0 at the first instant. But splitting the R of the RC network so that the output is taken across the capacitor and part of the total resistance produces the jump voltage.

Refer again to figure 3-50, view (A) and view (B). From T0 to T1, C2 begins charging toward 50 volts through R2 and R3. The time constant for this circuit is 10 milliseconds. If the input gate is 1,000 microseconds, the capacitor can charge for only 10 percent of 1TC, and the sawtooth part of the trapezoidal wave will be linear.

At T1, the input gate ends and Q1 begins to conduct heavily. C2 discharges through R3 and Q1. The time required to discharge C2 is primarily determined by the values of R3 and C2. The minimum discharge time (in this circuit) is 500 microseconds (5K x .02μF x 5). At T2, the capacitor has discharged back to 0 volts and the circuit is quiescent. It remains in this condition until T3 when another gate is applied to the transistor.

The amplitude of the jump voltage was calculated to be 0.5 volt. The sawtooth portion of the wave is linear because the time, T0 to T1, is only 10 percent of the total charge time. The amplitude of the trapezoidal wave is approximately 5 volts. The electrical length is the same as the input gate length, or 1,000 microseconds. Linearity is affected in the same manner as in the sawtooth generator. Increasing R2 or C2, or decreasing gate width, will improve linearity. Changing the applied voltage will increase output amplitude, but will not affect linearity.

Linearity of the trapezoidal waveform, produced by the circuit in figure 3-50, view (A) and view (B) depends on two factors, gate length and the time constant of the RC circuit. Recall that these are the same factors that controlled linearity in the sawtooth generator. The formula developed earlier still remains true and enables us to determine what effect these factors have on linearity.

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3-64 UNCLASSIFIED

An increase in gate length results in an increase in the number of time constants and an increase in the percentage of charge that the capacitor will take on during this time interval. As stated earlier, if the number of time constants were to exceed 0.1, linearity would decrease. The reason for a decrease in linearity is that a greater percentage of V CC is used. The Universal Time Constant Chart (figure 3-39) shows that the charge line begins to curve. A decrease in gate length has the opposite effect on linearity in that it causes linearity to increase. The reason for this increase is that a smaller number of time constants are used and, in turn, a smaller percentage of the applied V CC is used.

Changing the value of resistance or capacitance in the circuit also affects linearity. If the value of C2 or R3 is increased, the time is increased for 1 time constant. An increase in the time for 1TC results in a decrease in the number of time constants required for good linearity. As stated earlier, a decrease in the number of time constants results in an increase in linearity (less than 0.1TC). In addition to an increase in jump voltage (larger value of R3) and a decrease in the amplitude (physical length) of the sawtooth produced by the circuit, electrical length remains the same because the length of the gate was not changed.

R2 has a similar effect on linearity because it is in series with R3. As an example, decreasing the value of R2 results in a decrease in linearity. The equation

illustrates that by decreasing R (TC = RC), TC decreases and an increase in the number of time constants causes a decrease in linearity. Other effects are an increase in jump voltage and an increase in the amplitude (physical length) of the sawtooth.

Changing the value of V CC does not affect linearity. Linearity is dependent on gate length, R, and C. VCC does affect the amplitude of the waveform and the value of jump voltage that is obtained.

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3-65 UNCLASSIFIED Q11. For an RC circuit to produce a linear output across the capacitor, the voltage across the capacitor may not exceed what percent of the applied voltage? Q12. Increasing gate length in a sawtooth generator does what to linearity? Q13. In a sawtooth generator, why is the transistor turned on for a longer time than the discharge time of the RC network? Q14. What is added to a sawtooth generator to produce a trapezoidal wave? 3.3 SUMMARY This chapter has presented information on waveforms and wave generators. The information that follows summarizes the important points of this chapter.

A waveform which undergoes a pattern of changes, returns to its original pattern, and repeats that same pattern of changes is called a PERIODIC waveform.

Each completed pattern of a waveform is called a CYCLE.

A SQUARE WAVE is identified by, two alternations equal in time that are square in appearance. One alternation is called a PULSE. The time for one complete cycle is called the PULSE REPETITION TIME (prt). The number of times in one second that the cycle repeats itself is called PULSE REPETITION RATE (prr) or PULSE REPETITION FREQUENCY (prf). The length of the pulse measured in the figure (T0 to T1) is referred to as the PULSE WIDTH (pw). The left side of the pulse is referred to as the LEADING EDGE and the right side as the TRAILING EDGE.

A RECTANGULAR WAVE has two alternations that are unequal in time.

A SAWTOOTH WAVE has a linear increase in voltage followed by a rapid decrease of voltage at the end of the waveform.

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3-66 UNCLASSIFIED A TRAPEZOIDAL WAVE looks like a sawtooth wave sitting on top of a square wave. The leading edge is called the JUMP voltage.

A TRIGGER is a very narrow pulse used to turn on or off another circuit.

A MULTIVIBRATOR is used to generate a square or rectangular wave. A multivibrator is basically two amplifiers with regenerative feedback.

The ASTABLE MULTIVIBRATOR has no stable state. The transistors alternately switch from cutoff to saturation at a frequency determined by the RC time constants of the coupling circuits.

The MONOSTABLE MULTIVIBRATOR has one stable state. One transistor conducts while the other is cut off. An external trigger must be applied to change this condition.

The BISTABLE MULTIVIBRATOR has two steady states. It remains in one of the stable states until a trigger is applied. It then switches to the other stable state until another trigger is applied.

The bistable multivibrator is also known as a FLIP-FLOP. The two inputs are SET and CLEAR. The two outputs are "1" and "0." A trigger pulse on the set input will cause the "1" output (negative or positive voltage depending on the type transistor used). At the same time the "0" output will equal 0 volts. This is the SET state.

A CLEAR STATE of a flip-flop exists when the "1" output measures low voltage (or 0 volts) and the "0" output is high voltage. The flip-flop will flop to the CLEAR state only upon application of a trigger pulse to the CLEAR (C) input.

There is a third lead on some flip-flops. This lead is the TOGGLE (T) input. Every time a trigger pulse is applied to the (T) input, the flip-flop will change states.

BLOCKING OSCILLATORS are used in applications which require a narrow pulse with sharp leading and trailing edges. They are used as TRIGGER GENERATORS or FREQUENCY DIVIDERS.

A SAWTOOTH GENERATOR voltage waveform has a linear change in voltage and a fast recovery time. The linear change in voltage is generated by taking the output from a capacitor. The sawtooth voltage waveform is used to provide electrostatic deflection in oscilloscopes.

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3-67 UNCLASSIFIED A TRAPEZOIDAL GENERATOR voltage waveform is used to provide, a linear increase in current through a coil. A trapezoidal wave begins with a step or jump voltage, then a sawtooth wave. A trapezoidal wave of voltage is used in electromagnetic deflection display devices.

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3-68 UNCLASSIFIED ANSWERS TO QUESTIONS Q1. THROUGH Q14. A1. Multivibrator.

A2. Astable.

A3. Monostable.

A4. Bistable.

A5. RC coupling networks.

A6. One-shot.

A7. Two.

A8. Two.

A9. SET state.

A10. Transformer.

A11. Ten percent.

A12. Decreases linearity.

A13. To allow the capacitor time to discharge.

A14. A resistor.