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

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

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).

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

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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3-38 UNCLASSIFIED

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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3-48 UNCLASSIFIED

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

NEETS MODULE 9-Wave Generation and Wave Shaping UNCLASSIFIED

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.