NEETS Module 9 — Introduction to Wave- Generation and Wave-Shaping
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WAVEFORMS AND WAVE GENERATORS
Upon completion of this chapter you will be able to:
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
5. Explain how the jump voltage is produced in a trapezoidal wave generator.
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
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. 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.
Figure 3-1.—Periodic waveforms.
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
Figure 3-2.—Square wave.
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:
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
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. 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. 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.
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.
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.
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.
When an input signal to one amplifier is large enough, the transistor can be driven into cutoff, and its
collector voltage will be almost V CC. 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.
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.
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.
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?
type of multivibrator has two stable states?
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
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).
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
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
Figure 3-5.—Astable multivibrator.
Figure 3-6.—Astable multivibrator. (Q2 saturated).
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 -VCC, 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 3-7.—Square wave output from Q2.
Figure 3-8.—Rectangular waves.
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 3-9A.—Triggered astable multivibrator and output.
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 3-9B.—Triggered astable multivibrator and output.
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. Monostable Multivibrator
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.
Figure 3-10.—Monostable multivibrator block diagram.
Introduction to Matter, Energy, and Direct Current,
to Alternating Current and Transformers, Introduction to Circuit Protection,
Control, and Measurement
, Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading
, Introduction to Generators and Motors
Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to Solid-State Devices and Power Supplies
Introduction to Amplifiers, Introduction to
Wave-Generation and Wave-Shaping Circuits
, Introduction to Wave Propagation, Transmission
Lines, and Antennas
, Microwave Principles,
, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics, Principles of Synchros, Servos, and Gyros
Introduction to Test Equipment
, Radar Principles,
The Technician's Handbook,
Master Glossary, Test Methods and Practices,
Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics