NEETS Module 9 − Introduction to Wave− Generation and Wave−Shaping
and Direct Current
|Alternating Current and Transformers
|Circuit Protection, Control, and Measurement
|Electrical Conductors, Wiring Techniques,
and Schematic Reading
|Generators and Motors
|Electronic Emission, Tubes, and Power Supplies
|Solid-State Devices and Power Supplies
|Wave-Generation and Wave-Shaping Circuits
|Wave Propagation, Transmission Lines, and
|Introduction to Number Systems and Logic Circuits
|- Introduction to Microelectronics
|Principles of Synchros, Servos, and Gyros
|Introduction to Test Equipment
|Radio-Frequency Communications Principles
|The Technician's Handbook, Master Glossary
|Test Methods and Practices
|Introduction to Digital Computers
|Introduction to Fiber Optics
|Note: Navy Electricity and Electronics Training
Series (NEETS) content is U.S. Navy property in the public domain.
WAVEforMS and WAVE GENERATORS
Upon completion of this chapter you will be able to:
1. Explain the operation of a stable, monostable, and bistable
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
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.
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.
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 T3).
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:
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
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.
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.
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.
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?
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).
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
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 -VCC 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.
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.
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.
Figure 3-10. - Monostable multivibrator block diagram.