# Wave Shaping Circuits

Figure 1 shows three basic waveforms that are represented by the time domain concept. The three waveforms shown are sine wave, square wave, and sawtooth wave. Although the three waveforms are different, they all have the same period of frequency. By using various electronic circuits, these waveforms can be changed from one shape to another.

A periodic waveform is one with the same waveform for all cycles. According to the frequency domain concept, all periodic waveforms are made up of sine waves.

In other words, any periodic wave can be formed by superimposing a number of sine waves having different amplitudes, phases, and frequencies. Sine waves are important because they are the only waveform that cannot be distorted by RC, RL, or LC circuits.

The sine wave that has the same frequency as the periodic waveform is called the fundamental frequency. The fundamental frequency is also called the first harmonic. Harmonics are multiples of the fundamental frequency. The second harmonic is twice the fundamental, the third harmonic is three times the fundamental, and so on. Harmonics can be combined in an infinite number of ways to produce any periodic waveform.

The type and number of harmonics included in the periodic waveform depend on the shape of the waveform. For example, Figure 2 shows a square wave. Figure 3 shows how a square wave is formed by the combination of the fundamental frequency with an infinite number of odd harmonics that cross the zero reference line in phase with the fundamental.

Figure 4 shows the formation of a sawtooth waveform. It consists of the fundamental frequency plus odd harmonics in-phase and even harmonics crossing the zero reference line 180 degrees out of phase with the fundamental.

An oscilloscope displays waveforms in the time domain. A spectrum analyzer displays waveforms in the frequency domain. Frequency domain analysis can be used to determine how a circuit affects a waveform.

Periodic waveforms are waveforms that occur at regular intervals. The period of a waveform is measured from any point on one cycle to the same point on the next cycle (Figure 5).

The pulse width is the length of the pulse (Figure 6). The duty cycle is the ratio of the pulse width to the period. It can be represented as a percentage indicating the amount of time that the pulse exists during each cycle.

Duty cycle = pulse width/period

All pulses have rise and fall times. The rise time is the time it takes from the pulse to rise from 10%to 90% of its maximum amplitude. The fall time is the time it takes for a pulse to fall from 90% to 10% of its maximum amplitude (Figure 7).

Overshoot, undershoot, and ringing are conditions common to high-frequency pulses (Figure 8). Overshoot occurs when the leading edge of a waveform exceeds its normal maximum value.

Undershoot occurs when the trailing edge exceeds its normal minimum value. (The leading edge is the front edge of the waveform; the trailing edge is the back edge of the waveform.)

Both conditions are followed by damped oscillations known as ringing. These conditions are undesirable but exist because of imperfect circuits.

# Wave Shaping Circuits

An RC network can change the shape of complex waveforms so that the output barely resembles the input. The amount of distortion is determined by the RC time constant. The type of distortion is determined by the component the output is taken across.

If the output is taken across the resistor, the circuit is called a differentiator. A differentiator is used to produce a pip or peaked waveform from square or rectangular waveforms for timing or synchronizing circuits. It is also used to produce trigger or marker pulses.

If the output is taken across the capacitor, the circuit is called an integrator. An integrator is used for waveshaping in radio, television, radar, and computers.

Figure 9 shows a differentiator circuit. Recall that complex waveforms are made of the fundamental frequency plus a large number of harmonics. When a complex waveform is applied to a differentiator, each frequency is affected differently.

The ratio of the capacitive reactance (XC) to R is different for each harmonic. This results in each harmonic being shifted in phase and reduced in amplitude by a different amount. The net result is distortion of the original waveform.

Figure 10 shows what happens to a square wave applied to a differentiator. Figure 11 shows the effects of different RC time constants.

An integrator circuit is similar to a differentiator except that the output is taken across the capacitor (Figure 12). Figure 13 shows the result of applying a square wave to an integrator. The integrator changes the waveform in a different way than the differentiator. Figure 14 shows the effects of different RC time constants.

## Clipping Circuits

Another type of circuit that can change the shape of a waveform is a clipping, or limiter circuit (Figure 15). A clipping circuit can be used to square off the peaks of an applied signal, obtain a rectangular waveform from a sine-wave signal, eliminate positive or negative portions of a waveform, or keep an input amplitude at a constant level.

The diode is forward biased and conducts during the positive portion of the input signal. During the negative portion of the input signal, the diode is reverse biased and does not conduct. The circuit is essentially a half-wave rectifier. By using a bias voltage, the amount of signal that is clipped off can be regulated.

Figure 16 shows a biased series clipping circuit. The diode cannot conduct until the input signal exceeds the bias source.

A shunt clipping circuit performs the same function as the series clipper (Figure 17). The difference is that the output is taken across the diode. This circuit clips off the negative portion of the input signal. A shunt clipper can also be biased to change the clipping level as shown in Figures 18.

If both the positive and the negative peaks must be limited, two biased diodes are used (Figure 19). This prevents the output signal from exceeding predetermined values for both peaks. With the elimination of both peaks, the remaining signal is generally square-shaped. Therefore, this circuit is often referred to as a square-wave generator.

Figure 20 shows another clipping circuit that limits both positive and negative peaks. Therefore, the output is clamped to the breakdown voltage of the zeners. Between the two extremes, neither zener diode will conduct, and the input signal is passed to the output.

## Clamping Circuits

Sometimes it is desirable to change the DC reference level of a waveform. The DC reference level is the starting point from which measurements are made. A clamping circuit can be used to clamp the top or bottom of the waveform to a given DC voltage.

Unlike a clipper or limiter circuit, a clamping circuit does not change the shape of the waveform. A diode clamper (Figure 21) is also called a DC restorer. This circuit is commonly used in radar, television, telecommunications, and computers.

In the circuit shown, a square wave is applied to an input signal. The purpose of the circuit is to clamp the top of the square wave to 0 volts, without changing the shape of the waveform.

## Special Purpose Circuits

The prefix mono- means one. A monostable multivibrator has only one stable state. It is also called a one-shot multivibrator because it produces one output pulse for each input pulse. The output pulse is generally longer than the input pulse. Therefore, this circuit is also called pulse stretcher.

Typically, the circuit is used as a gate in computers, electronic control circuits, and communication equipment. Figure 22 shows a schematic diagram of a monostable multivibrator. The circuit is normally in its stable state.

When it receives an input trigger pulse, it switches to its unstable state. The length of time the circuit is in the unstable state is determined by the RC time constant of resistor R2 and capacitor C1. Capacitor C2 and resistor R5 form a differentiator circuit, which is used to convert the input pulse to a positive and negative spike. Diode D1 allows only the negative spike to pass through to turn on the circuit.

A bistable multivibrator is a multivibrator having two stable states (bi- meaning two). This circuit requires two inputs to complete one cycle. A pulse at one input sets the circuit to one of its stable states. A pulse at the other input resets it to its other stable state. This circuit is often called a flip-flop because of its mode of operation (Figure 23).

A basic flip-flop circuit produces a square or rectangular waveform for use in gating or timing signals or for on-off switching operations in binary counter circuits. A binary counter circuit is essentially two transistor amplifiers with the output of each transistor coupled to the input of the other transistor.

When an input signal is applied to the set input, transistor Q1 turns on, which turns transistor Q2 off. When transistor Q2 turns off, it places a positive potential on the base of transistor Q1, holding it on. If a pulse is not applied to the reset input, it causes transistor Q2 to conduct, turning off transistor Q1. Turning transistor Q1 off holds transistor Q2 on.

Discrete versions of the flip-flop find little application today. However, integrated circuit versions of the flip-flop find wide application. It is perhaps the most important circuit in digital electronics, used for frequency division, data storage, counting, and data manipulation.

Another bistable circuit is the Schmitt trigger (Figure 24). One application of the Schmitt trigger is to convert a sine-wave, sawtooth, or other irregularly shaped waveform to a square or rectangular wave.

The circuit differs from a conventional bistable multivibrator in that one of the coupling networks is replaced by a common-emitter resistor (R3). This provides additional regeneration for quicker action and straighter leading and trailing edges on the output waveform.