Figure 4. Sawtooth wave composition

Timing Circuits
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it can be seen that the even and odd harmonics are added with

opposite phase relationships. As each harmonic is added, the

resultant wave more closely resembles the sawtooth voltage. This is

illustrated by the addition of the fourth harmonic in Figure 4C, and

up to the ninth harmonic in Figure 4D. Triangular waves can be

constructed similarly by adding a series of sine waves in proper

phase and amplitude to the fundamental frequency.

Figure 4. Sawtooth wave composition

Section IV. BANDWIDTH

EFFECTS OF BANDWIDTH ON NONSINUSOIDAL WAVEFORMS.

a. Bandwidth represents the range of frequencies that a circuit

will pass. When a nonsinusoidal wave is applied to a circuit, the

number of harmonics that appear at the output depends upon the

bandwidth of the circuit. Consider the effect of a circuit with a 3

kHz (3000 kHz) bandwidth (from 0 Hz to 3 kHz) on a square wave having

a pulse repetition frequency (prf) of 1 kHz. Since the circuit will

pass only frequencies up to 3 kHz, only the fundamental frequency (1

kHz) and the third harmonic (3 kHz) will appear in the output (Figure

5A). Although a square wave is applied at the input, the output

waveform is badly distorted. If the bandwidth of this circuit is

increased to 7 kHz (from 0 Hz to 7 kHz), all of the harmonics up to

and including the seventh will be passed (Figure 5B), and the output

waveform is less distorted. As the bandwidth of this circuit is

increased, more harmonics are passed and the output waveform more

closely resembles the input waveform.