Page 116 - Schaum's Outline of Theory and Problems of Electric Circuits

WAVEFORMS AND SIGNALS
CHAP. 6]

Fig. 6-3 105

Fig. 6-4

Fig. 6-5

6
6
(a) 1 ¼ 10 ! 1 , 2 ¼ 10 ! 2 . Then
6 6
v 0 ðtÞ¼ cos ð! 1 t 10 ! 1 Þþ cos ð! 2 t 10 ! 2 Þ
6 6 6
¼ cos ! 1 ðt 10 Þþ cos ! 2 ðt 10 Þ¼ v i ðt 10 Þ¼ v i ðt Þ
where ¼ 10 6 s ¼ 1 ms. Thus a phase shift proportional to ! [Fig. 6-5(a)] delays all frequency components of
the input signal by 1 ms. The output follows the input with no distortion.
6
(b) 1 ¼ 2 ¼ 10 . Then
6 6
v 0 ðtÞ¼ cos ð! 1 t 10 Þþ cos ð! 2 t 10 Þ
6 6
¼ cos ! 1 ðt 10 =! 1 Þþ cos ! 2 ðt 10 =! 2 Þ
A constant phase shift [Fig. 6-5(b)] delays different frequency components of the input signal by different
amounts. The output is a distorted form of the input.