Question 10.10: Phase Distortion , Suppose that the input signal given by, v...
Phase Distortion
Suppose that the input signal given by
v_i(t)=3 \cos(2000 \pi t)- \cos(6000 \pi t)
is applied to the inputs of three amplifiers having the gains shown in Table 10.2. Find and plot the output of each amplifier.
Table 10.2 Complex Gains of the Amplifiers Considered in Example 10.10
| Amplifier | Gain at 1000 Hz | Gain at 3000 Hz |
| A | 10∠0° | 10∠0° |
| B | 10∠-45° | 10∠-135° |
| C | 10∠-45° | 10∠-45° |
Applying the gains and phase shifts to the input signal, we find the output signals for the amplifiers to be
\begin{matrix} v_{oA}(t) &=& 30 \cos(2000 \pi t) – 10 \cos(6000 \pi t) \\ v_{oB}(t) &=& 30 \cos(2000\pi t – 45^\circ) – 10 \cos(6000\pi t – 135^\circ) \\ v_{oC}(t) &=& 30 \cos(2000\pi t – 45^\circ) – 10 \cos(6000 \pi t – 45^\circ) \end{matrix}
Plots of the output waveforms are shown in Figure 10.27. Amplifier A produces an output waveform identical to the input, and amplifier B produces an output wave-form identical to the input, except for a time delay. For amplifier A, the phase shift is zero for both frequency components, whereas the phase shift of amplifier B is proportional to frequency. (The phase shift for the 3000-Hz component is three times the phase shift for the 1000-Hz component.) Amplifier C produces a distorted output waveform because its phase response is not proportional to frequency.
