Question

A DSB signal is squared to generate a carrier component
that may then be used for demodulation. (A technique
for doing this, namely the phase-locked loop, will
be studied in the next chapter.) Derive an expression that
illustrates the impact of interference on this technique.

Answer 1

In DSB demodulation process we need to regenerate carrier signal for this we are using phase-locked loop as a carrier recovery circuit. It is therefore, a useful device for synchronous demodulation of AM signal with a suppressed carrier. A PLL has three basic components

1. A voltage-controlled oscillator (VCO)

2. A multiplier

3. A loop filter H(s).

In PLL it has a feedback system follow to the input signal , The VCO adjust it's own frequency such that it's frequency and phase can track those of the input signal. The VCO is an oscillator whose frequency can be linearly controlled by an input voltage . If a VCO input volatge is e₀(t), its output is a sinusoid with instantaneous frequency given by ,

where c is constant of VCO and w_c is free-running frequency of the VCO. The multiplier output is further low pass filtered by the loop filter and then applied to the input of the VCO. This voltage changes the frequency of the oscilator and keeps the loop locked by forcing the VCO outputto track the phase of the input sinusoid.