## Example 5.5

#### A coherent PSK demodulator uses a carrier recovery circuit which introduces a time delay in the recovered reference equal to 7% of the carrier period. What will be the degradation in noise power immunity for this system compared with an ideal demodulator?

### Solution

#### A time delay of 7% of the carrier period results in a phase error in the recovered carrier of 7% or 360o = 25.2o.
The voltage output of the mixer used to compare the incoming symbol a(t) cos wct with the reference cos(wct + 25.2o) will be reduced by a factor cos(25.2o) from its maximum value as a result of the carrier phase error.
This in turn equates to a reduction in symbol energy at the input to the receiver of cos2(25.2o). (Symbol energy is proportional to power x symbol length or voltage2 x symbol length.)

The noise components passing through the mixer will also be affected by the phase error in the carrier reference, but since the noise vectors are assumed to be randomly distributed through 360o, the carrier phase error will reduce the effect of some noise vectors and enhance others with the net effect that the average noise voltage at the mixer output will remain unchanged. Hence it is only the symbol energy that is truly affected by carrier reference phase error and not the noise power. This means that the effective received symbol energy to noise power density will be reduced by a factor 1 / cos2(25.2o) = 1.22, or 0.87 dB, as a result of the phase error.