Achieving Simultaneous Tracking and Noise Rejection Performance

 From equations (3.17) and (3.20) the reason for the prevalence of second order loops may be seen. Since the input frequency almost always differs from the free running frequency, it is important that K_oK_dF(0) is as large as possible. But at the same time, the noise bandwidth $B_L\propto K_oK_d$ must be minimised. The presence of the F(0) term in (3.20) but not (3.17) means that maximising F(0) is highly beneficial. It is for this reason that active second order phaselock loops where, from equation (3.15) F_A(0)=-A rather than unity for both passive and 1st order loops. This allows good tracking to be achieved without compromising noise bandwidth, an impossibility with a 1st order loop.