2.5 Definition of Loop Order

Recall the form of the phase-locked loop's transfer function, . The order of the PLL is defined as the highest order of s in the denominator of the loop transfer function. For the first order loop, corresponding to Equation 2-50, the highest order of s is one. In the next section, we will study second order loops which have a term s ² in the numerator. As the phase-locked loop's order is increased, it tends to compensate for an instantaneous change in the next higher derivative of the input ^[12].

The type of the loop refers to the number of perfect integrators in the loop. A PLL has an implicit perfect integrator with the VCO, so the first order loop is a first order, type 1, loop. A filter, F(s), with a perfect integrator would yield a type 2 loop.