Advanced Frequency Synthesis by Phase Lock

APPENDIX G

USING Gsmpl

G.1   OPEN-LOOP TRANSFER FUNCTION

G.1.1   Without Sampling

In the absence of sampling, the open-loop transfer function G(ω_m) is given by

where T is the loop type and h = 1. If there is sampling and a zero-order hold (as with a sample-and-hold phase detector),

is a first-order approximation for the effect of the sample-and-hold on the fundamental modulation frequency.

For a type-1 loop (one zero-frequency pole), the value of K in Eq. (G.1) is the same as K/N in FS2 and K in Phase-Lock Basics (PLB), where N = 1. For a type-2 loop, K in Eq. (G.1) equals ω_n² sec, the square of the natural frequency (except for the “sec” unit factor).

G.1.2   Using Gsmpl

Gsmpl allows us to specify the parameters in Eq. (G.1) and to obtain G(ω_m) for a specified range of frequencies. A command line window opens and we are invited to

Enter Command (? for help)

(the parenthetical expression is a constant reminder). If we do enter ?, we obtain a list of commands, which is expanded below.

d: display parameters gives a list of current parameter values such as is shown in Fig. G.1.

ra causes radian units to be used, whereas Hz causes Hz units (entries are case sensitive). If a pole is entered in rad/s, for example, and Hz is then entered, the pole’s units will be changed from rad/s to ...