A VCO has a DC-coupled input port where a control voltage may be applied and must also receive power to drive the oscillator circuit. It also has one or more AC-coupled ports where a sinusoidal signal is generated. As the control voltage is increased, the frequency of the output sinusoid increases. Typically, the increase in frequency is greater per unit increase in voltage at lower control voltages and less per unit increase in voltage at higher control voltages. The response can be modeled as locally linear around the anticipated mean control voltage of the VCO when placed into a working PLL.

Since, normally, VCOs have a non-linear input/output relationship that causes the above linearized model to depend heavily upon the frequency of which it is expected to operate. A more accurate representation of Ko Ko would be Ko(norm) = Ko fo Ko(norm)= Ko fo . In this model, Ko(norm)Ko(norm) should be approximately constant and Ko Kois the linear, tangental curve-fit to the measured input/output data. In this way, Ko(norm)Ko(norm) could be the average value of Ko(norm) = Ko fo Ko(norm)= Ko fo measured at various values of fo fo and then Ko Ko could later be extracted (albiet approximately) from the recorded value of Ko(norm)Ko(norm).

The output frequency can be written as w_o = w_c+K_oV_c (radians/sec). Here, w_c is the "free-running frequency" of the VCO...the frequency at which it is biased to run in absense of the PLL's loop feedback. The output of the VCO can be written as cos(w_ct+theta_o(t)). The instantaneous frequency is given by w_o = d/dt [w_ct+theta_o(t)] = w_c+dtheta_o/dt. Comparing with the earlier equation verifies that dtheta_o/dt = K_oV_c