Editing Phase-locked loop (section)

===Feedback path and optional divider===
{{More citations needed|section|date=June 2022}}[[File:Divide 4.svg|thumb|An example digital divider (by 4) for use in the feedback path of a multiplying PLL]]
PLLs may include a divider between the oscillator and the feedback input to the phase detector to produce a [[frequency synthesizer]]. A programmable divider is particularly useful in radio transmitter applications and for computer clocking, since a large number of frequencies can be produced from a single stable, accurate, [[crystal oscillator|quartz crystal–controlled reference oscillator]] (which were expensive before commercial-scale [[hydrothermal synthesis]] provided cheap synthetic quartz).

Some PLLs also include a divider between the reference clock and the reference input to the phase detector. If the divider in the feedback path divides by <math>N</math> and the reference input divider divides by <math>M</math>, it allows the PLL to multiply the reference frequency by <math>N/M</math>. It might seem simpler to just feed the PLL a lower frequency, but in some cases the reference frequency may be constrained by other issues, and then the reference divider is useful.

Frequency multiplication can also be attained by locking the VCO output to the ''N''th harmonic of the reference signal. Instead of a simple phase detector, the design uses a harmonic mixer (sampling mixer). The harmonic mixer turns the reference signal into an impulse train that is rich in harmonics.{{Efn|Typically, the reference sinewave drives a [[step recovery diode]] circuit to make this impulse train. The resulting impulse train drives a sample gate.}} The VCO output is coarse tuned to be close to one of those harmonics. Consequently, the desired harmonic mixer output (representing the difference between the ''N'' harmonic and the VCO output) falls within the loop filter passband.<!-- HP had a harmonic mixer and synchronizer that turned its microwave sweep generators into PLLs. -->

It should also be noted that the feedback is not limited to a frequency divider. This element can be other elements such as a frequency multiplier, or a mixer. The multiplier will make the VCO output a sub-multiple (rather than a multiple) of the reference frequency. A mixer can translate the VCO frequency by a fixed offset. It may also be a combination of these. For example, a divider following a mixer allows the divider to operate at a much lower frequency than the VCO without a loss in loop gain.