The Phase-Locked Loop

Every loop so far feeds back an amplitude - a voltage, an angle, a speed - and settles when the correction balances the error, which means a little error always remains. Henri de Bellescize's synchronous receiver of 1932 feeds back something else: the PHASE difference between an incoming signal and a local oscillator. That one change buys a property no amplitude loop can offer. Frequency is the rate of change of phase, so an oscillator is already an integrator. Hold the phase error at any constant value and the two frequencies must be EXACTLY equal - not close, equal to the last decimal place - for as long as the lock holds. The remaining error is pushed entirely into the phase, which sits wherever it must to keep the oscillator pulled to the right frequency. Three blocks do it. A phase detector, which is a multiplier; a loop filter, which decides the dynamics; and a voltage-controlled oscillator, which is the plant. The filter's time constant sets a trade you cannot avoid: a narrow loop rejects noise and rides through a dropout but takes a long time to acquire, and a wide loop locks instantly and passes the noise straight onto the recovered clock. It is worth seeing this next to the regenerative receiver, because they are the same circuit pushed in opposite directions. Regeneration uses positive feedback and is set as close to oscillating as the operator dares. A phase-locked loop lets its oscillator run freely and uses negative feedback to drag it into step with something outside. One asks a human to hold a circuit on the edge of instability; the other never goes near it - which is why a locked receiver can be sealed in a box and forgotten.