THE PHASE-LOCKED LOOP a feedback that chases a phase until the error is zero — it locks
A phase-locked loop is a control loop that makes one oscillator match the phase of a reference. It compares its phase to the incoming signal, feeds the error back to nudge its own frequency, and converges until the error is driven to zero — it locks. From that lock it can recover a carrier, synthesize a clean multiple of a clock, demodulate FM, or extract timing from a data stream. It is negative feedback applied to phase, and it is everywhere a system must agree with an external rhythm. The loop converges to the locked state from anywhere in its range — which is why it is a keeper shot.
THE TECHNIQUE out += k·(ref − out) — feedback drives the phase error to 0
The demo runs a first-order PLL from phase 0 toward a reference of 5; the error shrinks each step until it locks: live demo
HISTORY & CREDIT de Bellescize 1932 · the PLL
“To match a signal’s phase you must measure it perfectly.” — a PLL just feeds the error back and converges to lock, no perfect measurement needed. cited
the loop · phase detector → loop filter → oscillator → back — out += k·(ref−out). lock · the error decays to zero; the oscillator tracks the reference’s phase and frequency. 1932 · Henri de Bellescize — the phase-locked loop; carrier recovery, clocks, FM demod.
An oscillator that chases a phase until it catches it — feedback converging to lock. convergence
RECOMMEND FOR I-13 the lock, on the compiler
On the canonical compiler, the PLL starts at phase 0 and converges to the reference 5 — the phase error driven below 10⁻⁴:
$ i13 run cr_pll.i13 # out += 0.5*(ref - out)
RUN OK · 305 step(s) · peak stack 6 · call depth 13
ref = 5
locked = 4.9988 -- converged from 0
is_locked = 1 -- phase error < 1e-4
Recommend as a keeper shot — the convergence reading of the phase channel. A PLL drives a phase error to zero and converges to a locked state from any starting phase in range — a genuine trajectory, not a static identity, which is the bar that distinguishes enacted structure from witnessed theorem. Under David’s PHASE TEST the honest question is whether “converge to phase agreement by feedback” is a new axis or duplicates the seated confluence axis (independent parties driven to the same state). My read leans confluence-duplicate — feedback-to-agreement is convergence — but it is the batch’s clearest enacted candidate, so it goes to the panel as the phase channel’s dynamic form.