VIC-5: will the phase-locked loop find this cell's resonance?

With these chokes and this cell, where is the resonance — and can this PLL reach it, hold it, and build the rise inside each gate?

The formula

f₀ = \frac{1}{2 π \sqrt{L \cdot C}} Δ = | f₀ - x |

LaTeX

f₀ = \frac{1}{2\pi \sqrt{L \cdot C}} \qquad Δ = \left| f₀ - x \right|

Work it out

Fill from a part the library

L₁ Charging choke

The choke on the positive side of the cell.

L₂ Blocking choke

The choke on the return side.

k Coupling coefficient

How much of one choke's flux threads the other.

c Choke arrangement

Separate, or on one core with fields aiding or opposing.

C Cell capacitance

The cell as a capacitor.

R Series resistance

Everything resistive in the loop.

V Drive amplitude

The peak voltage applied across the loop — after the transformer, if there is one.

x VCO centre frequency

kHz

Where the VCO sits with no correction — the middle of its range.

v VCO gain

Hertz per volt of control voltage.

d Phase detector gain

Volts per radian of phase error.

R₁ Filter resistor R₁

kΩ

The lag-lead filter's series resistor.

R₂ Filter resistor R₂

kΩ

The resistor in series with the filter capacitor.

C₁ Filter capacitor

µF

The filter capacitor.

g Gate frequency

The slow gate switching the locked drive on and off.

G Gate duty

How much of each gate period the drive is let through.

or see a worked example with typical numbers

Add the chokes, find the resonance and the Q — the same first steps as the VIC simulation.
Work out the PLL from its parts: natural frequency, damping, lock range, hold range, lock time.
Compare the resonance to the VCO centre. Within the lock range, the loop snaps to it; within the hold range but outside the lock range, it pulls in after slipping cycles, which takes longer; outside the hold range, the VCO cannot be driven far enough and there is no lock.
Count the cycles of resonance each gate admits, and ask how much of the resonant rise they build — the build-up calculation.

Every assumption of every step. In particular the PLL is the linear second-order loop with a passive lag-lead filter, and the pickup coil gives the phase detector a clean signal at the resonant frequency.
The VCO centre is where it sits at mid control voltage, and its gain is linear across the range. A 4046's tuning curve is not very linear.
The pulse duty is fixed at 50 %, which is what the VCO's square-wave output gives before any pulse shaping.
What is Meyer's here is the claim that the VIC-5 tracks the cell's resonance automatically. Loop theory says what it takes to do that; it does not say his circuit did.