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Simulate a VIC: chokes, cell and pulsed drive

With these chokes, this cell and this drive, where does the loop ring, what does the drive draw, and does the cell step-charge?

The formula
f₀=12πL·C
f₀
Resonant frequency, Hz
L
Loop inductance, mH
C
Cell capacitance, nF
LaTeX 
f₀ = \frac{1}{2\pi \sqrt{L \cdot C}}

Work it out

Fill from a part the library

mH

The choke on the positive side of the cell.

mH

The choke on the return side.

How much of one choke's flux threads the other. Zero for separate cores.

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

nF

The cell as a capacitor. The cell calculations give this from geometry and water.

Ω

Everything resistive in the loop — both chokes' wire, the cell's ESR, wiring.

kHz

The pulse frequency the loop is driven at.

V

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

%

How much of each pulse period the drive is on.

Hz

The slow gate switching the pulse train on and off.

%

How much of each gate period the pulses are let through.

kΩ

The water's resistance across the gap — what the charge drains through between pulses. The leak resistance calculation gives this from geometry and conductivity.

or see a worked example with typical numbers

Method

  1. Turn the drive into timing: pulse period, on-time, pulses per gate and effective duty — the pulse train timing calculation.
  2. Add the two chokes, with the mutual inductance if they share a core — the coupled chokes calculation. Everything after this uses that loop inductance.
  3. Find where the loop rings with the cell — series LC resonance — and how sharply, against the series resistance — the Q factor calculation.
  4. Ask what happens after each pulse — damping and ringdown — and what the drive is asked for at its own frequency, which is not the resonance unless the two were made to agree — the pulsed drive power calculation.
  5. Run the pulse train against the cell and its leak — step charging.
  6. Then compare the drive frequency to the resonance. If they differ by more than a tenth, the resonant rise reported is what the loop would do if driven on resonance; what it actually does at the drive frequency is the current and impedance the drive-power step reports.

Assumptions

  • Every assumption of every step applies. In particular the loop is a linear series RLC; the water is a fixed capacitor with a fixed leak; the chokes are lossless inductors; and the drive is a stiff voltage source.
  • The series resistance damps the ring and the leak resistance drains the cell. They are two different things — the first is wire and ESR, the second is water across the gap — and are entered separately.
  • The drive amplitude is what reaches the loop. If a transformer stands in front of the chokes, enter its secondary voltage; the simulator page does that arithmetic through the transformer calculation when a transformer is chosen from the library.
  • The cell capacitance and the leak are inputs here, not derived. On the simulator page they come from the cell's geometry and the water through the cell calculations; on this page they are whatever is typed.
  • This is standard circuit theory. What is Meyer's is the claim about what the arrangement is for — a water capacitor rung by chokes so that voltage rises while current does not — and that claim lives in the sources.