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Inductance needed for a target frequency

What choke do I need to make this cell resonate where I want it?

The formula
L=14⁢π2⁢f2·C
L
Required inductance, H
f
Target frequency, kHz
C
Cell capacitance, nF
LaTeX 
L = \frac{1}{4\pi^{2} \cdot \left(f\right)^{2} \cdot C}

Work it out

Fill from a part the library

kHz

Where you want the circuit to ring.

nF

What the cell measures, or what the capacitance calculation gave you.

Compare with a variation

Result

L Required inductance 253.3 µH

Total series inductance. In a VIC this is split across the charging chokes.

H Per choke, if two 126.7 µH

Half the total, for the usual arrangement of two chokes in series.

Z Characteristic impedance 15.92 Ω

The reactance of each element at resonance — what the drive will be working against.

With your numbers
253.3 µH=14⁢π2⁢10 kHz2·1000 nF
LaTeX 
253.3\,\mathrm{µH} = \frac{1}{4\pi^{2} \cdot \left(10\,\mathrm{kHz}\right)^{2} \cdot 1000\,\mathrm{nF}}

This result is a link — the address bar holds your numbers, so it can be pasted into a post and opened to the same answer.

What this looks like

Required inductance against target frequency Target frequency swept from 5 kHz to 15 kHz with everything else held at your numbers. The dashed lines cross where you are.
Required inductance against target frequencyRequired inductance falls from 1013 µH to 113 µH as target frequency rises from 5 kHz to 15 kHz. At your target frequency of 10 kHz it is 253 µH.0250500750100057.51012.51510 kHz253 µHTarget frequency (kHz)Required inductance (µH)
The formula behind the curve
L=14⁢π2⁢f2·C
L
Required inductance, H
f
Target frequency, kHz
C
Cell capacitance, nF
LaTeX 
L = \frac{1}{4\pi^{2} \cdot \left(f\right)^{2} \cdot C}
What moves the answer Each input moved 10% either way, with the others held still, and the effect on required inductance.
What moves the answerRequired inductance is most sensitive to Target frequency, which moves it by about 23.5% for a 10% change. It is least sensitive to Cell capacitance, at about 11.1%.Change in the answer when each input moves by 10%-40%-20%20%40%Target frequency±23.5Cell capacitance±11.1
The formula behind the curve
L=14⁢π2⁢f2·C
L
Required inductance, H
f
Target frequency, kHz
C
Cell capacitance, nF
LaTeX 
L = \frac{1}{4\pi^{2} \cdot \left(f\right)^{2} \cdot C}

Method

  1. Convert the frequency to hertz and the capacitance to farads. Everything below is SI.
  2. Square the frequency. This is the step that makes the answer sensitive: halving the target frequency quadruples the inductance you have to wind.
  3. Multiply by 4π² — about 39.48 — and by the capacitance.
  4. Take the reciprocal. The result is the total series inductance in henries.
  5. If the design uses two chokes in series, each needs half of this, because inductances in series add.
  6. Check the characteristic impedance √(L ÷ C) before winding anything: it tells you the reactance the drive has to push against, and a number in the hundreds of kilohms means very little current will flow.

Assumptions

  • The chokes are ideal inductors. A real coil with the henries this calculation asks for has substantial resistance and its own self-capacitance, and both pull the actual resonance below this figure.
  • The capacitance is what you think it is. Cell capacitance moves with temperature, with gas in the gap, and with how much of the electrode is actually submerged.
  • Series connection, with the chokes adding. Coils wound on a shared core couple to each other, and mutual inductance can add or subtract depending on winding sense — the total is then not simply the sum.
  • The result must be below the chokes’ own self-resonant frequency to mean anything. A coil driven above its SRF behaves as a capacitor, and no amount of turns will fix that.