WPT compensation capacitors, SS and SP done right.
Resonant capacitors for series–series and series–parallel links from L1, L2 and M or k — with the voltage each capacitor has to survive.
WPT compensation capacitor calculator
- Primary capacitor C₁
- 146.1 nF
- Secondary capacitor C₂
- 146.1 nF
- Voltage across C₁ (RMS)
- 64.09 Vpeak 90.63 V
- Voltage across C₂ (RMS)
- 16.43 Vpeak 23.23 V
- Current in C₂ (RMS)
- 1.282 A
- Secondary coil current (RMS)
- 1.282 A
- Load voltage / current
- 12.82 V / 1.282 A
- Output power
- 16.43 W
- Input resistance at resonance
- 657.2 mΩ
Lossless coils and capacitors, sinusoidal (first-harmonic) operation, RMS values.
How do you calculate WPT compensation capacitors?
The compensation capacitors of a wireless power link are chosen to resonate each coil at the operating frequency: in series–series (SS) compensation C1 = 1/(ω²L1) and C2 = 1/(ω²L2), while in series–parallel (SP) compensation C2 = 1/(ω²L2) but C1 = 1/(ω²(L1 − M²/L2)). The SP primary is different because the parallel-tuned receiver reflects a reactance back into the transmitter, so tuning C1 to L1 alone leaves the input out of resonance — a common mistake in online formulas. This calculator handles both topologies from L1, L2 and either M or k, at any frequency from kHz to MHz. Enter the primary current and load resistance to see the RMS and peak voltage across each capacitor, the secondary currents and the delivered power, so you can pick capacitors with the right voltage rating. AirInduct Sim computes L1, L2 and M from coil geometry, and its AI Copilot sizes SS, SP and LCC networks from them.
How it's calculated
With ω = 2πf and M = k√(L₁L₂) when k is given:
Currents and voltages at resonance, for primary current I₁ (RMS) and load resistance R_L:
- Lossless coils and capacitors, sinusoidal first-harmonic operation; all values RMS (peak = √2 × RMS).
- In SP the secondary coil current is the phasor sum of load and capacitor currents: √(I_load² + I_C2²).
- The SP primary formula follows Wang, Covic and Stielau (IEEE Trans. Industrial Electronics, 2004). We checked it by solving the full circuit: the input reactance is zero to machine precision.
- Don’t have L₁, L₂ and M yet? Get them from geometry with the coupling coefficient calculator.
Worked example
Two 24 µH coils at k = 0.2 (M = 4.8 µH), 85 kHz, 5 A RMS in the primary, 10 Ω load:
| SS: C₁ = C₂ | 146.1 nF |
|---|---|
| SS: voltage across C₁ (RMS / peak) | 64.09 V / 90.63 V |
| SS: load current, output power | 1.282 A, 16.43 W |
| SP: C₁ (tunes L₁ − M²/L₂) | 152.2 nF |
| SP: C₂ | 146.1 nF |
| SP: load current, output power | 1 A, 10 W |
The SP primary capacitor is 4.2 % larger than the SS one at this coupling — using the SS value would detune the input. The primary capacitor sees ωL₁·I₁ (in SS), which grows linearly with frequency, inductance and current, so check it again whenever you scale the design.
When you need the full simulator
This calculator is free to use and answers one question at a time. The full AirInduct Sim simulator takes the same physics further:
- L₁, L₂ and M computed from the actual coil geometry, so the capacitors match the coils you will build.
- SS, SP and LCC–LCC capacitors with efficiency, coil losses and a frequency-splitting check (Copilot link analysis).
- Class-D and Class-E inverter matching with ZVS checks, plus synchronous rectifier analysis.
- SPICE netlist export to verify the tank in your circuit simulator.
More free calculators
- Mutual inductance calculatorM between two circular or square coils from turns, size, axial gap and lateral offset — or from k, L1 and L2.
- Coupling coefficient calculatork from coil geometry (with both self-inductances) or from L1, L2 and M, plus a k-versus-gap curve.
- Helmholtz coil calculatorCentre field, required current and optimal spacing for circular and square Helmholtz pairs, with axial uniformity.
- Square Helmholtz coil calculatorSquare pairs at the 0.5445·a spacing: centre field, current for a target field and the uniform region.
- WPT efficiency calculatorMaximum link efficiency and figure of merit U = k√(Q1Q2), the optimal load and the k needed for a target η.
Frequently asked questions
Why is the SP primary capacitor different from the SS one?
With a parallel capacitor tuned to L2, the receiver reflects an impedance (ωM)²/Z2 that contains a capacitive part, −jωM²/L2 in effect. The primary therefore sees an inductance of L1 − M²/L2, and C1 must resonate that: C1 = 1/(ω²(L1 − M²/L2)). Because it depends on M, an SP primary capacitor is only exactly right at one coupling. In SS compensation the reflected impedance is purely resistive at resonance, so C1 = 1/(ω²L1) regardless of coupling or load.
Should I use SS or SP compensation?
SS is the usual default: both capacitors are independent of coupling and load, which makes it tolerant of misalignment, and with a fixed primary current the receiver behaves as a voltage source (V = ωM·I1). SP makes the receiver behave as a current source (I = M·I1/L2), which suits some battery-charging and constant-current loads, but its primary tuning shifts with coupling. LCC networks add more freedom at the cost of more components.
How do I size the capacitor voltage rating?
A series capacitor sees V = I/(ωC) = ωL·I, which equals the voltage across the coil it tunes and reaches hundreds of volts or more in kilowatt-class systems. Use the peak value (√2 × RMS for a sine wave), add margin for misalignment and tolerance, and choose a capacitor type rated for that voltage and RMS current at your frequency — typically film or C0G/NP0 ceramic.
What frequency should I use?
It depends on the standard and power level. SAE J2954 light-duty EV charging uses a nominal 85 kHz (79–90 kHz band); Qi phone charging operates roughly in the 87–205 kHz range; AirFuel resonant systems use 6.78 MHz. Higher frequency shrinks the capacitors and raises ωM, but increases switching and AC-resistance losses.