Hello,

I am currently trying to estimate the parasitic capacitance of an inductor using the electrostatic solver in CST Studio Suite and compare the simulation result with measurements obtained using an impedance analyzer.

For the hardware measurement, I first measured the low-frequency inductance, L, in the frequency range where the inductance remains approximately constant.

I then measured the first self-resonant frequency, f_SRF, and the impedance magnitude at that frequency.

Assuming a simplified parallel-resonant equivalent circuit consisting of an inductance, L, and an effective parasitic capacitance, C_p, I estimated the capacitance using:

f_SRF = 1 / (2 * pi * sqrt(L * C_p))

Rearranging the equation gives:

C_p = 1 / ((2 * pi * f_SRF)^2 * L)

For my inductor, the measured values are approximately:

L = 10 uH
f_SRF = 14.627 MHz
|Z(f_SRF)| = 2.07 kOhm

Using the equation above, the estimated effective parasitic capacitance is approximately:

C_p = 11.8 pF

I am now trying to obtain a comparable result using the CST electrostatic solver.

In my model, the winding is represented by separate torus sections. So far, I have tried the following approaches:

1. Defining all winding sections as PEC and assigning the same potential of 1 V to each section.
2. Defining the winding sections as PEC and assigning linearly increasing potentials along the winding: 0 V, 1 V, 2 V, ..., 8 V
3. Defining the winding sections as PEC and assigning linearly increasing potentials centered around 0 V: -4 V, -3 V, -2 V, ..., 3 V, 4 V

For the cases with a prescribed voltage distribution, I calculated the equivalent capacitance from the stored electrostatic energy using:

C_eq = 2 * W_e / (Delta_V)^2

where:

C_eq = equivalent capacitance
W_e = total stored electrostatic energy
Delta_V = voltage difference between the two ends of the winding

4. Cutting through the turns to separate them into two parts, defining PEC regions at the cross-sections, keeping the remaining winding sections as copper, and repeating the potential-assignment methods described above.
5. Modelling the core in different ways:

• as ferrite material;
• as PEC with a floating potential.

However, I am still unable to obtain a capacitance value that agrees with the measurement-based estimate.

Could you please guide me on how to model this correctly in CST Studio Suite and obtain a meaningful estimate of the inductor self-capacitance?

Thank you in advance for your support.

Best regards,