Electrical – Equivalent circuit for a real capacitor


A real capacitor can be modeled using a series RLC equivalent circuit.
However, there are still discrepancies between the two.
I've generated a waveform from the lab and I've modelled the equivalent series RLC. Why are there discrepancies between the two circuits and how can I generate a model that more closely resembles the lab generated waveform?

The first image is the lab-generated waveform for the voltage across a 2.2uF capacitor, second image is the simulated waveform resulting from the series RLC equivalent. Both have 200k Hz, 10Vp-p square wave input
Lab generated waveform
Simulated readings from modelled series RLC circuit

Best Answer

If we had an FFT amplitude and phase, one could get a perfect passive model of all the elements, knowing that the source is 50Ω and thus the transfer function.

The signal has the following characteristics from which a model can be generated.

  • Slew rate dV/dt= 200mV/1us or dt/dV=5us/V (*)
  • ΔVin=10Vpp thus with 50Ω source
  • ΔIc=10V/50Ω=200mA
  • Vpp= 200mV but asymptotic slopes of Vout project to 222 mVpp thus
    • fundamental dt/dV becomes 4.5us/V (*)

Since C=Ic dt/dV = 200mA * 4.5us/V = **0.9 uF and not 2.2 uF**

However with a simulator you can model the waveform and adjust the parameters. From this I get RLC1= 0.6uF+ 20nH + 50mΩ and RLC2 = 0.8uF + 0nH + 300mΩ (in //)

enter image description here

It is either Rs=100 Ohm source and 1.8uF or 50 Ohm source and 0.9uF with an ESR=50mΩ approx with about 20nH of ESL and many other RLC smaller networks shunting the RL network.


simulate this circuit – Schematic created using CircuitLab

This is also why C(f), ESR and ESL changes value with sine frequency due to reactance model. But SRF and PRF will give a better model and a scatttering s22 plot is the best from the OEM.