Nonlinear Capacitor (Debye Relaxation Model)

Question

Tamal Sarkar 2022-4-21

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https://ww2.mathworks.cn/matlabcentral/answers/1701970-nonlinear-capacitor-debye-relaxation-model

评论： Tamal Sarkar 2022-5-24

Hi!

I am trying to model the nonlinear capacitor using the Simscape Electrical capacitor block. While modeling a 8nF Capacitor, I have put the frequency range [f1 f2]=[100 700] kHz with [DF1 DF2]=[0.1 0.15]%. The series resistance I have used is 0.5 Ohm.

When I am trying to run the basic RLC circuit with the Cap I keep getting the following error message:

'f2 times the intrinsic DF2 (corrected for the terminal resistance) must be greater than f1 times the intrinsic DF1 (corrected for the terminal resistance).'

I looked up the model documentation and have found relevant equations but having a hard time to understand how the 'corrected for the terminal resistance' works.

It would be great if someone can explain the process behind the correction so that I can figure out what is wrong with my approach.

Thanks in Advance.

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Answer 1

David John 2022-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/1701970-nonlinear-capacitor-debye-relaxation-model#answer_969905

If your "Series resistance" is zero, then DF1 and DF2 are just the same as your values for "Dissipation factors (%) at f1 and f2 [DF1 DF2]". If the resistance is non-zero, then we have to make a correction to account for the series resistance. In that case, you have a resistor in series with a nonlinear resistance. The dissipation due to a series resistor (by itself) is simply 2*pi*f*R*C. If we write the complex impedance for the Debye equations, then the real part will be R plus a term related to the permittivity.

To make things easier to unravel, I would suggest setting the series resistance to 0 in the capacitor block and use an external series resistor if you really need it. Then, the DF for the capacitor will be exactly what you input to the block and it should be easier to figure out.