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Modeling >> Passive Devices >> Capacitor modeling
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Message started by Kyle on Mar 9^th, 2015, 1:41am

Title: Capacitor modeling
Post by Kyle on Mar 9^th, 2015, 1:41am

Hi， everyone, I have a question about the capacitor modeling.
We all know there will be time-varying electrical coupling between the two plates, in the form of displacement current. Since there is the time-varying electrical coupling, it will cause the time-varying magnetic field, which means part of the energy is stored in magnetic field. And the electrical coupling can be represented by a capacitor for simplicity. So, my question is that can I use a inductor to represent the induced magnetic field?
Usually, the definition of the inductor is derived on the basis of the conducting current not the displacement current, but according to the maxwell function, the time-varying displacement currents also contribute to the induced magnetic field. This puzzled me a lot :-/

Anyone how knows the answer, please help me!

Title: Re: Capacitor modeling
Post by boe on Mar 9^th, 2015, 2:04am

Hi Kyle,
see Maxwell's equations in Wikipedia: The capacitor is described by Ampère's law, while the inductor obeys Faraday's law.
- B O E

Title: Re: Capacitor modeling
Post by Kyle on Mar 9^th, 2015, 3:10am

Thank you for your advice. But it seems that the wiki just provide the conception. And I think it's ok to use a inductor in the model to describe the capacitor's high frequency behavior especially over the resonate frequency. While I'm not sure about this idea, could you give me some more details, thank you agian!
boe wrote on Mar 9^th, 2015, 2:04am:

Hi Kyle,
see Maxwell's equations in Wikipedia: The capacitor is described by Ampère's law, while the inductor obeys Faraday's law.
- B O E

Title: Re: Capacitor modeling
Post by boe on Mar 9^th, 2015, 9:42am

Kyle,
assuming the capacitor dimensions are negligible compared to the wavelength at the frequency of interest (and the plates big compared to their spacing), I do not see (at a quick glance) why the inductance should play a role in the region between the plates of the cap.
Does this help?
- B O E

Title: Re: Capacitor modeling
Post by Kyle on Mar 9^th, 2015, 7:05pm

Thank you for your reply. And If the plate is not big enough and even smaller to the space, and there still exits enough electrical coupling, can I use the inductance to represent the induced magnetic field?

For example, there are two co-planar lines, one is the signal line, and another one is the ground line, there still exist electrical coupling, as shown in the following figure.

boe wrote on Mar 9^th, 2015, 9:42am:

Title: Re: Capacitor modeling
Post by Geoffrey_Coram on Mar 27^th, 2015, 5:04am

I'm with BOE, I don't see that you'll get any significant magnetic effect. Usually, one has the magnetic field encircling the wire carrying electric current. In your first drawing, you don't know the leads that carry current to the capacitor plates; if the leads are centered on the plate, then the current spreads out on the plate and the magnetic fields would mostly cancel out.

Title: Re: Capacitor modeling
Post by Kyle on Mar 30^th, 2015, 3:46am

Geoffrey_Coram wrote on Mar 27^th, 2015, 5:04am:

Thank you for your explanation. And I think I have understand the problem. :)