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Skin  effect and inductor model (Read 5952 times)
rfmagic
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Skin  effect and inductor model
May 14th, 2014, 1:52pm
 
Hi all,

While investigating an equivalent lumped model for RFIC inductor I was trying to get some intuition of the different high frequency effects if the inductor.
I find it hard to understand the self inductance variation due to the skin effect.
It is well known that the effective resistance increases with frequency due to current flowing near the conductor surface.
As for the effective inductance all of the papers show that the self inductance decreases with frequency. My intuition tells me that the self inductance should increase with frequency the same way that the inductance increases with narrower trace widths.

Am I missing something????

I appreciate your comments and insights on this subject.

Thanks
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weber8722
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Re: Skin  effect and inductor model
Reply #1 - Feb 27th, 2015, 10:09am
 
Hi,

in the Designers-Guide "model" section you can find a pdf on modeling of skin-effect. To some degree I like it (because easy to understand & efficient), to some degree NOT (because its non-physical!).

But what happens in reality?
You can model a big wire with many elements in Parallel, e.g. 10 series R + series L elements.
Of course, all these L couple against eachother! THIS coupling causes that  the over-all effective L drops vs f and eff. R increases vs f (with famous sqrt(f)-law!).
In a spice-simulation you can even monitor the current through each segment vs f - and the result is that the outer wires conduct more and more current vs f, and the inner less and less!

This can be course also implemented in veriloga or as spice subckt - real impressive to see that, and all very physical  :)!

Bye Stephan
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Ken Kundert
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Re: Skin  effect and inductor model
Reply #2 - Feb 28th, 2015, 4:20pm
 
As described in http://www.designers-guide.org/Modeling/ind.pdf, you model skin effect in an inductor by adding an additional impedance in series with your inductor. The details of this additional impedance is affected by the physical geometry of the inductor, but it in most cases it is well approximated by:
   Z(f) = √(jf) = √(2f) (1 + j)/(2H)
You can further break this down in to resistive and reactive components:
   Z(f) = R(f) + X(f)
   R(f) = √(2f)/(2H)
   X(f) = j√(2f)/(2H)
From the first equation, you can clearly see that the resistance increases with √f. Clearly so does the reactance. But if we model the reactance as an inductance:
   jωL = X(f) = j√(2f)/(2H)
   L = √2/(4πH√f)
So while the reactance due to the inductive part of skin effect is increasing with frequency, the actual extra inductance decreases with frequency.

-Ken
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Ken Kundert
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Re: Skin  effect and inductor model
Reply #3 - Feb 28th, 2015, 4:36pm
 
Stephen,
   Why do you say the inductor in my paper is non-physical? I'd like to point out that the word 'physical' may not mean what you think it means. A model is 'physical' if it represents a behavior that could exist in the natural world. Many frequency domain models are non-physical because they are non-causal. Nonlinear capacitor model would be non-physical if it does not conserve charge. Finally, models whose behavior depends strongly on the simulator time steps are are also non-physical (because the real world does not have time steps). My inductor model is clearly physical because it is constructed from a collection of two terminal resistors and inductors.

Perhaps you mean to say it is empirical? It models skin effect using Zskin(f) = √(jf)/H. That is clearly an empirical model with H being the fitting factor. It does not fit the behavior of skin effect in an inductor precisely because it does not account for the effect of the geometry, but it is consistent with the overall assumption that the extra accuracy provided by accounting for the effect of geometry is relatively small.

-Ken
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rfmagic
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Re: Skin  effect and inductor model
Reply #4 - Aug 3rd, 2015, 1:28pm
 
Thank you Ken And Stephan. this is well understood now.

And sorry for my late response...
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R.kumar
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Re: Skin  effect and inductor model
Reply #5 - Dec 1st, 2017, 8:29am
 
In skin effect region, since all the current flow is happening at the surface, the conductor can be treated as a hollow tube. There is a secondary (induced) magnetic field inside the conductor which opposes the primary magnetic field. This causes the reduction of inductance with frequency.
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