# Frequency-dependent resistor

Discussion in 'General Electronics Chat' started by Dauria Maximo, Aug 3, 2009.

1. ### Dauria Maximo Thread Starter New Member

Aug 3, 2009
2
0
Hi!!
I really need your help with something: i have a resonant circuit with a capacitor, an inductor and a frequency-dependent resistor, all in parallel. To calculate the impedance of the circuit i use:

impedance=1/((1/Gω)+(1/iLω)+iωC));
Gω represents the frequency-dependent resistor.

I am trying to use ZView to modelate this circuit but, i don´t know how to represent a frequency dependent resistor. How can i simulate that?? ZView only has capacitors, inductors, resistores, impedances, CPE's...

2. ### beenthere Retired Moderator

Apr 20, 2004
15,808
294
About the only frequency dependent resistor that comes to mind is one that's wirewound and so is inductive. How is this resistor supposed to behave?

3. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,182
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Skin effect is also a frequency dependent resistance, but I don't think that's what the O.P. is looking for.

4. ### Søren Senior Member

Sep 2, 2006
472
30
Hi,

Capacitance is a frequency dependant resistance as well.

5. ### beenthere Retired Moderator

Apr 20, 2004
15,808
294
Agreed - so does this beast get more or less resistive with increasing frequency?

6. ### steveb Senior Member

Jul 3, 2008
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469
I don't think you can get that exact impedance function with physically realizable components - at least not with a linear system using resistors, capacitors and inductors. I think the best you can do is decide what frequency range you are working over and try to approximate the magnitude and phase response. It can be useful to utilize a delay line along with the resistors capacitors and inductors.

I've attached an example where I assume that G=L=C=1 and find that if I use a parallel RLC circuit with C=1, L=1.41 and R=1.11, and then add a delay line with a 0.6 second delay, I get an approximation shown in the attached figure. The blue curve is your desired impedance and the green is my attempt to approximate. You can taylor the approximation to be better in whatever frequency band you are operating in. My assumption here is that you care less about high frequency and want the low frequency band to match.

You could refine the approximation with more elaborate circuitry and better component choice.

CORRECTION: L was 0.707

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Last edited: Aug 3, 2009
7. ### t06afre AAC Fanatic!

May 11, 2009
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And also the human skin. No kidding this is a fact

8. ### steveb Senior Member

Jul 3, 2008
2,432
469
Sorry, I need to correct that previous post. I messed up the implementation of delay in Matlab. Please see corrected plot. Now, there are three curves. The required impedance (shown in blue) starts with a phase of 45 degrees at low frequency. The RLC approximation with no delay is shown in green and the RLC with a 0.2 second delay is shown in the red curve.

It's difficult to get good matching over a wide frequency range.

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9. ### The Electrician AAC Fanatic!

Oct 9, 2007
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Maybe this will give you some ideas:

focus.ti.com/lit/an/sbaa001/sbaa001.pdf

10. ### Ron H AAC Fanatic!

Apr 14, 2005
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The Yahoo LTspice group has some examples. You may need to join the group to see them, and you need to have LTspice installed in order to view them.
Capacitors and inductors (and wirewound resistors) are not frequency-dependent resistors. In a resistor, the voltage and current are in phase. Not so with L's and C's.

11. ### Dauria Maximo Thread Starter New Member

Aug 3, 2009
2
0

Steveb, my frequency range is 100 to 2000HZ.
“I don't think you can get that exact impedance function with physically realizable components - at least not with a linear system using resistors, capacitors and inductors.”…I was afraid of that!

The issue is: I am trying to modulate a resonant curve using Table Curve (an example in annex). I am using a model that doesn’t represent the real circuit that i have so, i am obtaining that effect in residuals, as u can see. To create this graph I have an output file, obtained by using a lock-in, that contains frequency, impedance magnitude, phase and other information that is not relevant for the circuit.

To modulate the real circuit (also in annex) I need to calculate the magnitude of the impedance symbolically but i don't know the value of all resistors, inductors and capacitors in the circuit so, i was trying to use Zview to solve this problem. Another problem is the complexity of the circuit, the formula for the impedance magnitude is too complex to translate in one expression and use it on table curve.

The problem with software’s like ZView and others is the frequency-dependent resistor…

The only information that i have, is for the resonant circuit and the values are approximations: G =0.03; L =E-7; C=0.2.

Hope u can give me a clue.

Last edited: Aug 11, 2009