Is There a Relationship Between Resistance and Frequency in Circuit Impedance?

[Antros48]

Hi everyone,
I am trying to simulate a circuit containing resistors, inductors and capacitors. When i calculate the Impedance of the circuit i find it to be for example 150+100j for a frequency of 5Hz. When i run the same simulation for a frequency of 15 Hz i find it to be 162+134j. I understand that inductive impedance increases with frequency but what about resistance? It cannot be independent since it changes too! Is there any possible relationship formula connecting these two parameters?
Thank you

 

[phinds]

Ohmic resistance doesn't change until you get up to frequencies where the skin effect becomes significant; it's the impedance that is changing.

 

[Antros48]

But i run the simulation on very low frequencies. Is it possible that skin effect takes place in such spectrum?

 

[donpacino]

what is the circuit layout?

 

[phinds]

But i run the simulation on very low frequencies. Is it possible that skin effect takes place in such spectrum?

No, but again, it doesn't have to. You are not seeing any change in the ohmic resistance, you are seeing a change in the impedance. Resistance does not change with frequency until you get to very high frequency. Impedance of a reactive circuit changes with any frequency change.

 

[Antros48]

Plinds you are correct but let me type my question differently. I know the formula for changing the imaginary part of the impedance and it comes from 2 x pi x f x L. But how does the real part change? Is there a formula for that? And let's say that the real part is the total resistance of the circuit, including the inductor series resistance. How can someone describe the change in that parameter?
Thanks for the response btw

 

[sophiecentaur]

Plinds you are correct but let me type my question differently. I know the formula for changing the imaginary part of the impedance and it comes from 2 x pi x f x L. But how does the real part change? Is there a formula for that? And let's say that the real part is the total resistance of the circuit, including the inductor series resistance. How can someone describe the change in that parameter?
Thanks for the response btw

I think you are making an unwarranted assumption that the Resistive Component must stay the same for all circuits. If you have an R in series with a C, the R will stay the same with frequency but a more complicated circuit will not necessarily pan out that way - as you have shown. Believe the results and not your intuition. :)

PS I think the comments about skin effect are not relevant here and just likely to confuse a chap. Unless you actually model the skin effect in the simulation (straightforward circuit analysis) you can't include it in the calculations.

 

[Antros48]

Thank you for the answer sophiecentaur. The fact is i understand that the combination of resistances and other elements in a circuit has different results. Let's say i have an RL circuit containing only a resistance and an inductor. When i simulate that with LTSpice the total impedance is changing with frequency. My question is if i can have the impedance data for 10 Hz using field measurement, could i possibly calculate the impedance at 50 Hz using some kind of relationship formula between frequency and impedance or resistance?

 

[donpacino]

lets take a look at a simple circuit, a capacito

At DC the resistance of that circuit is inf, or open. at very high frequency the circuit is zero, or short.

 

[Antros48]

Ok agree with that.

 

[zoki85]

But i run the simulation on very low frequencies. Is it possible that skin effect takes place in such spectrum?

If a very good conductor has a large enough cross section, skin effect ( in a relative sense) can be significant at low frequencies too.

 

[donpacino]

If a very good conductor has a large enough cross section, skin effect ( in a relative sense) can be significant at low frequencies too.

Hes running this in LTSPICE

I am assuming he is using ideal components, in which case you would not see skin effect at all.
op can you confirm?

 

[zoki85]

Hes running this in LTSPICE

Than it is just a matter of reactance change.

 

[sophiecentaur]

Thank you for the answer sophiecentaur. The fact is i understand that the combination of resistances and other elements in a circuit has different results. Let's say i have an RL circuit containing only a resistance and an inductor. When i simulate that with LTSpice the total impedance is changing with frequency. My question is if i can have the impedance data for 10 Hz using field measurement, could i possibly calculate the impedance at 50 Hz using some kind of relationship formula between frequency and impedance or resistance?

Using a simulation is all very well but it does nothing more than save you the effort of building the circuit. It doesn't actually show the relationships between the circuit components and the input signal values. If you want this "some kind of relationship formula etc. etc " you need to go through the proper analysis. That is the relationship you are after. There is no quick way into that sort of knowledge. I often get a bit grumpy about simulation software but you prove my point about this completely. Very few simulations (of anything) yield a good understanding of the way things work; they usually introduce as many pitfalls as good learning experiences when taken on their own.

 

[phinds]

Than it is just a matter of reactance change.

Which is exactly what I've been telling him since post #2

 

[sophiecentaur]

Than it is just a matter of reactance change.

Actually, a similar problem would arise if you just made up a reasonably complicated network of resistances and then asked for a 'simple relationship' between one of the resistances ( a variable one) and the overall resistance.

 

[Antros48]

Ok because maybe my question got a little complicated in the way. I know that impedance changes with frequency, i am also familiar with skin effect and especially i am not lazy enough to expect from couple simulations to extract a relationship between two variables. I have build at least 15 different circuits and ran over 200 simulations for different frequencies so i have a pretty big database! My original problem is that i want to apply a low frequency, low voltage signal in a 240 V, 50 Hz distribution power system, and by measuring the impedance in 5 Hz to calculate the impedance in 50 Hz. I know how to do this for the imaginary part of the impedance and it is 2*pi*f*L in a lagginc circuit. But how can i calculate the real part too? That is my question.

 

[zoki85]

Ok because maybe my question got a little complicated in the way. I know that impedance changes with frequency, i am also familiar with skin effect and especially i am not lazy enough to expect from couple simulations to extract a relationship between two variables. I have build at least 15 different circuits and ran over 200 simulations for different frequencies so i have a pretty big database! My original problem is that i want to apply a low frequency, low voltage signal in a 240 V, 50 Hz distribution power system, and by measuring the impedance in 5 Hz to calculate the impedance in 50 Hz. I know how to do this for the imaginary part of the impedance and it is 2*pi*f*L in a lagginc circuit. But how can i calculate the real part too? That is my question.

Simply put, in general case you can't do that. Just from equivalent input impedance Z₁=R₁ + jX₁ at some frequency ω₁ you can't determine what would be equivalent impedance Z₂=R₂ + jX₂ of the network at some other frequency ω₁.

 

[Antros48]

Yes that what i figured out after a lot of simulation. the equations on different circuit configurations simply don't match.. Maybe there is indeed a palindrome that i cannot figure out but for now i have to declare that it is not achievable to predict it! Thanks anw

 

[donpacino]

Ok because maybe my question got a little complicated in the way. I know that impedance changes with frequency, i am also familiar with skin effect and especially i am not lazy enough to expect from couple simulations to extract a relationship between two variables. I have build at least 15 different circuits and ran over 200 simulations for different frequencies so i have a pretty big database! My original problem is that i want to apply a low frequency, low voltage signal in a 240 V, 50 Hz distribution power system, and by measuring the impedance in 5 Hz to calculate the impedance in 50 Hz. I know how to do this for the imaginary part of the impedance and it is 2*pi*f*L in a lagginc circuit. But how can i calculate the real part too? That is my question.

To understand why this doesn't work, look at the frequency response of a complicated circuit.

 

[zoki85]

To understand why this doesn't work, look at the frequency response of a complicated circuit.

Good advice

 

[Antros48]

thanks for the advice. My answer from post 19 is still valid.

 

[sophiecentaur]

The OP seems to have stumbled on the fact that Science is based on relationships and not just instances. The results of simulated or real experiments are useful when they are used to verify a theory but they do not constitute one.

 

[donpacino]

thanks for the advice. My answer from post 19 is still valid.

Very true!

 

[Antros48]

Making an assumption, even a wrong one, based on experiment results does not necessarily means constituting a theory. Besides i am a fan of the fact that nothing happens randomly and everything has an explanation, no matter that cannot be explained yet..

 

[meBigGuy]

Hi everyone,
I am trying to simulate a circuit containing resistors, inductors and capacitors. When i calculate the Impedance of the circuit i find it to be for example 150+100j for a frequency of 5Hz. When i run the same simulation for a frequency of 15 Hz i find it to be 162+134j. I understand that inductive impedance increases with frequency but what about resistance? It cannot be independent since it changes too! Is there any possible relationship formula connecting these two parameters?
Thank you

I noticed no one has actually answered your original question.
Why, in *your simulations*, does the real part of the impedance change when the frequency is varied?
Could you post your circuit? And, include how you determine the real and imaginary part of the impedance taken from your simulation.

 

[Antros48]

To determine the impedance i run ac analysis with list option for specific frequency. Then i divide the source voltage with the source current (with a negative sign cause of LTSpice convention).

 

[sophiecentaur]

To determine the impedance i run ac analysis with list option for specific frequency. Then i divide the source voltage with the source current (with a negative sign cause of LTSpice convention).

It's hardly surprising that the impedance of that circuit changes in a way that's not intuitively predictable. Spice uses an analysis that will give you the Impedance and what Spice does uses the 'relationship' that you are after. In a relatively simple circuit, you can just apply Kirchoff's laws 'by hand' but, for more complex circuits, K will just give you too many equations to solve on paper.

 

[Antros48]

Ok after a lot of simulations it is appropriate to write down my results just to clarify them. The real and imaginary part change indeed with frequency, and the feedback was confirmed in an excel sheet too. The reason is when there is parallel connection of elements, the result is mathematically changing and that can be proved with KVL. Also my earlier thought that the imaginary part can be predicted is no longer valid cause it may be correct for some circuits but after trying it to a lot more showed that has no trust in using it. Thanks for the interesting discussion btw.