comparison of formulas and simulation results for resistance

I am currently working on a project where my prof. ask me to prove that the equations to calculate the resistance of a simple conductor, where in this case refers to a copper micro strip on a FR4 pcb with a ground layer below the substrate layer, assuming the ground to be infinite. I have used the simple formula of R= rho*(length of conductor)/ (cross section area of conductor), where I found the results yielded by simulations are much more higher than the results obtained by calculation with the above formula. Can anyone tell me why is that and any other formulas or problems I should consider?

Any help is deeply appreciated =)

Can you provide more details about the simulation?

That's correct for low frequency. At high frequency, the effective conductor cross section is reduced by skin effect.

moreover, it is best suited to calculate the input impedance of the patch antenna by using the cavity model specified by Balanis and taking the equivalent circuit of the antenna structure as a parallel R-L-C resonant circuit where each of the R, L and C have their own formulas.

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and simulators are based on this cavity model only.

posted to the wrong thread?

dear volker_muehlhaus,

I don't think so, as it is clearly mentioned that the impedance is to be find of the microstrip as conductor, place over grounded FR4 substrate.
am i correct? or still you think i did the mistake in understanding the question?

Yes, it is a question about transmission line losses. Patch antenna is a completely different topic.

edit: But maybe I misunderstood the question also ... is it about the ohmic resistance of the conductor, or about the transmission line impedance Z0=sqrt((R'+jωL')/(G'+jωC')) ?

0k. got it. my mistake.
in that case Zin is to be the function of the "electrical length", Zo (characteristic impedance), and load impedance (Zl).

According to the formulas and model in the simulation it is stated that 2-Port PI with series RL and shunt RC which is equivalent to:

-------R----L-------- Is this correct?
| | | |
R C R C
| | | |
--------------------- <=ground

By the way when you guys talked about effective resistance you are talking about equivalent impedance or just resistance excluding capacitance and inductance? Because in the results shown it's stated in separation the values of R, C and L and I am referring to the R given in results.

I read some replies from you guys and found that I forgot to pay attention to frequency-dependency of skin effect in this case, really thanks a lot. Now I am trying to figure out how to calculate the resistivity of copper that may vary with frequencies of inputted source. The formulas I found online is resistivity = (magnitude of electric field)/(current density)

Do I still have to include the skin effect consideration after calculating the resistivity of each different frequencies? And if yes, how do I include it because the formula of skin-depth does not provide a distinct equivalent effective thickness of the conductor?

Really thankful for all the help =)

Looking at your line pi model:

when you talk about resistance, what resistance is that? Do you really mean resistance (loss) or do you mean the transmission line impedance (like "Z0=50 ohm line").