Hi!
I'm simulating TiNO thin film resistor embedded into Cu coplanar microstrip line (GSG) at RF frequencies (0.1-50GGz). I would like to verify the simulation results by checking the low frequency matching of Z12-parameter postprocessed from S-parameters obtaind. I assume Z12 should match the resistor DC value but it does not. Are my fundamentals wrong or CST results are wrong?
I'm not sure of your measurement method, but at DC the resistor may appear in series with the source and/or load impedances, so might look 50 or 100 ohms too high. What was the value of the S-parameter at DC?
I use ports for excitation/measurements and obtain the effective DC values:
S12=-0.0056dB
S11=-39.25dB
Z12=68.45Ohm
Z11=68.45Ohm
Effective DC meaning they were calculated at the lowest simulated frequency of 100MHz.
Trying to shed more light on the issue I also simulated single 50Ohm transmission line on 250um al2o3 substrate with metalized backside ground plane (fabricated and verified by RF network analyzer) with the same port setup, and that gave me DC values of the kind of " through test" of the 50Ohm microstrip line (i e. short, no resistor):
S12 = -0.0019dB
S11 = -48.52dB
Z12 = 73Ohm
Z11 = 73Ohm
I don't know how the Z values above were calculated, but from the S11 the impedance seen by the source is 1.022 times the source impedance, or 1/1.022 times the source impedance. That would give a series impedance of about 1.1 ohms.
For the straight through line the S11 gives a lower value of 0.37 ohms, which is presumably caused by the ports not being properly matched.
I think, looking at the definitions of z-parameters, the z-parameters of the circuit you want to measure (a series resistance) are all infinite. The y-parameters are well behaved though, and are all 1/R. Because your reported z-parameters are not infinite I suspect there are other things in your circuit with loss comparable to the resistor.
Malcom, thanks a lot for your answer!
Indeed, z-parameters diverge at low frequencies in both hand cslculations and CST postprocessing of s-parameters. This was a bit unexpected to me since Z-matrix is essentially impedances, so one would think Z21 would become real at low frequencies to match the dc impedance of the series resistor. Apperently it is not the case for some reason I do not understand at this point.
One thing that happens with distributed series resistance is that at low frequencies when it is much shorter than a wavelength it becomes lumped resistance, so something that just looks like a well-matched attenuator becomes an impedance mismatch at low frequencies.
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