ADS and S11 Equations for L & C

Hi,

I have an s-parameter file from a measured passive structure from a VNA. I have used equations in ADS to generate Inductance and Capacitance from Impedance and Admittance of the measured s-parameters. The Capacitance is in the ball park with expected values. however the Inductance is not. Some questions:

1. Any experts on ADS that can take a look at the equations/formulas. Do they look correct?
2. if the equations are right why is there a difference in the two methods? Is it just due to conversion numerical error?
3. The Capacitance values are in the ball park with expected values from simulation but not the inductance. why could that be? I expected about 7 nH of Inductance from this structure.

TIA

With a single measurement you cannot separate the inductive from the capacitive contribution of a network. Istead you will see the total impedance:

Z = R + j[wL - 1/(wc)]

If, for a given frequency imag(Z) < 0 the behavior will be capacitive, otherwise inductive. The special case imag(Z) = 0 indicates a resonant frequency.
The capacitive behaviour is represented on the smith chart in the lower part of the graph (as in you measurment), while the inductive in the upper part.

By the way, the inductance is given as: L = imag(Z)/w and not L = -imag(Z)/w as per you equation.

I don't understand the difference between the values calculated using Y instead of Z.

I recommend to test with data from an ideal schematic that you create yourself, with known values.

As a second step, you can then add small parasitics (e.g. shunt capacitance) to see what that does to your extraction.

Plot "ipart" on a Smith Chart and see how reactive part of the Input Impedance changes..
As seen from S11, Input Impedance has no inductive part.

Yep, I corrected that.

Without looking deeper too much my guess is that it's numerical error when converting S to Y paramters.

Yeah, I had tried that but had made a mistake that I just noticed. Since my DUT is open ended when I did the schematic with lumped/ideal Capacior/inductor I left the Ideal lumped L or C without ground. Once they are porperly terminated. I can see the known value from the schemtic in the table across all frequencies. I also am able to see the behavior of the impedance in the correct half of the smith chart.

Yeah, I can now see that using ideal elements in the schematic. C always shows negative ipart while L shows always positive ipart.

What confused me is that I expected this trace to be more inductive but based on the plot from my DUT it is seen as Capacitve (up to that frequency)

So, Will it eventually look inductive if it follows the same trend, correct? and assuming you increase the frequency sweep and the the DUT structure is uniform .

It is unclear what you are trying to do, i.e. what you physical device looks like.
Your curve starts from an open circuit (at lowest freq) so obviously it is not a series inductance.

The goal is to try to characterize a Microstrip trace on a substrate and to extract RLC from S11 measurements with the far end Open Circuit. However I am thinking the experiment setup is is not correct.

The trace is open ended so the S11 measurement is into an open. I think only Capacitance may be possible to extract from S11 into an open.

To extract Inductance and Resistance from S11, I think we may need to have the far end connected to ground and/or add other measurement port.

What do you think?

S11 from a DUT connected to an open -- Extract Cap. Possible. Data measured looks like a Cap (i.e imaginary part is negative).
S11 from a DUT connected to an open -- Extract R (not possible, not enough information). Needs short to GND or additional measurement Port
S11 from a DUT connected to an open -- Extract L (not possible, not enough information). Needs short to GND or additional measurement Port

Can you do a two port measurement? From that it is much easier to separate series and shunt path elements.

Current DUT does not allow us to do a 2 port measurement. However, it may be possible but need to look further into the probing and test fixture requirements to be able do do so.

Do you have any white paper and/or links that detail how to separate RLC strictly from S11 and S12 measured data.

One way I have done it in the past is to match lumped different element networks against the measured s-parameters and come up with an equivalent circuit that matches S11 AND S12.

TIA

I guess you know this: https://www.mathworks.com/help/rf/ug/s2rlgc.html

When I worked with Sonnet, we did the RLGC model extraction from 2-port data and known phyiscal length, but I don't know a published reference on that method used by Sonnet.

If you can only do 1-port measurement, I would try to extract the shunt capacitance from low frequency S11 measurement, and then use TDR (time domain reflectometry) to get the line impedance, so that you can calculate L' from known C' and Zline. I explicitely mention TDR because then you can measure Zline no matter what the termination is.

Thanks for sharing that reference. Had not seen nor used that before.

I did not think of TDR. Will try this in simulation on ADS. So yeah from Zline = sqrt {L/C) only one unknown that can be solved for.

BTW, why do you limit calculating C shunt from low frequency? With the method shown in first post we can see the broad frequency of C from DUT. Just trying to understand the difference of using low freq C vs High freq C. If I recall the change is not very significant across frequency anyways.

Many years of experience with extracting RLGC and circuit models from S-params

Sure, you always get some numbers as a result, but these don't have a physical meaning (as a capacitance) at high frequencies where transmission lines effect become relevant. To put it in simple words: when your capacitance is rotated around the Smith chart, due to line length, and you interpret the results as a lumped C, you will not get useful results. If your line is lambda/4 you will get an infinite value for C if you evaluate it your way. Not useful, not correct.

So we only used low frequency data where the impedance into the DUT can be evaluated as a lumped component. At low frequency we know the input impedance of the open ended line is effectively shunt C. and not troubled by inductance.

You can create a little testbench in simulation and try yourself.

Thanks for the clarification. So one more question. :^)

In this context what is your definition of "low frequency"? did you use a ratio from your max operating frequency? or some other factor?

A frequency where the line can still be considered short, so that the curve is flat. For my RFIC component extraction with tiny dimensions, that low frequency could be 1GHz, but in other cases it might be 1MHz.

So just extract the C and look for the "flat" part at the beginning of the curve. Looking at your data from post 1, the 50MHz point looks like a glitch and C=1.1pF would be my choice.

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