Impedance Transfer from 50ohm to Complex Impedance (28.4 - j135.4)

Hi,

I have 3-port S-parameter data measured in 50Ohm system. Now I want transfer my measured data to an another impedance level with his complex (28.4 - j135.4).

I am looking for some equation & math to peform this but not successful. Is their any simulator or software which can help me to do this?

Please help

Regards!
Bharat A

I am not sure, but do not think it is possible. S parameters relate forwavd and reflected wave amplitudes on a physical transmission line. The transmission line can have real impedances, like 50 ohms or 28.4 ohms, which relate to the ratio Z=V/I or E/H. There is no thing as a transmission line with a 28.4 ohm -j135.4 characteristic impedance. So I think it can not be done.

You CAN have complex propagation constants in a transmission line, but they relate to velocity and loss per length, rather than impedance=V/I measurement.

Hi,

Thanks for your reply. Let me elaborate more.

I have SAW filter device covering WCDMA band. All my Rx port are differential and they are matched to complex load such as 28.4 - j 135.4. My bench top is using VNA to measure this device. As you may know most of system is 50Ohm system.

But since the Rx port is matched to complex impedance I have check the performance of the part by converting impedance from 50Ohm to my target impedance. I think there are some simulator which can do this such as ADS but I am looking for real maths which can establish this impedance transformation.

Regards!
Bharat A

Yes. One tool which can do this is ZMatch from Nuhertz:
Zmatch, Impdedance Matching Network Synthesis and Analysis Software for Electrical Engineers

I can't determine from the screenshots, if the said Zmatch tool handles S parameters with a complex Z0 and particularly can perform the requested calculations. Following the basic S-parameter definition, a conversion is possible in any case. You can even have different complex refernce impedances for each port of a n-port device. The calculation should be possible by converting S-Parameters to V- and I quantities and then back to S parameters of a different reference impedance.

"Generalized S-Parameters"..This subject is rarely expressed in advanced microwave textbook.Transforming is not easy wit hand calculations.But..
If you put your black box with measured s-parameters data in-for instance-ADS and define your port impedances as you want, then if you simulate your black box with these complex port impedances, you'll get a new dataset of s-parameters with complex system impedance which you would.

Hi all,

Thanks for your replies & suggestions. But it seems ZMatch from Nuhertz is a pretty expensive software simulation tool for this purpose. In the end I have to implement this feature in my final ATE test solution and mathematical formula will be an cost effective solution for me. I do have an app notes from Anritsu to perform this impedance transfer but the results were not encouraging perhaps I got my math wrong their.

Regards!
Bharat A

I am sorry for mis-interpreting the question. I was thinking that the question was about impedance matching of complex source and load, not re-normalizing to the new impedance level.

Re-normalizing to a complex Z0 can be done with RF circuit simulators. If you post your 50 Ohm *.s3p data, someone here will be able to do the conversion for you. However, for the result file, the Touchstone file format might be non-standard: the ref impedance value in the file has to be complex now, and some EDA software might no be ready to take that complex value for Z0.
Best regards
Volker

Convert S-parameter of Z0=50ohm to Y-parameter.
Then convert Y-parameter to S-parameter of Z0=28.4-j*135.4.

If you have Agilent ADS, you can do this very esaily by using "stos()".
See the followings.
stos() - ADS 2009 -*Agilent EEsof Documentation Center
The Designer's Guide Community Forum - How to plot "input reflection coefficient" in ADS

If you don't have Agilent ADS, build your own necessary equations.
See RF Cafe - S to h T Y Z Parameter Conversion, although this is for two-port parameters.

Hi Pancho,

Thanks we managed to do convert s-param to Y-param and convert it back to S-param with complex impedance.

Wonder if there is any documentation of how ADS is doing this in their tool.

Regards!
Bharat A

See "SHPEESOF_DIR/expressions/ael/network_fun.ael".

You can see code of "stos()" there.