# [SOLVED]Z-parameters and the nominal impedance

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#### grit_fire

##### Member level 5
Hello Guys,

I have a very fundamental question.

I understand that the nominal impedance (Zo) together with S-parameters define a system. Now, if I already got Z-parameters, do I need the nominal impedance to define a system? that is to say, if Zo changes, will Z parameters change?

I also have some follow-up questions depend on the answer to this question..

Thanks!!

In the definition of Z-parameters or Y-parameters, there isn't any Zo characteristic impedance.
Z-parameters are "open circuit" parameters and they can not be considered as s-parameters.But they can be converted between them..

• grit_fire

### grit_fire

Points: 2
In the definition of Z-parameters or Y-parameters, there isn't any Zo characteristic impedance.
Z-parameters are "open circuit" parameters and they can not be considered as s-parameters.But they can be converted between them..

Thank you very much. Sounds like the Z parameters are independent of the nominal impedance, therefore, Z parameters should be the same no matter what the load is, right? (since they are obtained when open circuit the load).

Then why will the following phenomenon happen? (a little long, thanks for your patience) It is now confusing me a lot.

I have a two port system (two antennas), I obtained the s-parameters using 50 Ohm nominal port impedance in Agilent ADS layout using Momentum and then converted those to Z-parameters. Then I created a component based on the layout.

I use this component in a Agilent ADS schematic. I measure the voltage across the ports and current going through the antenna in schematic window using probes. I wanted to check if my measurement makes sense. I used the equation V=Z*I, all in matrix. But the left hand side doesn't equal to right hand side.

Then I found that only when I have a 50 Ohm at the source and 50 Ohm at the load for my schematic, that equation will hold. Looks like the Z parameters changes when my load is different ()... But that shouldn't be the case since Z parameters should be independent of the load...so why..?

Thank you!

edits: earlier I had a capacitive load and V doesnt equal to Z*I. After I changed the capacitive load to 50 Ohm, V equals to Z*I.

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Alrite, here is a follow-up question that confuses me. I appreciate for your time and help.

By definition V=Z*I, where V and I are two 2X1 column vectors and Z is a 2x2 matrix. I did some experiments in ADS Momentum, I realize that after finding Z (this is done using S-parameter simulation using the "Term" components), since Z is independent of the loading (because they are obtained under open circuit conditions), then I am expecting V=Z*I no matter what my source and load impedance are. However, the equation only holds when source and load impedance are 50 Ohm while LHS doesn't equal to RHS when other source and load impedance are used. Why is that so?

Thanks!!!

edits: the schematic of my measurement circuit is attached. V doesn't equal to Z*I

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Z parameters are measured/defined in a short circuit/open circuit measuring environment. They can be converted into S parameters, but the S parameter value will of course change with the measuring systems characteristic impedance.

• grit_fire

### grit_fire

Points: 2
so why the equation only holds when load and source equal to 50 Ohms?

so why the equation only holds when load and source equal to 50 Ohms?
Because s-parameters are "travelling power wave" equations, they are neither voltages nor currents,therefore a characteristic impedance should defined as a reference.

• grit_fire

### grit_fire

Points: 2
Because s-parameters are "travelling power wave" equations, they are neither voltages nor currents,therefore a characteristic impedance should defined as a reference.

Hello, thanks a lot but I didn't mean S parameters. I meant V=Z*I only hold when 50 Ohm load and source are used?

Quote from the ADS knowledge center. Does it make sense at all to all of you? I don't understand why there are two sets of Z-parameters at all
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Why (Z11)s are different?
Issue
I have a two port network. It is set up to run S-parameter simulation and with 50 ohm terms at both input and output ports. I want to calculate the z11 parameter use the following methods:

· Z11-params calculated directly from the S-parameter controller:Z11=real(Z11)
· Z11-params calculated using stoz(): Z11=real(stoz(S,50)(1,1))
· Z11-params calculated using stoz(): Z11=real(stoz(S11,50))
· Z11-parameter calculated using Zin(): Z11=real(Zin(S11,50))
But the method 1 and method 2 give one answer and method 3 and method 4 give a different answer, which one is right and why?

Solution
All the 4 methods are give the right answers for their setups. The reason the simulation results are different is due to the different loading impedances are used based on different method. The results for the method 1 and method 2 are two port simulation while the results for method 3 and method 4 are one ports simulation.

For the method 1 and method 2, the loading condition is based on the Z parameter definition that is Z11 is V1/I1 with port 2 open. So to calculate the Z11 impedance, the method 1 and method 2 assume there is no loading impedance, the load is open circuited.

For method 3 and method 4, the loading condition is based on the S parameter definition that is S11=b1/a1 with a2=0 that means the port 2 is loaded with Z0, in this case Z0=50 ohm.

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