Z and Y parameter in RL modeling

Hallo,

if measured Z parameter from a two port device are known.
Lets say there is a capacitance to ground (between port 1 and GND).

If I try to model the circuit with an R L series circuit.
R - L between port 1 and port2.
This means Y11=R+jwL.

Is it possible to also cover the effects from the capacitance in my
Y parameters....or is the assumed equivalent circuit invalid.

elektr0

electr0,

The answer is yes. But first you need decide what type of model you wish to use. For a two port device, either a "pi" topology or a "T" topology is common. From your post it sounds like you are making a "pi" model. For either model, you will need to fill all branches, otherwise you can make a circuit whose Y or Z parameters do not exist or are not invertible.

Now define the following
C10 is the capacitance between port 1 and ground
C20 is the capacitance between port 2 and ground
Y_pi is 1/(R + j*w*L), the admittance between port 1 and port 2

The Y parameters for this circuit are
Y11 = Y_pi + j*w*C10
Y12 = Y21 = -Y_pi
Y22 = Y_pi + j*w*C20

Hope this helps,

-Wiley

Hallo Wiley,
thanks for your answer.

I do not use a PI equivalent circuit.
Lets think of a bonwire, which is mainly an inductance.
I use an RL equivalent circuit as underlying topology.
Measured Z parameters are mapped to R and L.

Of course these R,L values are not frequency independent, because the wire
needs a more complex equivalent circuit.
I see resonance phenomena of R and L.
I dont know if the influence from the capacitance from wire to GND is
included in this frequency dependent R L equivalent parameters.
The ocurring resonance frequency should be a measure for the
ignored capacitance.
BUT IS IT POSSIBLE THAT DEVICE BEHAVIOR IS LOST, IF WE MAP MEASURED DATA TO TOO SIMPLE EQUIVALENT TOPOLOGIES.

Your answer is YES ?

greets elektr0

Greetings, Electr0,

I am confused here. For Z parameters to exist, you some connection to ground. Recall the defintion of Z parameters: Z_ij = Vi/Ij with port i connected to an open circuit. Without some connection to ground Ij will be zero, and the Z parameters are undefined.

Are you actually mapping Z12 to R + j*w*L? If this is the case, you should map to either a "pi" or "T" model. The connection to ground for a bond wire will be a capacitance.


Frequency independent R and L should not have a resonant behaviour. The resonance you are seeing is caused by the capacitance to ground, as you surmised. If you are ignoring the capacitance in your model, then R and L will have to vary with frequency to compensate.

If you are using Z parameters, I would define each of the top branches of the "T" model as (R/2 + j*w*L/2) and the connection to ground as 1/(j*w*C). I typically use Y parameters and map to a "pi" model. I think the algebra is significantly easier. For the "pi" model, each connection to ground has half the capacitance (or C10 = C20 = C/2).


If you want frequency independent values of RLGC, then yes. A very definite yes. For example, if you map a spiral inductor to a simple RL model, you won't capture the Q. It's the parasitic capacitance that reduces the Q at high frequencies.

Hope this helps,
-Wiley

Hallo Wiley,

ok. I did not distinguish Z and Y parameters. Yes, i am working with Y parameters.
I agree with all your statements.
The answer to my question is therefore, we do not loose information if we map
the bondwire behavior to an RL equivalent circuit, because the frquency dependency of R and L does also cover the capactiance influence.

I will have a closer look on PI and T circuits for the next extraction.
May be I will contact you again on this topic.

greets elektr0