[SOLVED] coupling factor and loss of a transformer

[rfcn]

Do the coupling factor and loss of a transformer mean the same thing? We can use s-paramter simulation to get the loss of the transformer. How can we simulate the coupling factor of a transformer with s-paramter file?

 

[vfone]

No they are not the same thing, but when doing a system analysis can see the coupling factor as a loss in the budget of the system.

 

[shlomo22]

Convert the S parameters to Z parameters.

Then:
L1=Im[Z11]/2/pi/f
L2=Im[Z22]/2/pi/f
M=Im[Z21]/2/pi/f
K=M/sqrt(L1*L2)

K is the coupling factor.

 

[rfcn]

Convert the S parameters to Z parameters.

Then:
L1=Im[Z11]/2/pi/f
L2=Im[Z22]/2/pi/f
M=Im[Z21]/2/pi/f
K=M/sqrt(L1*L2)

K is the coupling factor.

Hi, shlomo22,

Thanks for your answer! Do you have any reference paper or document on this?

According to my knowlage, to caluculate inductance we should use Y parameter as:
L1 = Im[1/Y11]/2/pi/f
L2 = Im[1/Y22]/2/pi/f
It should be differenct with that calculated by Z parameter. For a two-port network, Z11 != Zin. So, I don't think the first two equations for inductance calculation is corrent until you provide some reference.

regards,
rfcn

 

[shlomo22]

The equations for two-port Z parameters are:
V1=Z11*I1+Z12*I2
V2=Z21*I1+Z22*I2

The equations for an ideal transformer are:
V1=jwL1*I1+jwM*I2
V2=jwM*I1+jwL2*I2

The two sets of equations have the same form.

For a single inductor, you can used either Y-parameter or Z-parameter equations, they give the same result because it's a one-port situation and you are inverting a number not a matrix.