# How to split S-parameters into two symmetric halves? For de-embedding.

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#### mmrobles

##### Junior Member level 2
I'm trying to characterize a WR90 waveguide-to-coaxial adapter thru the VNA by attaching it to an identical pair. So the coaxial ends of each adapter are connected to the VNA ports while the rectangular ends are connected against each other. Now I measured the full S-parameters for these symmetric pair, now my problem is how can I split this result to represent the S-parameter for each adapter? Anyone who have done this before?

#### albbg

S-parameters cannot be directly cascaded. You have to transfom it to T parameters that are cascadable. A procedure could be:

1. measure the S parameter of the fixture (Sfix) i.e. left and right halves connected toghether
2. transform to Sfix into T matrix Sfix ==> Tfix
3. we know that Tfix = Tleft*Tright
4. set Tleft = [T11 T12, T21 T22] and Tright = [T22 T21, T12 T11]
5. furthermore T21 = T12
6. from Tfix apply some math to calculate T11, T22 and T21
7. with DUT you will have Ttot = Tleft*Tdut*Tright
8. Tdut = Tleft-1*Ttot*Tright-1
9. transform back Tdut ==> Sdut

I hope can help

#### mmrobles

##### Junior Member level 2
Thanks for the reply. I got a problem with the #4 though. So if I have a connected symmetric DUT such that Sleft = [S11 S12; S21 S22] and Sright = [S22 S21; S12 S11], does converting Sleft->Tleft=[T11 T12;T21 T22] make the Tright=[T22 T21; T12 T11]??

It's the S-parameters of my left and right component that should be mirrored, not the T-parameters right?

---------- Post added at 11:06 ---------- Previous post was at 09:34 ----------

Ok after some math manipulation, I derived that an [S11 S12; S21 S22] conversion to [T11 T12; T21 T22] would make its counterpart [S22 S21; S12 S11] into [T22 T21; T12 T11]-1. It should be inversed. Now, I wonder if this is correct?

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#### Mazz

The argument is know in literature as S-parameter bisection.

There are different studies about that, google it or take a look at IEEE. The problem is about the possibility to find a single solution in closed form, that is not always guaranteed.

If you are an Agilent ADS user, there is an example at: **broken link removed**

The main issue with this techniques is that it works with simulated (no noise, perfect data) data, but if you use measurement data (that usually has some ripple and are not perfectly symmetrical) you can easily have glitches in the final results.

I hope it can help.

Mazz

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mmrobles

### mmrobles

Points: 2

#### Colin Warwick

##### Newbie level 4
The argument is know in literature as S-parameter bisection.

...If you are an Agilent ADS user, there is an example at: **broken link removed**

Mazz

#### mmrobles

##### Junior Member level 2
The argument is know in literature as S-parameter bisection.

There are different studies about that, google it or take a look at IEEE. The problem is about the possibility to find a single solution in closed form, that is not always guaranteed.

If you are an Agilent ADS user, there is an example at: **broken link removed**

The main issue with this techniques is that it works with simulated (no noise, perfect data) data, but if you use measurement data (that usually has some ripple and are not perfectly symmetrical) you can easily have glitches in the final results.

I hope it can help.

Mazz

Thanks a lot for this. I'm trying to look for it at Google for days and I can't find the right keyword. So it's called "S-parameter bisection". I'm not an ADS user, but I'm trying to read the literature. I thought it was just a straightforward mathematical calculation, but seems like it is not. My measurements are real s2p files from a VNA, so I dunno if it can be split accurately?

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