[SI-LIST] Re: Question about S-parameter and ABCD matrix

• From: "Saoer Sinaga" <saoer.sinaga@xxxxxxxxx>
• To: si-list@xxxxxxxxxxxxx
• Date: Fri, 2 May 2008 09:21:38 +0200

```Hi Sid,
This question is actually originated from TRL calibration technique. In
Pozar's book, it is written (in terms of ABCD matrix):
[Measurement]=[Error]*[DUT]*inv[Error]

But I would say, suppose:
[Error]=[A,B;C,D], then
[Measurement]=[A,B;C,D]*[DUT]*[D,B;C,A]

regards,
Saoer

On Thu, May 1, 2008 at 9:20 PM, Sid Singh <siddharth019@xxxxxxxxx> wrote:

> Saeor,
> The answer lies in definition of ABCD matrix. They are used for
> correlating inout voltage/current to output side.
> [v1, i1] = [A, B ;C, D]  *  [v2, -i2]
>
> When you swap the I/O you end up rearraging above matrix equation with v2
> and i2 on LHS. The math will result in inverse of ABCD matrix being the
> multiplier coefficient.
> [v2, i2] = inv { [A, B ;C, D] }  *  [v1, -i1]
>
> For Scattering parameters the math is more intutive since they represent
> the ratio of reflected vs incident waveform assuming matched termination at
> other port.
>
> Sid.
>
>
>
> On 5/1/08, Saoer Sinaga <saoer.sinaga@xxxxxxxxx> wrote:
>
> > Hi all,
> > I am not really sure if this is a relevant question for this forum.
> > Suppose I have a two-port non-symmetric passive network whose S-par is
> > Sx=[S11,S12;S21,S22]=[S11,S12;S12,S22].
> > Let's say the ABCD matrix of this network is Ax=[A,B;C,D].
> >
> > If I rotate the device 180 degree, meaning port2 becomes port1 and vice
> > versa, then the S-parameter would be Sy=[S22,S12;S12,S11]. Hence, the
> > ABCD
> > matrix would then be Ay=[D,B;C,A].
> >
> > Am I missing something here?
> > In the "Microwave Engineering" by David M. Pozar book, it is written
> > that
> > Ay=inverse[Ax].
> >
> > regards,
> > Saoer
> > NXP Semiconductors
> >
> >
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