FreeLists / si-list / [SI-LIST] Re: Question about S-parameter and ABCD matrix

["Sid Singh" <siddharth019@xxxxxxxxx>]

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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