[SI-LIST] Re: Question about S-parameter and ABCD matrix
- From: "Sid Singh" <siddharth019@xxxxxxxxx>
- To: "Saoer Sinaga" <saoer.sinaga@xxxxxxxxx>
- Date: Thu, 1 May 2008 12:20:37 -0700
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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