The Y-parameters of a multi-port component defined by its S-parameters required for a small signal AC analysis can be obtained by converting the S-parameters into Y-parameters.
In order to extend a -port to have a S-parameter device with
ports assuming that the original reference port had a reflection
coefficient
the new S-parameters are according to
T. O. Grosch and L. A. Carpenter [12]:
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(9.227) | |
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(9.228) |
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(9.229) |
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(9.230) |
If the reference port has been ground potential, then
simply folds to -1. The reverse transformation by connecting a
termination with a reflection coefficient of
to the
th
port writes as follows.
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(9.231) |
With the S-parameter transformation done the -port noise wave
correlation matrix is
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(9.232) |
with
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(9.233) |
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(9.234) |
whence denotes the equivalent noise temperature of the original
reference port and the
operator indicates the transposed
conjugate matrix (also called adjoint or adjugate).
The reverse transformation can be written as
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(9.235) |
with
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(9.236) |
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(9.237) |