According to the port numbers in fig. 9.5
the Y-parameters of a coupler write as follows.
 |
 |
(9.111) |
 |
 |
(9.112) |
 |
 |
(9.113) |
 |
 |
(9.114) |
with
 |
 |
(9.115) |
 |
 |
(9.116) |
 |
 |
(9.117) |
 |
 |
(9.118) |
whereas
denotes the coupling factor,
the phase shift of
the coupling path and
the reference impedance. The coupler
can also be used as hybrid by setting
. For a 90 degree
hybrid, for example, set
to
. Note that for most
couplers no real DC model exists. Taking the real part of the AC
matrix often leads to non-logical results. Thus, it is better to
model the coupler for DC by making a short between port 1 and port 2
and between port 3 and port 4. The rest should be an open. This
leads to the following MNA matrix.
 |
(9.119) |
Figure 9.5:
ideal coupler device
|
The scattering parameters of a coupler are:
 |
(9.120) |
 |
(9.121) |
 |
(9.122) |
 |
(9.123) |
whereas
denotes the coupling factor,
the phase shift of
the coupling path. Extending them for an arbitrary reference
impedance
, they already become quite complex:
 |
 |
(9.124) |
 |
 |
(9.125) |
 |
 |
(9.126) |
 |
 |
(9.127) |
 |
 |
(9.128) |
 |
(9.129) |
 |
(9.130) |
 |
(9.131) |
 |
(9.132) |
An ideal coupler is noise free.
This document was generated by Stefan Jahn on 2007-12-30 using latex2html.