Differential Transmission Line

A differential (4-port) transmission line is not referenced to ground potential, i.e. the wave from the input (port 1 and 4) is distributed to the output (port 2 and 3). Its admittance parameters are:

$\displaystyle Y_{11} = Y_{22} = Y_{33} = Y_{44} = -Y_{14} = -Y_{41} = -Y_{23} = -Y_{32} = \dfrac{1}{Z_L \cdot \tanh(\gamma\cdot l)}$ (9.210)

$\displaystyle Y_{13} = Y_{31} = Y_{24} = Y_{42} = -Y_{12} = -Y_{21} = -Y_{34} = -Y_{43} = \dfrac{1}{Z_L \cdot \sinh(\gamma\cdot l)}$ (9.211)

The scattering parameters writes:

$\displaystyle S_{11} = S_{22} = S_{33} = S_{44} = Z_L \cdot \dfrac{(2\cdot Z_0 ...
...)} {(2\cdot Z_0 + Z_L)^2\cdot \exp(2\cdot\gamma\cdot l) - (2\cdot Z_0 - Z_L)^2}$ (9.212)

$\displaystyle S_{14} = S_{41} = S_{23} = S_{32} = 1 - S_{11}$ (9.213)

$\displaystyle S_{12}$ $\displaystyle = S_{21} = S_{34} = S_{43} = -S_{13} = -S_{31} = -S_{24} = -S_{42}$ (9.214)
  $\displaystyle = \dfrac{4\cdot Z_L \cdot Z_0 \cdot \exp(\gamma\cdot l)} {(2\cdot Z_0 + Z_L)^2\cdot \exp(2\cdot\gamma\cdot l) - (2\cdot Z_0 - Z_L)^2}$ (9.215)

Note: As already stated, this is a pure differential transmission line without ground reference. It is not a three-wire system. I.e. there is only one mode. The next section describes a differential line with ground reference.


This document was generated by Stefan Jahn on 2007-12-30 using latex2html.