Editing Transmission line (section)

=== Admittance parameters ===
Admittance (Y) parameters may be defined by applying a fixed voltage to one port (V1) of a transmission line with the other end shorted to ground and measuring the resulting current running into each port (I1, I2)<ref name=":4">{{Cite book |last1=Leon |first1=Benjamin J. |url=https://archive.org/details/basiclinearnetwo0000leon/mode/2up |title=Basic Linear Networks for Electrical and Electronics Engineer |last2=Wintz |first2=Paul A. |date=1970 |publisher=Holt, Rinehart, and Winston |isbn=0030783259 |location=US |pages=127 to 129 |language=English}}</ref><ref name=":5">{{Cite book |last=Pozar |first=David M. |title=Microwave Engineering |date=2013 |publisher=John Wiley & Sones, Inc. |isbn=978-81-265-4190-4 |edition=4th |location=Hoboken, NJ, US |publication-date=2013 |pages=174, 175 |language=English}}</ref> and computing the admittance on each port as a ratio of I/V  The admittance parameter Y11 is I1/V1, and the admittance parameter Y12 is I2/V1.  Since transmission lines are electrically passive and symmetric devices, Y12 = Y21, and Y11 = Y22.

For lossless and lossy transmission lines respectively, the Y parameter matrix is as follows:<ref name=":2">{{Cite book |last1=Matthaei |first1=George L. |url=https://archive.org/details/microwavefilters0000matt |title=Microwave Filters, Impudence-Matching Networks, and Coupling Structures |last2=Young |first2=Leo |last3=Jones |first3=E. M. T. |date=1984 |publisher=Artech House, Inc. |isbn=0-89006-099-1 |location=610 Washington Street, Dedham, Massachusetts, US |publication-date=1985 |pages=30 |language=English}}</ref><ref name=":0">{{Cite web |last1=Drakos |first1=Nikos |last2=Hennecke |first2=Marcus |last3=Moore |first3=Ross |last4=Swan |first4=Herb |date=November 22, 2013 |title=Transmission Line |url=https://qucs.sourceforge.net/tech/node61.html |website=Quite Universal Circuit Simulator (Qucs)}}</ref>

<math>Y_{\text{Lossless}}=\begin{bmatrix} 
\frac{-jcot(\beta l)}{Z_o} & \frac{jcsc(\beta l)}{Z_o} \\ 
\frac{jcsc(\beta l)}{Z_o}  & \frac{-jcot(\beta l)}{Z_o}
\end{bmatrix}
\text{    }
Y_{\text{Lossy}}=\begin{bmatrix} 
\frac{coth(\gamma l)}{Z_o} & \frac{-csch(\gamma l)}{Z_o} \\ 
\frac{-csch(\gamma l)}{Z_o} & \frac{coth(\gamma l)}{Z_o} 
\end{bmatrix}</math>