ABCD and S Matrix of a Lossy Transmission Line

Generated from LOSSY_TL.wxm with rfMaxima 0.2.5 on Maxima 5.46.0. All results were computed by executing the notebook; none is transcribed.

/* Put rfMaxima.mac in the same directory as this notebook, or add its
   directory to file_search_maxima. */
load("rfMaxima.mac")$

(See "Microwave Engineering, 2nd Ed., by D. Pozar, Wiley, 1998, p. 90)

ABCD:ABCD_LossyTL(%gamma,l,Z_0);
(cosh⁡(γ l)Z0 sinh⁡(γ l)sinh⁡(γ l)Z0cosh⁡(γ l))\begin{pmatrix} \cosh \left(\gamma\,l\right)&Z_{0}\,\sinh \left(\gamma\,l\right)\\ {{\sinh \left(\gamma\,l\right)}\over{Z_{0}}}&\cosh \left(\gamma\,l\right) \end{pmatrix}
exponentialize(ABCD);
(eγ l+e−γ l2Z0 (eγ l−e−γ l)2eγ l−e−γ l2 Z0eγ l+e−γ l2)\begin{pmatrix} {{e^{\gamma\,l}+e^ {- \gamma\,l }}\over{2}}&{{Z_{0}\,\left(e^{\gamma\,l}-e^ {- \gamma\,l }\right)}\over{2}}\\ {{e^{\gamma\,l}-e^ {- \gamma\,l }}\over{2\,Z_{0}}}&{{e^{\gamma\,l}+e^ {- \gamma\,l }}\over{2}} \end{pmatrix}
S:ABCD2S(ABCD);
(0cosh⁡(γ l)−sinh⁡(γ l)1sinh⁡(γ l)+cosh⁡(γ l)0)\begin{pmatrix} 0&\cosh \left(\gamma\,l\right)-\sinh \left(\gamma\,l\right)\\ {{1}\over{\sinh \left(\gamma\,l\right)+\cosh \left(\gamma\,l\right)}}&0 \end{pmatrix}
ratsimp(exponentialize(S));
(0e−γ le−γ l0)\begin{pmatrix} 0&e^ {- \gamma\,l }\\ e^ {- \gamma\,l }&0 \end{pmatrix}
S2ABCD(%);
(e−γ l (e2 γ l+1)2e−γ l (Z0 e2 γ l−Z0)2e−γ l (e2 γ l−1)2 Z0e−γ l (e2 γ l+1)2)\begin{pmatrix} {{e^ {- \gamma\,l }\,\left(e^{2\,\gamma\,l}+1\right)}\over{2}}&{{e^ {- \gamma\,l }\,\left(Z_{0}\,e^{2\,\gamma\,l}-Z_{0}\right)}\over{2}}\\ {{e^ {- \gamma\,l }\,\left(e^{2\,\gamma\,l}-1\right)}\over{2\,Z_{0}}}&{{e^ {- \gamma\,l }\,\left(e^{2\,\gamma\,l}+1\right)}\over{2}} \end{pmatrix}