0
\$\begingroup\$

Consider a transmission line circuit like the following but where \$Z_{o2}\$ was also unique (say \$Z_{o2}=7\,\Omega\$):

enter image description here

I know how I would find \$l_1\$ and \$l_2\$ using smith charts:

$$Re\left\{Y_n(z=-l_1)\right\}=\frac{Z_{o1}}{Z_o}=0.5\rightarrow l_1=\left(0.106\lambda,\,0.394\lambda\right)$$

$$Y(z=-l_1)=Y_n(z=-l_1)\cdot Y_{o1}$$

$$Y_n(z=-l_2)=\frac{-Im\left\{Y(z=-l_1)\right\}}{Y_{o2}}=0.161j\rightarrow l_2=(0.161\lambda,\,0.349\lambda)$$

but, since I would like to write a program for calculating this, I need to be able to solve this from the governing equations.

Starting on page 230 in this book, the author describes the equations used for matching a circuit where \$Z_o=Z_{o1}=Z_{o2}\$ but how would I solve this problem in the more general case?

\$\endgroup\$

1 Answer 1

1
\$\begingroup\$

More generally you could use this equation: -

enter image description here

So, the two t-lines will each present an impedance at the node where they join and that therefore becomes a parallel impedance that is then presented as the load on the output of the t-line coming from the left.

Formula Image from here.

\$\endgroup\$
2
  • \$\begingroup\$ Thanks! Say I am comfortable calculating l1 and just want to use this eq to find l2; could you help get me started on that? \$\endgroup\$
    – Landon
    Nov 20, 2020 at 18:02
  • 1
    \$\begingroup\$ @Landon are we done here? \$\endgroup\$
    – Andy aka
    Dec 30, 2022 at 10:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.