Lets say we have two transmission lines in parallel as shown in the figure below, what will be the total impedance of their combination? That rectangle is the way I am representing TL and Z is the characteristic impedance and theta is the electrical length.

enter image description here

I was thinking whether I can use the same formula as for the case of resistors. So, the characteristic impedance of two parallel transmission lines will be as shown below and electrical length is the same, theta: $$ Z_{total} = \frac{Z_1*Z_2}{Z_1+Z_2} $$ Is this correct?

  • \$\begingroup\$ It's not clear, from your diagram how the transmission lines are connected at the sending end and receiving end. There is more than one way of doing this. \$\endgroup\$ – Chu Jul 14 '19 at 0:07
  • \$\begingroup\$ Is the length of both transmission lines the same? \$\endgroup\$ – Eduardo1992 Jul 14 '19 at 0:11
  • \$\begingroup\$ Yes, they have similar electrical length. \$\endgroup\$ – BGA Jul 14 '19 at 5:37

Your schematic would be difficult to realize, because normally the two ends of a transmission line are far enough apart that you can't connect a lumped source across them. The whole point of a transmission line is that it is "long" relative to the wavelength of the signals it carries.

If you connect two transmission lines in parallel (and terminate the far ends with matched loads) like this:


simulate this circuit – Schematic created using CircuitLab

then you could use the formula you proposed to obtain the equivalent input impedance.

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  • \$\begingroup\$ I agree with The Photon that the configuration shown by the OP really doesn't make any sense. What The Photon showed is more likely to show up in the real world, and his analysis is correct. \$\endgroup\$ – SteveSh Dec 16 '19 at 14:08
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    \$\begingroup\$ For more information try to find a book by one of the high speed design experts such as Dr. Howard Johnson or Dr. Eric Bogatin. By Howard Johnson, "High-Speed Digital Design: A Handbook of Black Magic (1993), ISBN 978-0133957242", and "High-Speed Signal Propagation: Advanced Black Magic (2003), ISBN 978-0130844088.". I have both in my library. \$\endgroup\$ – SteveSh Dec 16 '19 at 14:13

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