# AC circuit analysis with a transmission line involved

I'm trying to perform an AC analysis of a circuit that contains a piece of coax cable. The input voltage 'Vs' is a swept frequency (1MHz-150MHz) voltage source with constant amplitude. What I'm looking for is a method of calculating 'Vo' as a function of frequency.

I know all of the impedances, the segment of coax, and Vs. Normally, with no t-line segment involved, I would do a mesh analysis, solve for the mesh currents, and then solve for 'Vo' as i3*ZL.

What methods can be used when performing an ac analysis of a circuit with a segment of transmission line involved?

A bit more about the coax: VF=0.77, er=1.69, Vp=2.31E8 m/s

Thanks in advance. AC circuit with T-Line segment

• Real coax has frequency dependent loss. Higher frequencies have higher losses. You may be able to find one that has negligible loss for such a short length at 150 MHz. But at least double-check it if you didn't already. Mar 25, 2020 at 20:48

1. Make a 2-port model of the transmission line. For mesh analysis, a Z-parameter model is probably most convenient. The Z-parameters of the transmission line will be different at each frequency.

If you know how to calculate the S-parameters of the transmission line, Wikipedia gives formulas for converting S-parameters to Z-parameters.

2. Solve the circuit using the 2-port representation of the transmission line.

• This is perfect. Thanks. This Wikipedia page gives the ABCD parameters for a transmission line, and also the conversion from ABCD parameters to Z parameters: en.wikipedia.org/wiki/Two-port_network Mar 26, 2020 at 15:13
• @user16487, The S-parameters will be even simpler. If it's a lossless, well-matched line, the S-matrix will only have diagonal elements. Mar 26, 2020 at 15:21

If you have all component values numerical you can use a circuit simulator which knows transmission line. At least Micro-Cap knows it. You simply do the most basic AC analysis with it. Forget analyzers if yo must do theoretical calculations where component values are variables (=letters).

100 millimeters of coax line at 150 MHz or less can well be presented with one inductor and one capacitor (the total capacitance, inductance of the loop when one end is shorted. Then you can use any calculation method you have learned or any circuit analyzing program. 100 mm is so small part of the wavelength that this simplification causes neglible error. The problems start when 100 mm is more than 10% of the wavelength. There's no strict limit.