# How is a transmission line with a different characterisitc impedance shown on the smith chart?

A transmission line can be shown on the smith chart as a clockwise rotation, each 180 degrees corresponding to a quarter wavelength. But this is when the characteristic impedance (Z0) of the transmission line is equal to that of the smith chart (for example, everything is in the 50 ohm system and the characteristic impedance of the transmission line is also 50 ohms).

My question is, how is a transmission line with a different characteristic impedance shown on the smith chart? For example, how to show a quarter-wave transmission line with Z0 = 100 ohm on a smith chart in the 50 ohm system?

• A Smith chart natively represents normalized impedances/admittances. In order to apply a mismatched quarter-wave section you'll likely need to convert impedances as you go down the line from load to source. Jan 13, 2020 at 3:20
• @ReinstateMonica-ζ-- Can it be equated to a matched transmission line with a different length? Jan 13, 2020 at 3:22