# How to get complex reflection coefficients?

If I terminate a line with an open circuit, I'll get reflections of any incoming signals with the same phase (a reflection coefficient of 1). If I terminate the line with a short circuit, I'll get reflections of any incoming signals with opposite phase (a reflection coefficient of -1).

What can I terminate the line with to get reflections with different phases, i.e. complex reflection coefficients with magnitude 1?

## 2 Answers

Terminate with an inductor or capacitor.

$$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$

$Z_0$ is char. impedance i.e. 50 Ohm. $Z_L$ is complex if you use inductor or capacitor; thus $\Gamma$ is complex.

• What reflection coefficients would those give? – awelkie Jul 26 '17 at 14:15
• Use the formula I've given. – Aenid Jul 26 '17 at 14:17

You wanted the reflection coefficient to have magnitude = 1. That means pure reactive load. A piece of transmission line with open or shorted termination can itself be any reactace - capacitive or inductive. You need no other components such as capacitors. Smith's diagram is the legacy tool to find the needed line length (unit=wavelengths).

So, put a short circuit at the end of your line. With Shmith's diagram you can find the place to where on your line you can paint a colored dot to mark "here the reflection coefficient is 1 with phase angle XX degrees"