# Waveguides question

A rectangular waveguide with dimensions $$\a=10~\mathrm{cm}, b=6~\mathrm{cm}\$$ is filled with dielectric material with an unknown relative coefficient $$\\epsilon_r\$$. The guide is terminated by an unknown load. It is excited by $$\TE_{3,0}\$$ modes at a frequency of $$\2.5~\mathrm{GHz}\$$. How can I determine $$\\epsilon_r\$$?

I know the cutoff frequency is given by:

$$f=c\frac{\sqrt{(n/a)^2+(m/b)^2}}{2\sqrt{\epsilon_r}}$$

I am also told that the first minima are at $$\s_a=5~\mathrm{mm}, s_b=30~\mathrm{mm}\$$ away from the load. I know that the distance between the minima is $$\\lambda/2\$$, hence $$\\lambda=50~\mathrm{mm}\$$. Does that mean that $$\c/(f\sqrt{\epsilon_r})=50\$$? Because if it is, then I can easily find $$\\epsilon_r\$$ to be approx. 1.55. Is that correct?

• is the source impedance unknown as well? May 26, 2017 at 21:52
• Yes, Tony, I don't know the source impedance. May 27, 2017 at 5:57
• Nope, $v=c/\sqrt{\epsilon_\mathrm{r}}$ holds true for TEM modes only. Dec 10, 2017 at 16:11

of course standing wave minima was given thus $$\lambda /2$$so you are almost correct ... calc error...
$$\epsilon_r = (\dfrac{c}{\lambda f })^2~~ \text{ so }~~\epsilon_r=5.76$$