Lecture -- TE Analysis of the Rectangular Metal Waveguide

This video builds on the analysis of a parallel plate waveguide (covered in a prior video) to step through the analysis of TE modes in a rectangular metal waveguide. For these modes, the z component of the electric field is zero. The video goes on to discuss and visualize the modes. The video ends with an example.
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[@douglasstrother6584]

"The Art and Science of UWB Antennas" by Hans G. Schrantz is a great read. The author's focuses on energy flow (Poynting Vector) to understand antennas, in particular, but presents a novel viewpoint on any RF/microwave/optical device.

[@empossible1577]

I don't think I have heard of that one, but it sounds interesting. Some of my research involves antennas.

[@tominku]

A quick question, how does the wave propagate when the metal guide is bent 90 degree (or some angle) somewhere ?

[@empossible1577]

The analysis here assumes the waveguide is uniform along the z direction. It is much more complicated to analyze the case of a discontinuity. In general, any discontinuity will introduce reflections. There are techniques for designing bends and other things while also minimizing reflections. The reason for the reflections is this. At a bend (or other discontinuity), the guided modes change their properties. Continuity of the field requires the tangential components to be continuous. If suddenly the modes change what they look like, there will have to be scattering and/or scrambling of power between the modes to satisfy the continuity of fields. This is important to understand because it is the origin of some ways to mitigate the reflections. For example, think of a horn antenna. The taper smooths the transition between a guided mode and propagating wave.

[@97mesut]

At 32:50 you say that TE01 is the lowest order mode, but you are showing a typical a>b waveguide, where TE10 should be the lowest order mode. Right?

[@empossible1577]

You are correct. It is just a convention to have a>b. The conventional thing for your b>a waveguide would be to rotate the waveguide so that a>b so that TE01 is still the lowest order. I personally have no problems breaking away from convention. Just be sure to be clear to others what you have done. Hope this helps!!

[@97mesut]

sir the velocity of the TE10 mode is bothering me and the police wont help me. can you upload a video clearing up that its not actually propagating faster than the speed of light? i cant sleep

[@empossible1577]

This is great to hear that you are curious about this! It has been on my to-do list to make a video on just this topic. I have something close in Lecture 1b here: empossible.net/academics/21cem/ The short answer is that guided modes are like two opposite plane waves bouncing between the metal plates. The velocity we calculate for guided modes is the velocity of the interference pattern of these two plane waves. This is more accurately called the "phase velocity." The waves of higher order modes do quite a bit of bouncing so they push energy more slowly. However, the interference pattern of those waves actually moves faster and easily exceeds the speed of light. Just remember that nothing other than an interference pattern is moving faster than light. A video with visuals will help explain the concept. The link above is old material, but is all I have on this subject. I hope it is enough until I get to the waveguide video. Hope this helps!!

[@senishkhadka4685]

but TE 01 shouldnt exist right according to the equations?

[@empossible1577]

It exists. It just has a higher cutoff frequency than TE10 (assuming a > b).