Lecture -- Rectangular waveguide

This lecture analyzes the TE and TM modes in a rectangular metal waveguide with a homogeneous fill. The lectures includes the analysis as well as visualization of the modes and a discussion of the waveguide.

[@kevinkillsit]

Dude! Thank you, I honestly felt like this was the best sense the math has made for me in years. great derivation and walkthrough.

[@empossible1577]

Thank you!

[@alexandermuller8858]

very good explanation as always. I recently discovered for myself an interesting way of how to look at this dispersive behavior you are talking about in min 34. Beta^2 = k^2 - (kx^2+ky^2) : So if you increase the frequency for one fixed mode you can neglect kx and ky compared to k at some point which means that we have "free space" conditions where Beta^2 = k^2 (no dispersion). It's like the wavelength of that mode gets so small, that the waveguide geometry looks infinite from its point of view, same as a plane wave traveling in free space.

[@jimgolab536]

Very nice and clear explanation of how to analyze a waveguide. Thanks for doing this!

[@empossible1577]

Thank you! These are newly recorded.

[@SrikrishnaSagar]

Great Lecture. And thanks for sharing the animations as well, not many do that... The visualisation of modes was exceptional.

[@empossible1577]

Thank you!

[@Makedonomaxos88]

Perfect video for our small electromagnetic engineering community. I saw your video about the dielectric slab waveguide, with a very good mathematical explanation on how the 2 sets of solutions (TE and TM) are naturally decoupling from each other, due to the invariability along one axis. However, for common metallic waveguides, I don’t see a similar explanation on why we have TE and TM modes. I mean that, in every relevant textbook, the analysis begins assuming the existence of TE and TM modes in advance. I understand that TEM modes are not supported in these waveguides, but what qualifies us to assume a priori TE and TM modes, rather than searching for hybrid modes from the very beginning of the analysis (and then maybe conclude the existence of TE and TM modes as a special case)? Actually, are hybrid modes (modes with both E- and H-field components along the waveguide axis) possible in metallic homogeneous waveguides?

[@empossible1577]

How did I miss this question? I see it is three years old! Very sorry!! I try to answer everything in less than 24 hours! Anyway, here goes... First, let me point you to the course website where all of this is laid out: empossible.net/academics/emp3302/ I think Lecture 9b outlines waveguide analysis pretty well. Start there. For TE and TM modes to exist in a metallic waveguide, the dielectric medium must be homogeneous. There are some other cases where TE and TM still exists, but homogeneous is easiest to explain. For homogeneous case, the wave equation for Ez and Hz become independent equations, thus the two independent modes. When the Ez equation is solved, that is TM since Hz=0 for those modes. When the Hz equation is solved, that is TE since Ez=0 for those modes. When the medium is inhomogeneous, the differential equations for Ez and Hz are coupled and they cannot be separated. We call these hybrid modes. I personally do not like that title because it make it seem like something strange is happening. Instead, this is the normal thing to happen for guided modes. The emergence of TE and TM modes is the special case, not hybrid modes. However, TE and TM is what we learn about because the math is simpler and the waveguides are easier to manufacture. Hope this helps!

[@NM0S.]

I wish you were my professor.

[@empossible1577]

Thank you!

[@kardebraj7532]

very well explained. Thanks

[@empossible1577]

Thank you!!

[@giorgitsintsadze9919]

My understanding is that only discrete modes are supported in rec waveguides, basically determined when E-field is 0 at boundaries. This physically makes sense but what happens if wave frequency is between two different modes say TE01 and TE02? in this case frequency is more than TE01 but boundary conditions are NOT met.

[@empossible1577]

The modes are discrete spatially, not by frequency. That is, each mode looks different. They will also propagate at different speeds. Each mode has its own cutoff frequency. Below this frequency that mode is not a guided mode. At any frequency above the cutoff, the mode is propagating. If you pick a frequency "between two modes" then I think you have picked a frequency above one mode's cutoff and below the other's. That will give you just one guided mode. BTW...at frequencies below the cutoff frequency, that mode still exists. It is just that the mode will decay quickly with distance and can usually be ignored. Hope this helps!

[@mathso-levelegypt1819]

THANK YOU!

[@empossible1577]

You are welcome!

[@michelsena2076]

Loved your work. I'm from Brazil and I am interested in making this kind of class, can you help me saying where you made these wonder animations and graphics?

[@empossible1577]

Hello Brazil! Thank you!! All of the graphics and animations are made in either MATLAB or Blender or a combination of both.

[@michelsena2076]

@@empossible1577 Thanks a lot, your work is perfect, the audio is really nice, the way you talk, the speed. I'd just change the duration, for me it's ok, but there are people that prefer shorter videos to maintain concentration.

[@empossible1577]

@@michelsena2076 I am definitely with you on shorter videos. The origin of the long videos is a long story, but I am making all the newer videos shorter in duration.

[@meghjitmajumder3468]

1. In slide 20(I guess) can't quite understand that what's going on or what is to be understood from the elbow region of the curve of effective phase constant. 2. Again an overall fantastic lecture but it would be great to have one also on circular waveguide

[@empossible1577]

An ordinary wave in vacuum would have a straight line. The curve, or elbow, is due to the wave interacting with the waveguide. This is the dispersion introduced by the waveguide.

[@alexandermuller8858]

@@empossible1577 is it correct to say that unless the frequency of a certain mode is way above the cut off there will always be dispersion in a wave guide because of the non linear relationship between omega and beta

[@empossible1577]

@@alexandermuller8858 For ordinary waveguides, yes I think so. However, there are waveguides that engineer the dispersion and sometimes even reverse it. Photonic crystal waveguides are a good example of engineering the dispersion of guided modes.

[@rachelpiteck]

I wish I found our videos sooner!

[@empossible1577]

Welcome!

[@aks8767]

correction on slide 63 - TE10 mode is the fundamental mode and not TE01!

[@empossible1577]

Woops! How embarrassing! Looks like I only made that mistake on one slide and handled it correctly everywhere else. Fixing it now...

[@tubalcain1]

I didn't understand a word of this.... all I know is I own about 255 of the rectangular waveguides... I just use them has shelf brackets!!...

[@empossible1577]

Great application! They can also be made into musical instruments.

[@zaidqureshi8442]

Thanks professor, in which university you work?

[@empossible1577]

I work at the University of Texas at El Paso. Here is a link to my research website that covers my work there: raymondrumpf.com/research/

[@zaidqureshi8442]

@@empossible1577 by the way, world need more teachers like you, honestly you just nailed it.

[@empossible1577]

@@zaidqureshi8442 Thank you!

[@eightfivezerobraxton5509]

travelling faster than the speed of light bothers me, why is that?

[@empossible1577]

It is very good that it bothers you! Check out Lecture 9e. Here is the link to the official course website that has all the latest notes, links to the latest videos, and other resources: empossible.net/academics/emp3302/

[@k192447]

horrivel as imagens.