# waveguide propagation

#### mentaaal

Joined Oct 17, 2005
451
hey guys, i was looking at this site: http://www.turnpoint.net/wireless/cantennahowto.html
and it explains how to build a waveguide out of a tin can. further down it has an automatic calculator and it shows the cutoff frequencies for te modes and tm modes... they are quite different... so how would one change the mode of propagation? or does the mode of propagation change itself based on the standing waves inside it?

thanks guys!

#### mentaaal

Joined Oct 17, 2005
451
anyone? i dont mean to nitpick just want to understand it

#### DrNick

Joined Dec 13, 2006
110
it is expected that the TM and TE modes will have different cutoff frequencies. The cutoff frequency tells you the lowest frequency that can fit in to the waveguide/resonator. So if you plug in the default 3.5 cm, we see that the TE modes Fc, is about 2 GHz, and TM is at about 2.5 GHz. This is good, because wi-fi is at 2.4 GHz, making it so oly TE11 propagates in the can ( making it a single mode waveguide).

Any way you can change cutoff frequencies by changing the radius of the can. An easy way to think about it is that the lower the frequency, the longer the wavelength. If the wavelength is too big to fit in to the can, it will not propagate.

#### mentaaal

Joined Oct 17, 2005
451
it is expected that the TM and TE modes will have different cutoff frequencies. The cutoff frequency tells you the lowest frequency that can fit in to the waveguide/resonator. So if you plug in the default 3.5 cm, we see that the TE modes Fc, is about 2 GHz, and TM is at about 2.5 GHz. This is good, because wi-fi is at 2.4 GHz, making it so oly TE11 propagates in the can ( making it a single mode waveguide).

Any way you can change cutoff frequencies by changing the radius of the can. An easy way to think about it is that the lower the frequency, the longer the wavelength. If the wavelength is too big to fit in to the can, it will not propagate.
thanks for the reply! But howcome Te modes cutoff point is lower than Tm? like howcome they arent exactly the same? And also what is Te11?

#### DrNick

Joined Dec 13, 2006
110
TEmn, and TMmn are modes of an EM wave that propagate in a circular waveguide (they are just solutions to helmholtz equation). TE means the electric field is transverse (perpendicular) to the direction of propagation. TM means the magnetic field is transverse to the direction of propagation. Lots of intense math goes in to solving helmholtz equation in cylindrical coordinates, so to make a long story short, TE11 turns out to be the dominant mode in a cylindrical waveguide, because when you plug stuff in the helmholtz equation, solve the boundry conditions you find you get bessel funcitons; Cut off frequencies depend on the values of these bessel functions that depend on an m and an n wich directly corrispond to the m and n in TEmn and TMmn; when m and n are 1 and 1 in the TE mode you get a lower cutoff frequency than any other mode that will propagate in the waveguide.

Incase you do not understand cutoff frequency, it is the lowest frequency that a mode can support. So if TE11 has a fc = 1 MHz, and you try to put a .9 MHz wave in to your wave guide, nothing will travel through the guide, it will just die off after a very short distance in the waveguide. So, as I said before, in the project you only want TE11 to propagate. So if you choose a tin can that has dimentions that give fcTE11 < 2.4 GHz and fcTM01 (the next lowest cutoff frequency for this topology) > 2.4 GHz, only TE11 will go through your waveguide, and you are in business.