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Please someone explain to me in Simple English or Basic equations as to why does a Transverse Electric and Magnetic Modes(TEM) propagate on only two surface Wave guide like a coaxial or a parallel plate wave guide?

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The paper you linked to (despite spelling and language errors) is actually pretty good. From page 4 ... " ... all transverse components of E and H can be determined from only the axial components Ez and Hz." For TEM mode support you need to have BOTH Ez=Hz=0 simultaneously. The paper deals with the mathematic reason nicely, what you are looking for is a physical sense of what is being said in the mathematics.

What is comes down to is that the H field is supported by induced currents in the walls and the E field is supported by induced voltages in the walls and in order for the wave to propagate these must reinforce each other, but in a single conductor system they cancel each other. The solution? If you have separate conductors then you can shape them to have the Voltage and Current in the conductors reinforce each other. The conductors will be capacitively and inductively linked, a single conductor can't be.

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That's because, the only way to propagate a TEM mode along a specific path is by flowing a physical current also along that specific path. To produce a current, you also need a physical voltage. Therefore you need 2 conductors.

Moreover, this is not the case with TE and TM modes, as they are able to manifest and be guided along the walls of a single conductor (due to boundary conditions). This is due to the fact that TE and TM modes have more freedom, as they bow only to 1 defining equation(ie. Ex = 0), where TEM must satisfy 2 equations (ie Ex = 0 and Hx = 0).

Infact, a single conductor waveguide has NO physical current (displacement current is there) or voltage.. only E and H waves. TEM can't be sustained in such environments.

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A waveguide is a single conductor with a dielectric inside it (Air is also a dielectric). TEM mode is characterised by electric fields and magnetic fields perpendicular to one another and perpendicular to the direction of propagation. Inorder to have such a configuration, there has to be a source of electric field at the centre from where E fields originate and terminate on the outer conductor and there has to be a current source which can generate magnetic fields. For TEM mode the current flow should be along the axis of the waveguide, which creates rotating magnetic fields which are normal to the electric fields generated due to the (moving) charges in the current carrying conductor. Since such a current source is absent and waveguide being a single conductor configuration, TEM mode cannot exist inside a waveguide. Also it is evident from the above explanation that for TEM mode to exist, presence of atleast two conductors is compulsory.

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Please take a look at the following link. As it says in the page consider we want to have TEM, which means that electric fields and magnetic fields are both pependicular to the direction of propagation, in waveguides. Then we know that magnetic fields are close loops and from Amper law we know that if we have a magnetic field, there should be a current in between which produces it. However, as there is no current in the middle of waveguide, TEM cannot be supported in such a one conductor structure.

https://www.ntnu.no/wiki/download/attachments/81790668/Waveguide_propagation_06.pdf?version=1&modificationDate=1443510894000&api=v2

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