How to identify TM/TE modes of an antenna?

I am designing a ring antenna. How do I know what mode it is propagating in (For any antenna e.g. Square patch, circular patch, etc) ? Basically, I will like to know the definition of Transverse Magnetic modes, Transverse Electric modes. Is there a formula to calculate the resonance frequency at a particular mode? Can anyone help me? Thanks in advance?

Hi, Element7k.

First, I consider you're talking about patch antenna

Any patch (consider lying in XY plane) supports only TM modes.
Imagine that under the patch you have only the z-component of electric field, Ez (simplified model). Patch is simplified to be only 2 dimensional. Magnetic fields you compute as follows:

H=(j*omega*mu0)^-1 z0 x grad(Ez)

z0 is unit vector in z direction and x is vector product

it results that H under the patch have x,y compontents only and because XY is the transversal plane, modes are called TransverseMagnetic

Resonant freqs. of the TM modes you can calculate in general as

f_n=(c*k_n)/(2*pi*sqrt(epsreff))

epsreff is efective relative epsilon of substrate and k_n is the eigennumber which depends on geometry only!!!
If geometry is separable (circle, ellipse, ring, rectangle, triangle) you can separate eigennumbers in coordinates also.

Look in Microstrip antenna design handbook, you'll find there the eigennumbers and eigenmodes (together called eigenpars) for all separable geometries.

This approach coming from the idea patch antenna as resonator with magnetic walls around their boundary. PEC condition at patch itself and ground is fulfiled automaticaly, because we suppose only Ez (normal component).

Regards,
Eirp

Thanks EIRP for the comprehensive explanation.

I have now another question:

say for example a square patch antenna which uses TM10 and TM30 modes to achieve 2 resonant frequencies. In this case, the TM20 mode naturally resonate at x1.5 the frequency of the TM01 mode. Why is the TM20 mode destructive then? How do I suppress the TM20 mode excitation then?

Any help will be greatly appreciated. Many thanks in advance.

Element7k