How to calculate the second over mode in the coaxial waveguide.

How to calculate the second over mode in the coaxial waveguide.I would like to calculate the second over mode in the coaxial waveguide, given the radius of the cladding and the core. The reason for this is that the desired mode in my waveguide is the TE11 (and not the TEM mode that is usual used in a coaxial cable). I now that the cutoff frequency for TE11 is given by the equation  fc=1/(pi*(a+b)*sqrt(mu*eps)) there a and b are the radius of the core and cladding respectively.I do not want any over mode in my waveguide and therefore I would like to calculate the cut of frequency for the TE21. I would appreciate if someone can give me a hint here.BR Thomas

Very nice picture, a whole hard way to be successful, let's do more. driving directions

These formulas are the exact calculations for capacitance and inductance per length for coax cable. We'll try to stick with the "prime" nomenclature whenever we are talking about quantities that are normalized per unit length.Note that the units of D and d don't matter, both calculations only use the ratio D/d. We can simplify them, noting that R is usually =1 for any dielectric we might be interested in. Then the equations can be expressed in SI units (per meter):or in English units (per foot)