# Cylindrical or Circular Waveguides

Cylindrical or circular waveguides are those that maintain a uniform circular cross section along their length.

The method of solution of the electromagnetic field equations for circular waveguides is similar to that for rectangular waveguides. However, in order to simplify the application of the boundary conditions that the tangential component of the electric field be zero, we convert all field equations in cylindrical coordinate systems.

The method of solution of the electromagnetic field equations for circular waveguides is similar to that for rectangular waveguides. However, in order to simplify the application of the boundary conditions that the tangential component of the electric field be zero, we convert all field equations in cylindrical coordinate systems.

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**Cylindrical or circular waveguide**# Properties of *TE* and *TM* Waves in Circular Waveguides

We find the following quantities for *TE*and

*TM*mode waves in circular waveguides:

*Propagation Constant (**Î³***)***h*is obtained from Tables for_{nm}*TE*and*TM*waves, respectively.*Phase Constant (***Î²****)***or,**Cut-off Frequency (f*_{c})*,**where is the phase velocity of a uniform plane wave in a lossless dielectric medium.*âˆ´ *From Eq. and from Tables. we see that the lowest cut-off frequency is with**TE*_{11}mode, the next higher modes being*TM*_{01}*, TE*_{21}*, TE*_{01}*.**Cut-off Wavelength (***Î»**_{c})*,**Phase Velocity (v*_{p})*Group Velocity (v*_{g})*From the relation that , the group velocity is obtained as**,**Guide Wavelength (**Î»*_{g})*Intrinsic Wave Impedance (***Î·****)***TE*and*TM*modes*.*- Intrinsic Wave Impedance for
Modes in Circular Waveguides*TE**TE*waves, from Eq., it is given as,*where is the intrinsic impedance of a uniform plane wave in a lossless dielectric medium**.*âˆ´ - Intrinsic Wave Impedance for
*TM*Modes in Circular WaveguidesFor*TM*waves, from Eq., it is given as,âˆ´

- Intrinsic Wave Impedance for