Summary
 A waveguide is a hollow conducting pipe, of uniform cross section, used to transport highfrequency electromagnetic waves (generally, in the microwave band) from one point to another.
 Waveguides can be generally classified as eithermetal waveguidesordielectric waveguides.
 There are different modes of wave propagation through a waveguide, e.g., TE mode, TM mode, TEM mode and Hybrid mode.
 For TE mode, no component of electric field exists in the direction of wave propagation.
 For TM mode, no component of magnetic field exists in the direction of wave propagation.
 For TEM mode, no component of either electric or magnetic field exists in the direction of wave propagation.
 For hybrid mode, both electric and magnetic field exists in the direction of wave propagation.
 For parallel plane waveguide, consisting of two infinite parallel conducting planes, there exist three modes of wave propagation, e.g., TE mode, TM mode and TEM mode.
 Different parameters for parallel plane waveguide are given in the table below.
Parameters 
TE and TM Modes 
TEM Mode 
Propagation constant 


Cutoff frequency 


Cutoff wavelength 


Guide wavelength 


Phase velocity 


Group velocity 

â€” 
Wave impedance 
; 

 A rectangular waveguide is formed by placing four conducting planes.
 For a rectangular waveguide, four modes of wave propagation, e.g., TE mode, TM mode, TEM mode and hybrid mode, exist. For TE_{mn} mode, m = ;0, 1, 2, â€¦; n = 1, 2, 3, â€¦ For TM_{mn }mode, m = 1, 2, 3, â€¦; n = 1, 2, 3,â€¦
 Different parameters for rectangular waveguides are given in the table below.
Parameters 
TE and TM Modes 
Propagation constant 

Cutoff frequency 

Cutoff wavelength 

Guide wavelength 

Phase velocity 

Group velocity 

Intrinsic wave impedance 
;where,. 
 For TEM mode in rectangular waveguide, , , so that .
 A TEM wave cannot exist in a singleconductor waveguide.
 Cylindrical or circular waveguides are those that maintain a uniform circular cross section along their length. Two modes of propagation, i.e.,TE and TM, exist in circular waveguides.
 Different parameters for circular waveguides are given in the table below.
Parameters 
TE and TM Modes 
Propagation constant 
where, 
Phase constant 

Cutoff frequency 

Cutoff wavelength 

Guide wavelength 

Phase velocity 

Group velocity 

Intrinsic wave impedance 
; where, 
 In a waveguide, since the guide walls are not perfectly conducting and the dielectric is lossy,there is a continuous loss of power as a wave propagates through the waveguide. These losses are mainly due to two reasons, represented by two attenuation constants:
 The attenuation constants due to conduction losses in a parallel plane waveguide for three different modes are as,
 The attenuation constant due to conduction losses for TE_{mn }waves in a rectangular waveguide is given as,
 The attenuation constant due to conduction losses for TM_{mn }waves in a rectangular waveguide is given as,
 The attenuation constant due to conduction losses for TE_{nm }waves in a circular waveguide is given as,
 The attenuation constant due to conduction losses for TM_{nm }waves in a circular waveguide is given as,
 A cavity resonator, usually used for energy storage at high frequencies, is one in which the electromagnetic waves exist in a hollow space inside the device.
 The rectangular waveguide resonator is basically a section of rectangular waveguide which is enclosed on both ends by conducting walls to form an enclosed conducting box.
 The resonant frequency in a rectangular cavity resonator for TE and TM mode waves is given as,
 The quality factor of a cavity resonator is defined as,
 For the dominant mode in a rectangular cavity resonator (i.e.,TE_{101 }mode), the quality factor is given as,
 The resonant frequency in a circular cavity resonator for TE and TM mode waves is given as,