Question

A 10 cm long rectangular waveguide is designed with side lengths of 3 mm and 4mm. The waveguide is filled with a dielectric that has a refractive index n=1.3.

a) Over what frequency range is this waveguide single mode?

A 50 GHz signal is modulated into one short pulse, then sent into the waveguide.

b) How many modes are supported by the waveguide? Also identify them by their name (for example TE32).

c) Resulting from one pulse sent at the input of the waveguide, how many pulses are expected to emerge out from the waveguide?

d) Consider the input pulse being sent at t=0 sec. After how much time the pulses predicted in question c) will emerge from the waveguide? Provide the delay taken by each output pulse.

Answer 1

Given: Rectangular wave guide (a > b) l = 10 cm , b = 3 mm = 3 times 10^-3 m a = 4 m = 4 times 10^-3 m. n = 1.3 Frequency range for single mode is given by following formula = C/2a lessthanorequalto f lessthanorequalto C/a because C = 3 times 10^8 m/s = 3 times 10^8/2 times 4 times 106-3 lessthanorequalto f lessthanorequalto 3 times 10^8 /4 times 10^-3 37.5 times 10^9 lessthanorequalto f lessthanorequalto 75 times 10^9 Hz leftarrow frequency range for single mode if f_1 = 50 GHz 1) TE_10 = c/2a = 3 times 10^8 /2 times 4 times 10^-3 = 37.5 GHz 2) TE_01 = c/2b = 3 times 10^8 /2 times 3 times 10^-3 = 50 GHz TE_11 = c/2 squareroot (1/a)^2 + (1/b)^2 = 3 times 10^8 /2 [squareroot (1/4 times 10^-3)^2 + (1/3 times 10^-3)^2] TE_11 mode = 62.5 times 10^9 Hz \r\n Here TE_11 & TM_11 are