Q. Calculate the diameter of an air-filled circular waveguide?

Unlike transmission lines, which operate at any frequency up to a cutoff value, waveguides have both upper and lower cutoff frequencies. For rectangular air-filled waveguides, the lower cutoff frequency (for propagation by the dominant mode) is given by f_c = c/2a, where c is the speed of light. Since the upper limit cannot be larger than 2f_c, practical waveguides are designed with b ≅ a/2 with a suggested frequency of 1.25 f_c ≤ f ≤ 1.9f_c. For a circular air-filled waveguide with inside radius a, the lower cutoff frequency (for propagation by the dominant mode) is f_c = 0.293 c/a. The operating band is usually f_c < f < 1.307 f_c. The characteristic impedance ¯Z₀ (= R₀) in waveguides is not constant with frequency, as it is in transmission lines. For rectangular or circular air-filled waveguides, the expression for ¯Z₀(= R₀) is given by

(a) For a rectangular air-filled waveguide with a = 4.8 cm and b = 2.4 cm, compute the cutoff frequency. If the operating frequency is 4 GHz, find the waveguide's characteristic impedance.

(b) Calculate the diameter of an air-filled circular waveguide that will have a lower cutoff frequency of 10 GHz.