Final answer:
To design an air-filled rectangular waveguide with a=2b, we can determine the dimensions by considering the resonant modes and the cutoff frequencies for TE and TM modes. The operating frequency should be in the middle of the dominant mode frequency range.
Step-by-step explanation:
To design an air-filled rectangular waveguide, we can use the given information a = 2b and the operating frequency ξ/9.3 GHz. The dimensions of the waveguide can be determined by considering the resonant modes. In this case, we want the operating frequency to be in the middle of the dominant mode frequency range for both TM and TE modes.
For a rectangular waveguide, the cutoff frequency for the nth mode in the TE family is given by fc = c / (2a), and for the TM family, fc = c / (2b), where c is the speed of light.
Since we want the operating frequency to be in the middle of the range, we can take the cutoff frequency of the first mode to be half of the operating frequency. Therefore, fc = ξ / (9.3 * 2) GHz.
Using the relationship a = 2b, we can substitute and solve for the dimensions of the waveguide:
a = c / (2fc)
b = a / 2
Finally, we can plug in the values of fc and c to find the dimensions of the waveguide in meters.