Final answer:
To determine the length of the waveguide for which the differential delay over the modulated signal bandwidth is equal to the bit period, we need to calculate the group delay of the waveguide. The group delay can be found using the carrier frequency and the speed of light in the waveguide. Once we have the group delay, we can solve for the length of the waveguide.
Step-by-step explanation:
To determine the length of the waveguide, we need to calculate the differential delay over the modulated signal bandwidth. The differential delay is equal to the reciprocal of the bandwidth. In this case, the bandwidth is equal to the bit rate, which is 1 Gb/s. Therefore, the differential delay is 1/1 Gb/s = 1 ns.
The waveguide provides a group delay, which is the time delay experienced by different frequencies within the signal. For the differential delay to be equal to the bit period, the group delay of the waveguide should also be 1 ns.
The group delay of a waveguide is given by the formula:
Group delay = (length of waveguide) / (speed of light in waveguide)
Given that the carrier frequency is 80 GHz, we can use the formula:
Speed of light in waveguide = (speed of light in vacuum) / (square root of relative permittivity of air-filled WR 12 waveguide)
Substituting the values, we can solve for the length of the waveguide in meters.