4.a 4.b 4.c You are asked to design a rectangular waveguide so that the excitation signal of 27 GHz is 1.35 times the dominant mode cut-off frequency and the waveguide is single mode. The rectangular waveguide is to be filled with a lossless ceramic material with a dielectric constant of 9.6. 4.a.i Determine suitable values of the cross sectional dimensions for the waveguide (a and b) to meet the design requirements. a 2.42 mm, b < 1.79 mm 4.a.ii 24.7% (5 marks] This waveguide is connected to an antenna with a 300 2 input impedance. What percentage of the dominant mode field is reflected by the antenna at the excitation frequency of 27 GHz? [4 marks] Determine the total radiated power and radiation resistance of the following antennas: 4.b.i A 12 mm long, infinitely thin dipole at 12.5 GHz with lo= 3 mA. 329.4 W, 732 4.b.ii [2 marks] A 8.3 cm long, infinitely thin dipole fed by a 2.2cos(1.3x 10%xt) Amp current signal. 0.617 W, 0.255 2 [2 marks] The transmitting and receiving antennas in a wireless communications system are half wavelength long dipole antennas with an efficiency of 90%. The antennas are polarisation aligned, and are located 3.5 km apart. The power at the receiver is 33 dB smaller than the power at the transmitter. The feeding transmission lines to both antennas have a characteristic impedance of 120 ohm. 4.c.i What is the operating frequency of the wireless communications system? 423 kHz 4.c.ii [5 marks] If the transmitting antenna is changed to a circularly polarised antenna with the same gain as a half wave dipole at the operating frequency, what would happen to the received power? It would be half. Explain why. [2 marks] Q3. a) Write the instantaneous field expression for the TM11 mode in a rectangular waveguide with sides a and b. b) Sketch the electric and magnetic field lines in a typical X-Y plane and Y-Z plane. c) If a 2.29 cm and b = 1.02 cm, calculate the cutoff frequency of the lowest two TM modes d) If the above waveguide is filled with a lossless dielectric material (&r=4.0) what will be the cutoff frequencies of the lowest two TM modes.