A dipole antenna has a sin$$\theta $$ radiation pattern where the angle $$\theta $$ is measured from the axis of the dipole. The dipole is vertically located above an ideal ground plane (Fig.). What should be the height of the dipole H in terms of wave length so as to get a null in the radiation pattern at an angle of 45⁰ from the ground plane? Find the direction of maximum radiation also.

Two isotropic antennas A and B from an array as shown in Fig. The currents fed to the two antennas are $${{\rm I}_0}\,\angle 0$$ and $${{\rm I}_0}\,\angle \alpha $$ respectively. What should be the value of $$\alpha $$ so that the radiation pattern has a null at $$\theta = {30^ \circ }$$. Find the direction of the maximum radiation for that value of $$\alpha $$ and draw the radiation pattern. ($$\lambda \,\,$$ is the wavelength of operation)

Two dipoles are so fed and oriented in free space that they produce the following electromagnetic waves: $$${E_x} = 10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$ $$${E_y} = j\,\,10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$

(a) Write down the expression for the corresponding magnetic field strength vector.
(b) Calculate the frequency of the wave.
(C) Give the complete description of the polarization of the wave.

Two spacecrafts are separated by 3000 km. Each has a paraboloidal reflector antenna of 0.85 m diameter operating at a frequency of 2 GHz with an aperture efficiency of 64%. If the space crafts A's receiver requires 1pW for a 20 dB signal-to-noise ratio, what transmitter power is required on the spacecraft B to achieve this signal-to-noise ratio?