The average power of an omni-directional antenna varies as the magnitude of cos($$\theta $$) where $$\theta $$ is the azimuthal angle. Calculate the maximum Directive Gain of the antenna and the angles at which it occurs.

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.