A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ }}$$ with positiv $$y$$-axis. The $$\overrightarrow E $$ field of the plane wave can be represented as ($${E_0}$$ is a constant)

A load of 50 $$\Omega $$ is connected in shunt in a 2-wire transmission line of $$Z_0$$ = 50 $$\Omega $$ as shown in the Fig. The 2-port scattering parameter matrix (S-matrix) of the shunt element is

A $$\lambda /2$$ dipole is kept horizontally at a height of $${\lambda _0}/2$$ above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole ($$\overrightarrow E $$ plane) looks approximately as

The $$\mathop E\limits^ \to $$ field in a rectangular waveguide of inner dimensions $$a\,\, \times \,\,b$$ is given by $$\mathop E\limits^ \to = {{\omega \,\mu } \over {{h^2}}}\,\left( {{\pi \over a}} \right)\,{H_0}\,\sin \,\left( {{{2\,\pi \,x} \over a}} \right)\,\,\sin \,(\omega \,t - \,\beta \,z)\hat y$$,

where $${H_0}$$ is a constant, a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is