A uniform plane wave in air impinges at 45° angle on a lossless dielectric material with dielectric constant $${\varepsilon _r}$$. The transmitted wave propagates in a 30° direction with respect to the normal. The value of $${\varepsilon _r}$$ is

The three regions shown in Fig. are all lossless and non-magnetic. Find

(a) Wave impedance in mediums 2 and 3.
(b) d such that medium 2 acts as a quarter wave $$(\lambda /40$$)transformer.
(c) Reflection coefficient $$(\Gamma )$$ and voltage standing wave ratio (VSWR) at the interface of the medium 1 and 2, when $$d = \lambda /4$$.

A rectangular waveguide has dimensions $$1\,\,cm\,\, \times \,\,0.5\,\,cm$$. Its cut-off frequency is

The half-power beam widths (HPBW) of an antenna in the two orthogonal planes are $${100^ \circ }$$ and $${60^ \circ }$$ respectively. The directivity of the antenna is approximately equal to