The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100$$\Omega \,$$ and 25$$\Omega \,$$ respectively. The characteristic impedance of the line 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

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

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