Two lossless X-band horn antennas are separated by a distance of $$200\lambda $$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are $$0.15$$ and $$0.18$$, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are $$18$$ $$dB$$ and $$22$$ $$dB$$, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is $$2$$ $$W$$, and that the antennas are perfectly aligned and polarization matched, the power ( in mW) delivered to the load at the receiver is ________ .

The far-zone power density radiated by a helical antenna is approximated as: $$$\overrightarrow W {\,_{rad}} = \overrightarrow W \,average\, \approx \,\widehat a{}_rC{}_0\,{1 \over {{r^2}}}{\cos ^4}\theta $$$

The radiated power density is symmetrical with respect to $$\phi $$ and exists only in the upper hemisphere: $$0 \le \theta \le {\pi \over 2};\,\,\,\,0 \le \theta \le 2\pi ;$$

$${C_0}$$ is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are

Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of $$\pi /2$$ between them (the element at the origin leads in phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle $${60^ \circ }$$, the distance d (in meters) between the antennas is ___________ .

At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is