Problem 1
An antenna is designed to operate between \(4.98 \mathrm{GHz}\) and \(5.02 \mathrm{GHz}\) for a bandwidth of \(\Delta f=0.04 \mathrm{GHz}\). Find \(\Delta \lambda,\) the wavelength range over which the antenna is designed to operate. Hint: The answer is NOT \(7.5 \mathrm{~m}\).
Problem 3
Some speculate that alien civilizations might be able to watch TV programs that escape the earth's atmosphere. To get an idea of the likelihood for this to occur, consider an isotropic antenna in outer space transmitting a \(200 \mathrm{MHz}\) TV signal. Assume that the alien civilization uses an antenna with surface area \(0.5 \mathrm{~m}^{2}\) and has the technology to detect a signal with power as low as \(5 \cdot 10^{-22} \mathrm{~W}\). What is the minimum power that must be transmitted for detection to occur at a distance of 1.0 light year?
Problem 4
Project ELF, described in Sec. 4.4.1, was an extremely low frequency, \(76 \mathrm{~Hz},\) radio system set by the military to communicate with submarines. It had facilities near Clam Lake, Wisconsin and Republic, Michigan, 148 miles apart [52]. Because these facilities were located a fraction of a wavelength apart, antennas at these locations acted as part of a single array. The length of all antenna elements was 84 miles [52]. Assume it took 18 minutes to transmit a three letters message using 8 bit ASCII, and assume signals travel close to the speed of light in free space. (a) Calculate the ratio of the distance between the transmitting facilities to the wavelength. (b) Calculate the ratio of the length of all antenna elements to the wavelength. (c) What was the speed of communication in bits per second? (d) How many wavelengths long were each bit?
Problem 9
Determine if the following electromagnetic waves are linearly polarized, right circularly polarized, left circularly polarized, right élliptically polarized, or left elliptically polarized. All of these waves travel in the \(\hat{a}_{z}\) direction, and \(\omega\) is a constants. (This is a modified version of \(\mathrm{P} 3.34\) from [11].) (a) \(\vec{E}=10 \cos (\omega t-8 z) \hat{a}_{x}+10 \sin (\omega t-8 z) \hat{a}_{y}\) (b) \(\vec{E}=10 \cos \left(\omega t-8 z+\frac{\pi}{4}\right) \hat{a}_{x}+10 \cos \left(\omega t-8 z+\frac{\pi}{4}\right) \hat{a}_{y}\) (c) \(\vec{E}=10 \cos (\omega t-8 z) \hat{a}_{x}-20 \sin (\omega t-8 z) \hat{a}_{y}\) (d) \(\vec{E}=10 \cos (\omega t-8 z) \hat{a}_{x}-10 \sin (\omega t-8 z) \hat{a}_{y}\)
