# Category: Fundamentals of Applied Electromagnetics 7th Ed solutions #### 9.33 An antenna with a circular aperture has a circular beamwith a beamwidth of 3◦ at 20 GHz.(a) What is the antenna directivity in dB?(b) If the antenna area is doubled, what will be the newdirectivity and new beamwidth?(c) If the aperture is kept the same as in (a), but the frequencyis doubled to 40 GHz, what will the directivity andbeamwidth become then?

... #### 9.26 Consider the communication system shown inFig. P9.26, with all components properly matched. IfPt = 10 W and f = 6 GHz:(a) What is the power density at the receiving antenna(assuming proper alignment of antennas)?(b) What is the received power?(c) If Tsys = 1,000 K and the receiver bandwidth is 20 MHz,what is the signal-to-noise ratio in decibels?

... #### 9.21 A car antenna is a vertical monopole over a conductingsurface. Repeat Problem 9.6 fora1m long car antennaoperating at 1 MHz. The antenna wire is made of aluminumwith µc = µ0 and σc = 3.5×107 S/m, and its diameter is 1 cm.

... #### 9.16 For a short dipole with length l such that l + λ, insteadof treating the current ˜I (z) as constant along the dipole, as wasdone in Section 9-1, a more realistic approximation that ensuresthe current goes to zero at the dipole ends is to describe ˜I (z) bythe triangular function˜I (z) =5 I0(1 − 2z/l) for 0 ≤ z ≤ l/2I0(1 + 2z/l) for − l/2 ≤ z ≤ 0as shown in Fig. P9.16. Use this current distribution todetermine the following:∗(a) The far-field !E(R, θ, φ).(b) The power density S(R, θ, φ).(c) The directivity D.(d) The radiation resistance Rrad

... #### 9.15 A 50 cm long dipole is excited by a sinusoidally varyingcurrent with an amplitude I0 = 5 A. Determine the totalradiated power if the oscillating frequency is:(a) 1 MHz,(b) 300 MHz

... #### 9.6 A 2 m long center-fed dipole antenna operates in the AMbroadcast band at 1 MHz. The dipole is made of copper wirewith a radius of 1 mm.(a) Determine the radiation efficiency of the antenna.∗(b) What is the antenna gain in decibels?∗Answer(s) available in Appendix D

... #### ∗8.35 A parallel-polarized beam of light with an electric fieldamplitude of 10 (V/m) is incident in air on polystyrene withµr = 1 and !r = 2.6. If the incidence angle at the air–polystyrene planar boundary is 50◦, determine the following:(a) The reflectivity and transmissivity.(b) The power carried by the incident, reflected, andtransmitted beams if the spot on the boundary illuminatedby the incident beam is 1 m2 in area.

... #### 8.16 A 0.5 MHz antenna carried by an airplane flying overthe ocean surface generates a wave that approaches the watersurface in the form of a normally incident plane wave withan electric-field amplitude of 3,000 (V/m). Seawater ischaracterized by !r = 72, µr = 1, and σ = 4 (S/m). The planeis trying to communicate a message to a submarine submergedat a depth d below the water surface. If the submarine’s receiverrequires a minimum signal amplitude of 0.01 (µV/m), what isthe maximum depth d to which successful communication isstill possible?

... #### 8.6 A 50 MHz plane wave with electric field amplitude of50 V/m is normally incident in air onto a semi-infinite, perfectdielectric medium with !r = 36. Determine the following:∗(a) \$(b) The average power densities of the incident and reflectedwaves.(c) The distance in the air medium from the boundary to thenearest minimum of the electric field intensity, |E|.

... #### ∗8.1 A plane wave in air with an electric field amplitude of20 V/m is incident normally upon the surface of a lossless,nonmagnetic medium with !r = 25. Determine the following:(a) The reflection and transmission coefficients.(b) The standing-wave ratio in the air medium.(c) The average power densities of the incident, reflected, andtransmitted waves

... 