Questions and Answers of Elements Of Electromagnetics

A distortionless transmission line satisfies RC = LG. If the line has R = 10 mΩ/m, C = 82 pF/m, and L = 0.6 μH/m, calculate its characteristic impedance and propagation constant. Assume that the
A lossy transmission line of length 2.1 m has characteristic impedance of 80 + j60Ω. When the line is short-circuited, the input impedance is 30 – j12Ω. (a) Determine α and β. (b)
A lossy transmission line with characteristic impedance of 75 + j60 Ω is connected to a 200 Ω load. If attenuation is 1.4 Np/m and phase constant is 2.6 rad/m, find the input impedance for
A 120 Ω lossless line is terminated at a load impedance 200 – j240Ω. Find ΓL and s.
Calculate the reflection coefficient due to ZL = (1 + 2j)Z0.
Normalize the following impedances with respect to 50 V and locate them on the Smith chart: (a) Za = 80 Ω, (b) Zb = 60 + j40Ω, (c) Zc = 30 – j120Ω.
Determine the impedance at a point λ/4 distant from a load of impedance (1 + j2)Zo.
A 50 Ω lossless line operates at 600 MHz and is terminated by a load of ZL. If the line is 0.1 m long and Zin = 100 – j120, find ZL and s. Assume u = 0.8 c.
A lossless transmission line, with characteristic impedance of 50 Ω and electrical length of ℓ = 0.27λ is terminated by a load impedance 40 – j25 Ω.Determine ΓL, s, and Zin.
A lossless 100 Ω transmission line is terminated in an unknown impedance ZL. The standing wave ratio is 2.4, and the nearest voltage minimum is 0.2 λ from the load. Find ZL and Γ.
The distance from the load to the first minimum voltage in a 50 Ω line is 0.12λ, and thestanding wave ratio s = 4.(a) Find the load impedance ZL.(b) Is the load inductive or capacitive?(c) How far
A lossless 50 V line is terminated by a load ZL = 75 + j60 Ω. Using a Smith chart, determine (a) The reflection coefficient Γ, (b) The standing wave ratio s, (c) The input
Using the Smith chart, determine the admittance of Z = 100 + j60 Ω with respect to Zo = 50 Ω.
A 50 Ω transmission line operates at 160 MHz and is terminated by a load of 50 + j30 Ω. If its wave speed is c/2 and the input impedance is to be made real, calculate the minimum possible length of
A 50 Ω transmission line, λ/4 in length, is connected to a λ/2 section of 100 Ω line terminated by a 60 Ω resistor. Calculate the input impedance to the 50 Ω line.
(a) Calculate the reflection coefficient corresponding to ZL = (0.5 – j)Zo.(b) Determine the load impedance corresponding to the reflection coefficient 0.4 ∠25°.
An 80 V lossless line has ZL = j60 Ω and Zin = j40 Ω. (a) Determine the shortest length of the line. (b) Calculate s and ΓL.
A 50 Ω air-filled line is terminated in a mismatched load of 40 + j25 Ω. Find the shortest distance from the load at which the voltage has the smallest magnitude.
A 12 V battery with an internal resistance of 10 Ω is connected to a 20 m length of 50 Ω coaxial cable with phase velocity of 2 x 108 m/s. If the receiving end is short-circuited, sketch the
At microwave frequencies, we prefer waveguides to transmission lines for transporting EM energy because of all the following except that(a) Losses in transmission lines are prohibitively large.(b)
An evanescent mode occurs when(a) A wave is attenuated rather than propagated.(b) The propagation constant is purely imaginary.(c) m = 0 = n so that all field components vanish.(d) The wave frequency
A rectangular waveguide (2.28 cm x 1.01 cm) is filled with polyethylene (εr = 2.25). Calculate the cutoff frequencies for the following modes:TE01, TE10, TE11, TE02, TE22, TM11, TM12, TM21. Assume
The dominant mode for rectangular waveguides is(a) TE11(b) TM11 (c) TE101(d) TE10
An air-filled waveguide has a cross section of 2.4 cm x 1.2 cm. A microwave signal of 12 GHz propagates down the guide. (a) Calculate the cutoff frequencies of TE10, TE01, TE20, and TE02
If the lines in Figure 11.53 are connected to a voltage source of 120Ω with an internal impedance of 80 Ω, calculate the average power delivered to either antenna.
Two identical antennas, each with input impedance 74 Ω, are fed with three identical 50 Ω quarter-wave lossless transmission lines as shown in Figure 11.53. Calculate the input impedance at the
A step current of 10 mA is turned on at t = 0, at z = 0 of a transmission line as shown in Figure 11.58. Determine the load voltage and current as functions of time. Let Zo = 50 Ω, μ = 2 x
A strip transmission line is shown in Figure 11.61. An approximate expression for the characteristic impedance isDetermine Zo for w = 0.5 cm, t = 0.1 cm, b= 1.2 cm, εr = 2. B ६
A load ZL = 75 + j100Ω is to be matched to a 50Ω line. A shorted shunt-stub tuner is preferred. Find the length of the stub in terms of λ.
A 50 Ω lossless transmission line that is 20 m long is terminated into a 120 + j220 Ω load. To perfectly match, what should be the length and location of a short-circuited stub line? Assume an
On a lossless line, measurements indicate s = 4.2 with the first maximum voltage at λ/4 from the load. Determine how far from the load a short-circuited stub should be located and calculate its
A 50 Ω coaxial cable is connected to an 80 Ω resistive load and a dc source with zero internal resistance. Calculate the voltage reflection coefficients at the source and at the load.
The effective relative permittivity εe is given by eq. (11.70). Use MATLAB to plot εe for 0.1 < w/h < 10. Assume εr = 2.2 (Teflon). Eeff (ε, + 1) 2 + (ε, - 1) 2V1 + 12h/w
A 50-cm-long cable, of characteristic impedance 75 Ω and wave velocity 2 x 108 m/s, is used to connect a source of internal impedance 32 Ω to an amplifier with an input impedance of 2 M Ω. If the
Suppose ZL = ZG and a dc voltage is turned on at t = 0 (i.e., a unit step function) of amplitude Vo. The voltage is launched on a lossless line with characteristic impedance Zo. Find the voltage
Find the return loss due to a 150 Ω cable terminated by a 100 Ω load.
The TM10 mode can exist in a rectangular waveguide.(a) True (b) False
For TE30 mode, which of the following field components exist?(a) Ex(b) Ey(c) Ez(d) Hx(e) Hy
If in a rectangular waveguide for which a 5 2b, the cutoff frequency for TE02 mode is 12 GHz, the cutoff frequency for TM11 mode is(a) 3 GHz (b) 3√5 GHz(c) 12 GHz(d) 6√5 GHz(e) None of the
If a tunnel is 4 m by 7 m in cross section, a car in the tunnel will not receive an AM radio signal (e.g., f = 10 MHz).(a) True (b) False
Show that the attenuation due to a waveguide operating below cutoff is α = 2πVμεΐν 1 ₁ - (-)² 1-
When the electric field is at its maximum value, the magnetic energy of a cavity is(a) At its maximum value(b) At √2 of its maximum value(c) At 1/√2 of Its maximum value(d) At 1/2 of its maximum
Analysis of a circular waveguide requires solution of the scalar Helmholtz equation in cylindrical coordinates, namely,orBy assuming the product solutionshow that the separated equations arewhere
An air-filled rectangular waveguide operates at 40 GHz. If the cutoff frequency of the TE12 mode is 25 GHz, calculate the wavelength, phase constant, phase velocity, and intrinsic impedance of this
Which of these modes does not exist in a rectangular resonant cavity?(a) TE110(b) TE011 (c) TM110(d) TM111
An air-filled rectangular waveguide of dimension 5 cm x 3 cm operates on the TE10 mode at a frequency of 12.5 GHz. Find the phase constant, phase velocity, and the wave impedance.
How many degenerate dominant modes exist in a rectangular resonant cavity for which a = b = c?(a) 0(b) 2(c) 3(d) 5(e) ∞
An air-filled waveguide has a = 2b = 4 cm and operates at the TE10 mode. Determine fc, β, and λ at 24 MHz.
A section of an air-filled rectangular waveguide (a = 2.4 cm, b = 1.2 cm) operates in the TE10 mode. The operating frequency is 25% higher than the cutoff frequency. Determine fc, f, and η.
A K-band waveguide (1.067 cm x 0.533 cm) is filled by a dielectric material with εr = 6.8. If it operates in the dominant TE10 mode at 6 GHz, determine the following:(a) The cutoff frequency(b)
For TE01 mode, Find Pave and Pave- Exs jωμπ bh² H, sin(my/b)e, Eys - 0
In a certain medium, the phase velocity iswhere c = 3 x 108 m/s. Obtain the expression for the group velocity. 1. с 0 A 12
For an air-filled waveguide, use MATLAB to plot up and ug for 10 GHz < f < 100 GHz. Assume that fc = 8 GHz.
Determine the values of β, μρ, μg, and ηTE10 for a 7.2 cm x 3.4 cm rectangular waveguide operating at 6.2 GHz (a) If the waveguide is air filled, (b) If the waveguide is filled
Consider a WR284 waveguide (a = 7.214 cm, b = 3.404 cm). If it is filled with polyethylene (εr = 2.5) and operates at 4 GHz, determine up and ug.
The group velocity of a dielectric-filled rectangular waveguide operating at 12 GHz is c/4. When the frequency becomes 15 GHz, the group velocity is c/3 for the same mode. Determine fc andεr.
A square waveguide operates at 4.5 GHz in the dominant mode. If the group velocity is determined to be 1.8 x 108 m/s, calculate the largest dimension of the waveguide. Assume that the
Use MATLAB to plot the attenuation for the TE10 mode a of waveguide with copper walls as a function of frequency. Do this for frequencies above cutoff. Keep in mind that Rs varies with frequency.
An air-filled X-band rectangular waveguide has dimensions a = 2.286 cm and b = 1.016 cm. If the waveguide has copper walls (ε = εo, μ = μo,σ = 5.8 x 107 S/m), find the attenuation in dB/m due to
A rectangular, air-filled waveguide has dimensions a = 3.8 cm and b = 1.6 cm, and walls are made of copper. For the dominant mode at f = 10 GHz, calculate(a) The group velocity(b) The attenuation dB/m
An air-filled waveguide has dimension 3 cm x 2.5 cm. The guide is 4 cm long. It is shorted at each end, forming a cavity. Determine the lowest three resonance frequency.
A rectangular cavity has dimension a = 1 cm, b = 2 cm, c = 3 cm. If it is filled with polyethylene (ε = 2.5εo), find the first five resonant frequencies.
For a cubical cavity (a = b = c) in the TE101 mode, show that Q = a / 3δ where δ is the skin depth.
An air-filled cavity has dimensions 20 mm x 8 mm x 10 mm. If the walls are silver- plated, find (a) Dominant resonant frequency, (b) Q for the TE101mode.
Design a cubical resonant cavity with a dominant frequency of 5.6 GHz. Assume that the cavity is filled with (a) Air, (b) Teflon having εr = 2.05.
(a) Determine the size of an air-filled cubical cavity made of copper that it will give a dominant resonant frequency of 12 GHz.(b) Calculate the quality factor Q at that frequency.
Shielded rooms act as resonant cavities. We must avoid operating equipment in any such room at a resonant frequency of the cavity. If an air-filled shielded room has the dimensions 10.2 m by 8.7 m by
The speed of light in a given medium is measured as 2.1 x 108 m/s. Find its refractive index.
Determine the numerical aperture of an optical fiber which has n1 = 1.51 and n2 = 1.45.
A glass fiber has a core diameter of 50 mm, a core refractive index of 1.62, and a cladding with a refractive index of 1.604. If light having a wavelength of 1300 nm is used, find(a) The numerical
A silicon fiber has a core index of 1.48 and a cladding index of 1.46. If the core radius is 5 μm, find the number of propagating modes for the source wavelength of 1300 nm.
In eq. (13.34a–c), which term is the radiation term?(a) 1/r term(b) 1/r2 term (c) 1/r3 term(d) All of the above Es = Hrs Hos = = -jωμί,S 4TT jωμί S Σπη jωμί.S 4πη -sin
A laser diode is capable of coupling 10 mW into a fiber with attenuation of 0.5 dB/km. If the fiber is 850 m long, calculate the power received at the end of the fiber.
Attenuation α10 in Chapter 10 is in nepers per meter (Np/m), whereas attenuation α12 in this chapter is in decibels per kilometer (dB/km). What is the relationship between the two?
A power of 1.25 mW is launched into an optical fiber that has a 0.4 dB/km attenuation. Determine the fiber length such that a power of 1 μW is received at the other end of the fiber.
A lightwave system uses a 30 km fiber link with a loss of 0.4 dB/km. If the system requires at least 0.2 mW at the receiver, calculate the minimum power that must be launched into the fiber.
(a) Discuss the advantages derived from using a fiber-optic cable.(b) What is pulse dispersion?
A dipole antenna has the following parameters :Antenna length ℓ = 0.02 λCurrent magnitude Io = 3 AOperating frequency f = 400 MHzRadiation range r = 60 mDetermine the following:(a)
A very small, thin wire of length λ/100 has a radiation resistance of(a) ≅ 0 Ω(b) 0.08 Ω (c) 7.9 Ω(d) 790 Ω
A Hertzian antenna in free space is 10 cm long. It is fed by a current of 20 A at frequency of 50 MHz. Find the electric and magnetic fields at far zone.
A quarter-wave monopole antenna operating in air at frequency 1 MHz must have an overall length of(a) ℓ >> λ(b) 300 m (c) 150 m (d) 75 m(e) ℓ << λ
Determine the current necessary for a 2 cm Hertzian dipole to radiate 12 W at 140 MHz.
If a small single-turn loop antenna has a radiation resistance of 0.04Ω, how many turns are needed to produce a radiation resistance of 1Ω?(a) 150(b) 125 (c) 50 (d) 25(e) 5
At a distance of 8 km from a differential antenna, the field strength is 12 μV/m. The field strength at a location 20 km from the antenna is(a) 75 μV/m(b) 30 μV/m (c) 4.8 μV/m(d) 1.92 μV/m
A short dipole antenna operates at the AM broadcast band at 1.2 MHz. To achieve a radiation resistance of 0.5Ω, how long must the antenna be?
An antenna has Umax = 10 W/sr, Uave = 4.5 W/sr, and ηr = 95%. The input power to the antenna is(a) 2.222 W(b) 12.11 W (c) 55.55 W(d) 59.52 W
A half-wave dipole antenna is driven by a 24 V, 200 MHz source having an internal impedance of 40Ω. Find the average power radiated by the antenna, given that Zin = 73 + j42Ω.
A receiving antenna in an airport has a maximum dimension of 3 m and operates at 100 MHz. An aircraft approaching the airport is 0.5 km from the antenna. The aircraft is in the far-field region of
A receiving antenna is located 100 m away from the transmitting antenna. If the effective area of the receiving antenna is 500 cm2 and the power density at the receiving location is 2 mW/m2, the
In the far field of a particular antenna located at the origin, the magnetic field intensity iswhere Io is the peak value of the input current. Show that the radiation resistance is given by
Let R be the maximum range of a monostatic radar. If a target with radar cross section of 5 m2 exists at R/2, what should be the target cross section at 3R/2 to result in an equal signal strength at
The radiation efficiency is given by eq. (13.50) aswhere Prad is the radiation power and Pohm is the power loss due to ohmic resistance of the antenna. For a cylindrical conductor of length Δz
An antenna engineer is asked to design a λ/2 dipole antenna to operate at 450 MHz.(a) Calculate the length of the antenna if it is located in free space.(b) Determine the length of the antenna if it
Quarter-wavelength antennas are used to transmit:(a) AM signals at 1150 kHz(b) FM signals at 90 MHz(c) VHF-TV signals at 80 MHz(d) UHF-TV signals at 600 MHzCalculate the respective antenna lengths.
An antenna located at the origin has a far-zone electric field as(a) Obtain the corresponding Hs field.(b) Determine the power radiated.(c) What fraction of the total power is radiated in the belt
A dipole antenna (ℓ = λ/8) operating at 400 MHz is used to send a message to a satellite in space. Find the radiation resistance of the antenna.
A circular loop antenna has a mean radius of 1.2 cm and N turns. If it operates at 80 MHz, find N that will produce a radiation resistance of 8 Ω.
Divide the interval 0 < θ < 2π into 20 equal parts and use MATLAB to show that 2πT (1 - cos 0) 0 de = 2.438
A loop antenna with loop radius of 0.4 m is made of copper wire of radius 4 mm. If the loop radiates at 6 MHz and carries a current of 50 A, find(a) The radiation resistance of the loop(b) The power
Determine the radiation efficiency of a half-wave dipole operating at 6 MHz. The wire is made of copper (σ = 58 MS/m) and is 1.2 mm in radius.

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