Engineering Electromagnetics 8th edition William H. Hayt, John A.Buck - Solutions

White noise with two-sided power spectral density 1/2 N0 is added to a signal having the power spectral density shown in Figure 8.22. The sum (signal plus noise) is filtered with an ideal low pass filter with unity pass band gain and bandwidth B > W. Determine the SNR at the filter output.
Consider the system shown in Figure 8.23 The signal x(t) is defined by x(t) = A cos (2Ï€fct)The low pass filter has unity gain in the pass band and bandwidth W, where fc < W. The noise n(t) is white with two-sided power spectral density 1/2 N0 . The signal component of
Consider the system shown in Figure 8.24. The noise is white with two-sided power spectral density 1/2 N0. The power spectral density of the signal isThe parameter f3 is the 3-dB bandwidth of the signal. The bandwidth of the ideal low pass filter is W. Determine the SNR of y(t). Plot the SNR as a
Derive an expression, similar to (8.172), that gives the output SNR of an FM discriminator output for the case in which the message signal is random with a Gaussian amplitude pdf. Assume that the message signal is zero mean and has variance σ2m.
Assume that a PPM system uses Nyquist rate sampling and that the minimum channel bandwidth is used for a given pulse duration. Show that the post detection SNR can be written as and evaluate K. Вт (SNR), = K Рт NoW
A planar transmission line consists of two conducting planes of width b separated d m in air, carrying equal and opposite currents of I A. If b >> d, find the force of repulsion per meter of length between the two conductors.
Show that the differential work in moving a current element IdL through a distance dl in a magetic field B is the negative of that done in moving the element Idl through a distance dL in the same field.
A rectangular loop of wire in free space joins point A(1, 0, 1) to point B(3, 0, 1) to point C(3, 0, 4) to point D(1, 0, 4) to point A. The wire carries a current of 6 mA, flowing in the az direction from B to C. A filamentary current of 15 A flows along the entire z axis in the az direction.(a)
Show that a charged particle in a uniform magnetic field describes a circular orbit with an orbital period that is independent of the radius. Find the relationship between the angular velocity and magnetic flux density for an electron (the cyclotron frequency).
A point charge for which Q = 2 × 10−16 C and m = 5 × 10−26 kg is moving in the combined fields E = 100ax − 200ay + 300az V/m and B =−3ax + 2ay − az mT. If the charge velocity at t = 0 is v(0) = (2ax − 3ay − 4az)105 m/s(a) Give the unit vector showing the direction in which the
Compare the magnitudes of the electric and magnetic forces on an electron that has attained a velocity of 107 m/s. Assume an electric field intensity of 105 V/m, and a magnetic flux density associated with that of the Earth’s magnetic field in temperate latitudes, 0.5 gauss.
A point charge, Q = −0.3μC and m = 3 × 10−16 kg, is moving through the field E = 30az V/m. Use Eq. (1) and Newton’s laws to develop the appropriate differential equations and solve them, subject to the initial conditions at t = 0, v = 3×105ax m/s at the origin. At t = 3μs, find(a) The
By expanding Eq. (58), Section 7.7 in rectangular coordinates, show that (59) is correct.Eq. (58)∇×∇×A ≡ ∇(∇ · A)−∇2A
Compute the vector magnetic potential within the outer conductor for the coaxial line whose vector magnetic potential is shown in Figure 7.20 if the outer radius of the outer conductor is 7a. Select the proper zero reference and sketch the results on the figure.Figure 7.20 Hol л 2л 3 4 pla A,
Show that ∇2(1/R12) = −∇1(1/R12) = R21/R312.
Assume that A = 50ρ2az Wb/m in a certain region of free space.(a) Find H and B.(b) Find J.(c) Use J to find the total current crossing the surface 0 ≤ ρ ≤ 1, 0 ≤ ϕ < 2π, z = 0.(d) Use the value of Hϕ at ρ = 1 to calculate H · dL for ρ = 1, z = 0.
A current sheet, K = 20 az A/m, is located at ρ = 2, and a second sheet, K = −10az A/m, is located at ρ = 4.(a) Let Vm = 0 at P(ρ = 3, ϕ = 0, z = 5) and place a barrier at ϕ = π. Find Vm(ρ, ϕ, z) for −π < ϕ <π.(b) Let A = 0 at P and find A(ρ, ϕ, z) for 2 < ρ < 4.
A solid cylinder of radius a and length L, where L >>a, contains volume charge of uniform density ρ0 C/m3. The cylinder rotates about its axis (the z axis) at angular velocity Ω rad/s.(a) Determine the current density J as a function of position within the rotating cylinder.(b) Determine H
In Figure 7.22, let the regions 0 < z < 0.3 m and 0.7 < z < 1.0 m be conducting slabs carrying uniform current densities of 10 A/m2in opposite directions as shown. Find H at z =:Figure 7.22(a) ˆ’0.2;(b) 0.2;(c) 0.4;(d) 0.75;(e) 1.2 m. Air 1.0 10 A/m? 0.7 Air 0.3 - 10 A/m? Air
An infinite filament on the z axis carries 20π mA in the az direction. Three az-directed uniform cylindrical current sheets are also present: 400 mA/m at ρ = 1 cm, −250 mA/m at ρ = 2 cm, and −300 mA/m at ρ = 3 cm. Calculate Hϕ at ρ = 0.5, 1.5, 2.5, and 3.5 cm.
A hollow spherical conducting shell of radius a has filamentary connections made at the top (r = a, θ = 0) and bottom (r = a, θ = π). A direct current I flows down the upper filament, down the spherical surface, and out the lower filament. Find H in spherical coordinates (a) Inside (b) Outside
A current sheet K = 8ax A/m flows in the region −2 < y < 2 in the plane z = 0. Calculate H at P(0, 0, 3).
For the finite-length current element on the z axis, as shown in Figure 7.5, use the Biot-Savart law to derive Eq. (9) of Section 7.1.Eq. (9)Figure 7.5 (sin a2 – sina1)as 4лр н Point 2
A filamentary conductor carrying current I in the az direction extends along the entire negative z axis. At z = 0 it connects to a copper sheet that fills the x > 0, y > 0 quadrant of the xy plane.(a) Set up the Biot-Savart law and find H everywhere on the z axis;(b) Repeat part (a), but with
A disk of radius a lies in the xy plane, with the z axis through its center. Surface charge of uniform density ρs lies on the disk, which rotates about the z axis at angular velocity Ω rad/s. Find H at any point on the z axis.
The parallel filamentary conductors shown in Figure 7.21 lie in free space. Plot |H| versus y,ˆ’4 < y < 4, along the line x = 0, z = 2.Figure 7.21 (0, -1, 0) (0, 1, 0) 1A/ 1A
Two circular current loops are centered on the z axis at z = ± h. Each loop has radius a and carries current I in the aϕ direction.(a) Find H on the z axis over the range −h < z < h. Take I = 1 A and plot |H| as a function of z/a if(b) h = a/4;(c) h = a/2;(d) h = a. Which choice for h
(a) Find H in rectangular components at P(2, 3, 4) if there is a current filament on the z axis carrying 8 mA in the az direction.(b) Repeat if the filament is located at x = −1, y = 2.(c) Find H if both filaments are present.
In free space, let ρν = 2000/r2.4.(a) Use Poisson’s equation to find V(r) if it is assumed that r2Er → 0 when r → 0, and also that V → 0 as r → ∞. (b) Now find V(r) by using Gauss’s law and a line integral.
A potential field in free space is given as V = 100 ln tan(θ/2) + 50 V.(a) Find the maximum value of |Eθ| on the surface θ = 40◦ for 0.1 < r < 0.8 m, 60◦ < ϕ < 90◦.(b) Describe the surface V = 80 V.
Two coaxial conducting cones have their vertices at the origin and the z axis as their axis. Cone A has the point A(1, 0, 2) on its surface, while cone B has the point B(0, 3, 2) on its surface. Let VA = 100 V and VB = 20 V. Find(a) α for each cone;(b) V at P(1, 1, 1).
The hemisphere 0 < r < a, 0 < θ < π/2, is composed of homogeneous conducting material of conductivity σ. The flat side of the hemisphere rests on a perfectly conducting plane. Now, the material within the conical region 0 < θ < α, 0 < r < a is drilled out and replaced
Concentric conducting spheres are located at r = 5 mm and r = 20 mm. The region between the spheres is filled with a perfect dielectric. If the inner sphere is at 100 V and the outer sphere is at 0 V(a) Find the location of the 20 V equipotential surface.(b) Find Er,max.(c) Find r if the surface
Repeat Problem 6.37, but with the dielectric only partially filling the volume, within 0 < ϕ < π, and with free space in the remaining volume.In ProblemCoaxial conducting cylinders are located at ρ = 0.5 cm and ρ = 1.2 cm. The region between the cylinders is filled with a homogeneous
A parallel-plate capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d, with its center on the z axis. Potential V0 is on the top plate; the bottom plate is grounded. Dielectric having radially
The conducting planes 2x + 3y = 12 and 2x + 3y = 18 are at potentials of 100 V and 0, respectively. Let ∈ = ∈0 and find(a) V at P(5, 2, 6);(b) E at P.
Consider the parallel-plate capacitor of Problem 6.30, but this time the charged dielectric exists only between z = 0 and z = b, where b < d. Free space fills the region b < z < d. Both plates are at ground potential. By solving Laplace’s and Poisson’s equations, find(a) V(z) for 0
A uniform volume charge has constant density ρν = ρ0 C/m3 and fills the region r < a, in which permittivity is assumed. A conducting spherical shell is located at r = a and is held at ground potential. Find(a) The potential everywhere;(b) The electric field intensity, E, everywhere.
Let V = (cos 2ϕ)/ρ in free space.(a) Find the volume charge density at point A(0.5, 60◦, 1).(b) Find the surface charge density on a conductor surface passing through the point B(2, 30◦, 1).
A parallel-plate capacitor has plates located at z = 0 and z = d. The region between plates is filled with a material that contains volume charge of uniform density ρ0 C/m3 and has permittivity ∈. Both plates are held at ground potential.(a) Determine the potential field between plates.(b)
Given the potential field V = (Aρ4 + Bρ−4) sin 4ϕ:(a) Show that ∇2V = 0.(b) Select A and B so that V = 100 V and |E| = 500 V/m at P(ρ = 1, ϕ = 22.5◦, z = 2).
The inner conductor of the transmission line shown in Figure 6.13 has a square cross section 2a Ã? 2a, whereas the outer square is 4a Ã? 5a. The axes are displaced as shown. (a) Construct a good-sized drawing of this transmission line, say with a = 2.5 cm, and then prepare a curvilinear-square
A solid conducting cylinder of 4 cm radius is centered within a rectangular conducting cylinder with a 12 cm by 20 cm cross section.(a) Make a full-size sketch of one quadrant of this configuration and construct a curvilinear-square map for its interior.(b) Assume ∈ = ∈0 and estimate C per
Construct a curvilinear-square map of the potential field between two parallel circular cylinders, one of 4 cm radius inside another of 8 cm radius. The two axes are displaced by 2.5 cm. These dimensions are suitable for the drawing. As a check on the accuracy, compute the capacitance per meter
Construct a curvilinear-square map of the potential field about two parallel circular cylinders, each of 2.5 cm radius, separated by a centerto-center distance of 13 cm. These dimensions are suitable for the actual sketch if symmetry is considered. As a check, compute the capacitance per meter both
Construct a curvilinear-square map for a coaxial capacitor of 3 cm inner radius and 8 cm outer radius. These dimensions are suitable for the drawing.(a) Use your sketch to calculate the capacitance per meter length, assuming ∈r = 1.(b) Calculate an exact value for the capacitance per unit length.
Consider an arrangement of two isolated conducting surfaces of any shape that form a capacitor. Use the definitions of capacitance (Eq. (2) in this chapter) and resistance (Eq. (14) in Chapter 5) to show that when the region between the conductors is filled with either conductive material
A 2-cm-diameter conductor is suspended in air with its axis 5 cm from a conducting plane. Let the potential of the cylinder be 100 V and that of the plane be 0 V.(a) Find the surface charge density on the cylinder at a point nearest the plane.(b) Plane at a point nearest the cylinder;(c) Find the
Two #16 copper conductors (1.29 mm diameter) are parallel with a separation d between axes. Determine d so that the capacitance between wires in air is 30 pF/m.
With reference to Figure 6.5, let b = 6 m, h = 15 m, and the conductor potential be 250 V. Take ∈ = 0. Find values for K1, ρL, a, and C.
(a) Determine the capacitance of an isolated conducting sphere of radius a in free space (consider an outer conductor existing at r → ∞).(b) The sphere is to be covered with a dielectric layer of thickness d and dielectric contant r. If ∈r = 3, find d in terms of a such that the capacitance
Two conducting spherical shells have radii a = 3 cm and b = 6 cm. The interior is a perfect dielectric for which r = 8.(a) Find C.(b) A portion of the dielectric is now removed so that ∈r = 1.0, 0 < ϕ < π/2, and r = 8, π/2 < ϕ < 2π. Again find C.
A coaxial cable has conductor dimensions of a = 1.0 mm and b = 2.7 mm. The inner conductor is supported by dielectric spacers (∈r = 5) in the form of washers with a hole radius of 1 mm and an outer radius of 2.7 mm, and with a thickness of 3.0 mm. The spacers are located every 2 cm down the
Two coaxial conducting cylinders of radius 2 cm and 4 cm have a length of 1 m. The region between the cylinders contains a layer of dielectric from ρ = c to ρ = d with r = 4. Find the capacitance if(a) c = 2 cm, d = 3 cm;(b) d = 4 cm, and the volume of the dielectric is the same as in part (a).
A parallel-plate capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d, with its center on the z axis. Potential V0 is on the top plate; the bottom plate is grounded. Dielectric having radially
Let ∈r1 = 2.5 for 0 < y < 1 mm, ∈r2 = 4 for 1 < y < 3 mm, and ∈r3 for 3 < y < 5 mm (region 3). Conducting surfaces are present at y = 0 and y = 5 mm. Calculate the capacitance per square meter of surface area if(a) Region 3 is air;(b) ∈r3 = ∈r1;(c) ∈r3 = ∈r2;(d)
Repeat Problem 6.4, assuming the battery is disconnected before the plate separation is increased.In ProblemAn air-filled parallel-plate capacitor with plate separation d and plate area A is connected to a battery that applies a voltage V0 between plates. With the battery left connected, the plates
Consider a composite material made up of two species, having number densities N1 and N2 molecules/m3, respectively. The two materials are uniformly mixed, yielding a total number density of N = N1 + N2. The presence of an electric field E induces molecular dipole moments p1 and p2 within the
A coaxial conductor has radii a = 0.8 mm and b = 3 mm and a polystyrene dielectric for which ∈r = 2.56. If P = (2/ρ)aρ nC/m2 in the dielectric, find(a) D and E as functions of ρ;(b) Vab and χe.(c) If there are 4×1019 molecules per cubic meter in the dielectric, find p(ρ).
Atomic hydrogen contains 5.5 × 1025 atoms/m3 at a certain temperature and pressure. When an electric field of 4 kV/m is applied, each dipole formed by the electron and positive nucleus has an effective length of 7.1 × 10−19 m.(a) Find P.(b) Find ∈r.
The line segment x = 0,−1 ≤ y ≤ 1, z = 1, carries a linear charge density ρL = π|y|μ C/m. Let z = 0 be a conducting plane and determine the surface charge density at:(a) (0, 0, 0);(b) (0, 1, 0).
In cylindrical coordinates, let ρν = 0 forρ < 1 mm, ρν = 2 sin(2000 πρ) nC/m3 for 1 mm < ρ < 1.5 mm, and ρν = 0 for ρ > 1.5 mm. Find D everywhere.
A crude device for measuring charge consists of two small insulating spheres of radius a, one of which is fixed in position. The other is movable along the x axis and is subject to a restraining force kx, where k is a spring constant. The uncharged spheres are centered at x = 0 and x = d, the
A hollow cylindrical shell of radius a is centered on the z axis and carries a uniform surface current density of Kaaφ.(a) Show that H is not a function of ϕ or z.(b) Show that Hϕ and Hρ are everywhere zero.(c) Show that Hz = 0 for ρ > a.(d) Show that Hz = Ka for ρ < a.(e) A second
A toroid having a cross section of rectangular shape is defined by the following surfaces: the cylinders ρ = 2 and ρ = 3 cm, and the planes z = 1 and z = 2.5 cm. The toroid carries a surface current density of −50az A/m on the surface ρ = 3 cm. Find H at the point P(ρ, ϕ, z):(a) PA(1.5 cm,
Assume that there is a region with cylindrical symmetry in which the conductivity is given by σ = 1.5e−150ρ kS/m. An electric field of 30az V/m is present.(a) Find J.(b) Find the total current crossing the surfaceρ < ρ0, z = 0, all ϕ.(c) Make use of Ampere’s circuital law to find H.
A current filament carrying I in the −az direction lies along the entire positive z axis. At the origin, it connects to a conducting sheet that forms the xy plane.(a) Find K in the conducting sheet.(b) Use Ampere’s circuital law to find H everywhere for z > 0;(c) Find H for z < 0.
A current filament on the z axis carries a current of 7 mA in the az direction, and current sheets of 0.5 az A/m and −0.2 az A/m are located at ρ = 1 cm and ρ = 0.5 cm, respectively. Calculate H at:(a) ρ = 0.5 cm;(b) ρ = 1.5 cm;(c) ρ = 4 cm.(d) What current sheet should be located at ρ = 4
A wire of 3 mm radius is made up of an inner material (0 < ρ < 2 mm) for which σ = 107 S/m, and an outer material (2 mm < ρ < 3 mm) for which σ = 4×107 S/m. If the wire carries a total current of 100 mA dc, determine H everywhere as a function of ρ.
In spherical coordinates, the surface of a solid conducting cone is described by θ = π/4 and a conducting plane by θ = π/2. Each carries a total current I. The current flows as a surface current radially inward on the plane to the vertex of the cone, and then flows radially outward throughout
A solid conductor of circular cross section with a radius of 5 mm has a conductivity that varies with radius. The conductor is 20 m long, and there is a potential difference of 0.1 V dc between its two ends. Within the conductor, H = 105ρ2aϕ A/m.(a) Find σ as a function of ρ.(b) What is the
A cylindrical wire of radius a is oriented with the z axis down its center line. The wire carries a nonuniform current down its length of density J = bρ az A/m2 where b is a constant.(a) What total current flows in the wire?(b) Find Hin (0 < ρ < a), as a function of ρ;(c) find Hout (ρ
Given the field H = 20ρ2aϕ A/m:(a) Determine the current density J.(b) Integrate J over the circular surface ρ ≤ 1, 0 < ϕ < 2π, z = 0, to determine the total current passing through that surface in the az direction.(c) Find the total current once more, this time by a line integral
Infinitely long filamentary conductors are located in the y = 0 plane at x = n meters where n = 0, ±1, ±2, . . . Each carries 1 A in the azdirection.(a) Find H on the y axis. As a help,(b) Compare your result of part (a) to that obtained if the filaments are replaced by a current
When x, y, and z are positive and less than 5, a certain magnetic field intensity may be expressed as H = [x2yz/(y + 1)]ax + 3x2z2ay − [xyz2/(y + 1)]az. Find the total current in the ax direction that crosses the strip x = 2, 1 ≤ y ≤ 4, 3 ≤ z ≤ 4, by a method utilizing:(a) A surface
Consider a sphere of radius r = 4 centered at (0, 0, 3). Let S1 be that portion of the spherical surface that lies above the xy plane. Find ʃS1 (∇ × H) · dS if H = 3ρ aϕ in cylindrical coordinates.
The magnetic field intensity is given in a certain region of space as H = [(x + 2y)/z2]ay + (2/z)az A/m.(a) Find ∇× H.(b) Find J.(c) Use J to find the total current passing through the surface z = 4, 1 ≤ x ≤ 2, 3 ≤ z ≤ 5, in the az direction.(d) Show that the same result is obtained
Given H = (3r2/ sin θ)aθ + 54r cos θaϕ A/m in free space:(a) Find the total current in the aθ direction through the conical surface θ = 20◦, 0 ≤ ϕ ≤ 2π, 0 ≤ r ≤ 5, by whatever side of Stokes’ theorem you like the best.(b) Check the result by using the other side of Stokes’
A long, straight, nonmagnetic conductor of 0.2 mm radius carries a uniformly distributed current of 2 A dc.(a) Find J within the conductor.(b) Use Ampere’s circuital law to find H and B within the conductor.(c) Show that ∇× H = J within the conductor.(d) Find H and B outside the conductor.(e)
A solid, nonmagnetic conductor of circular cross section has a radius of 2 mm. The conductor is in homogeneous, with σ = 106(1 + 106ρ2) S/m. If the conductor is 1 m in length and has a voltage of 1 mV between its ends, find:(a) H inside;(b) The total magnetic flux inside the conductor.
The cylindrical shell defined by 1 cm < ρ < 1.4 cm consists of a nonmagnetic conducting material and carries a total current of 50 A in the az direction. Find the total magnetic flux crossing the plane ϕ = 0, 0 < z < 1:(a) 0 < ρ < 1.2 cm;(b) 1.0 cm < ρ < 1.4 cm;(c) 1.4
The free space region defined by 1 < z < 4 cm and 2 < ρ < 3 cm is a toroid of rectangular cross section. Let the surface at ρ = 3 cm carry a surface current K = 2az kA/m.(a) Specify the current densities on the surfaces at ρ = 2 cm, z = 1 cm, and z = 4 cm.(b) Find H everywhere.(c)
Use an expansion in rectangular coordinates to show that the curl of the gradient of any scalar field G is identically equal to zero.
A filamentary conductor on the z axis carries a current of 16 A in the az direction, a conducting shell at ρ = 6 carries a total current of 12 A in the −az direction, and another shell at ρ = 10 carries a total current of 4 A in the −az direction.(a) Find H for 0 < ρ < 12.(b) Plot Hϕ
Let A = (3y − z)ax + 2xzay Wb/m in a certain region of free space.(a) Show that ∇ · A = 0.(b) At P(2,−1, 3), find A, B, H, and J.
Let N = 1000, I = 0.8 A, Ï0= 2 cm, and a = 0.8 cm for the toroid shown in Figure 7.12b. Find Vmin the interior of the toroid if Vm= 0 at Ï = 2.5 cm, Ï• = 0.3Ï€. Keep Ï• within the range 0 < Ï• < 2Ï€.Figure 7.12b. z axis
A square filamentary differential current loop, dL on a side, is centered at the origin in the z = 0 plane in free space. The current I flows generally in the aÏ•direction.(a) Assuming that r >> dL, and following a method similar to that in Section 4.7, show that(b) Show thatThe
Planar current sheets of K = 30az A/m and −30az A/m are located in free space at x = 0.2 and x = −0.2, respectively. For the region −0.2 < x < 0.2(a) Find H;(b) Obtain an expression for Vm if Vm = 0 at P(0.1, 0.2, 0.3);(c) Find B;(d) Obtain an expression for A if A = 0 at P.
Show that the line integral of the vector potential A about any closed path is equal to the magnetic flux enclosed by the path, or ∮ A· dL = ʃ B · dS.
A half-wave dipole antenna is known to have a maximum effective area, given as Amax.(a) Write the maximum directivity of this antenna in terms of Amax and wavelength λ.(b) Express the current amplitude, I0, needed to radiate total power, Pr, in terms of Pr, Amax, and λ.(c) At what values of θ
Signals are transmitted at a 1-m carrier wavelength between two identical half-wave dipole antennas spaced by 1 km. The antennas are oriented such that they are exactly parallel to each other.(a) If the transmitting antenna radiates 100 watts, how much power is dissipated by a matched load at the
A large ground-based transmitter radiates 10 kW and communicates with a mobile receiving station that dissipates 1mW on the matched load of its antenna. The receiver (not having moved) now transmits back to the ground station. If the mobile unit radiates 100 W, what power is received (at a matched
Consider an n-element broadside linear array. Increasing the number of elements has the effect of narrowing the main beam. Demonstrate this by evaluating the separation in ϕ between the zeros on either side of the principal maximum at ϕ = 90◦. Show that for large n this separation is
In a linear endfire array of n elements, a choice of current phasing that improves the directivity is given by the Hansen€“Woodyard condition:where the plus or minus sign choices give maximum radiation along Ï• = 180—¦ and 0—¦, respectively. Applying this
A six-element linear dipole array has element spacing d = λ/2.(a) Select the appropriate current phasing, ξ, to achieve maximum radiation along ϕ = ±60◦.(b) With the phase set as in part (a), evaluate the intensities (relative to the maximum) in the broadside and endfire directions.
Consider a linear endfire array, designed for maximum radiation intensity at ϕ = 0, using ξ and d values as suggested in Example 14.5. Determine an expression for the front-to-back ratio (defined in Problem 14.22) as a function of the number of elements, n, if n is an odd number.
A turnstile antenna consists of two crossed dipole antennas, positioned in this case in the xy plane. The dipoles are identical, lie along the x and y axes, and are both fed at the origin. Assume that equal currents are supplied to each antenna and that a zero phase reference is applied to the
In the two-element endfire array of Example 14.4, consider the effect of varying the operating frequency, f, away from the original design frequency, f0, while maintaining the original current phasing, ξ = −π/2. Determine the values of ϕ at which the maxima occur when the frequency is changed
Design a two-element dipole array that will radiate equal intensities in the ϕ = 0, π/2, π, and 3π/2 directions in the H plane. Specify the smallest relative current phasing, ξ, and the smallest element spacing, d.
Consider a lossless half-wave dipole in free space, with radiation resistance, Rrad = 73 ohms, and maximum directivity Dmax = 1.64. If the antenna carries a 1-A current amplitude,(a) How much total power (in watts) is radiated?(b) How much power is intercepted by a 1-m2 aperture situated at

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Engineering Electromagnetics 8th edition William H. Hayt, John A.Buck - Solutions

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