Introduction to Engineering Electromagnetics by Yeon Ho Lee | 9783642361173 | 364236117X

Electromagnetics

Introduction to Engineering Electromagnetics

142 SOLVED PROBLEMS

Question: 10.6

The TE10 mode of frequency 3[GHz] propagates in a rectangular waveguide with dimensions a = 2b = 4[cm] , which is filled with a nonmagnetic, lossless dielectric( n = 1.4 ). Find (a) cutoff frequency, (b) phase constant, (c) phase velocity, and (d) wave impedance. ...

Verified Answer:

(a) From Eq. (10-46), the cutoff frequency is [lat...

Question: 10.10

Show that the TMmn and TEmn modes are independent of each other in a rectangular waveguide, even though they have the same phase constant and the same group velocity. ...

Verified Answer:

The electric and magnetic field phasors of the [la...

Question: 10.8

How many component plane-waves does the TE10 mode contain in a rectangular waveguide with dimensions a and b?? ...

Verified Answer:

For the

TE_{10}

mode, let us rewrit...

Question: 10.7

In a hollow rectangular waveguide with an aspect ratio a/b = 2 (a < 10[cm] ), the TE mode of propagation gives E = 4(ax – ay)sin (20πz – 1.8π ×10^10 t) [V/m] at a point ( x = a/8 and y = b / 4 ) on the cross section of the waveguide. Find (a) phase velocity, (b) cutoff frequency, and (c) complete ...

Verified Answer:

(a) From the given

\mathscr{E}

, we ...

Question: 9.2

A distortionless line has a characteristic impedance Zo = 50[Ω] and a propagation constant γ = 0.01 + j 4.0 [m^-1]at frequency f = 100[MHz] . Find R, L, G, C, and vp. ...

Verified Answer:

From Eqs. (9-25c) and (9-25d), we have

\bet...

Question: 9.3

The power reduces by 1.5dB every 100[m] on a transmission line. Find (a) attenuation constant, and (b) fraction of power at a distance 1[Km] from the input end. ...

Verified Answer:

(a) From Eq. (9-32) we obtain

dB power lo...

Question: 8.22

With reference to the wavepacket expressed by Eq. (8-173), propagating in free space, find (a) H (z , t), and (b) 〈S〉 . ...

Verified Answer:

(a) With the help of the relations

\left|\m...

Question: 8.21

With reference to the three waves expressed by Eqs. (8-153a), (8-153b), and (8- 153c) in Example 8-18, (a) find the power of each wave per unit area of the interface, and (b) verify the law of conservation of energy at the interface. ...

Verified Answer:

(a) Incident power per unit area of the interface ...

Question: 8.20

The dielectric slab waveguide shown in Fig. 8.20 is infinite in extent in the x- and y-directions, having refractive indices n1 > n2. Find the maximum angle of incidence θm for total internal reflection at the interface between the core and cladding. ...

Verified Answer:

Applying Snell’s law to the entrance surface, we h...

Question: 8.19

On the front surface of a dielectric slab as shown in Fig. 8.19, a uniform plane wave with parallel polarization is incident at Brewster angle θB . Show that the wave also experiences no reflection at the rear surface which is parallel to the front one. ...

Verified Answer:

Substituting

\theta _{B} = 90^{\circ } - \t...