Bài giảng Electromagnetic Fields – Prob - Chapter 7

Electromagnetic Fields – Prob – ch_7

P7.1:

(Ans: a) 15 GHz b) 2.27 cm )

P7.2: The dimension a of an air-dielectric parallel-plate waveguide

is 2 cm. A 20 GHz signal is launched in the waveguide: (a) Find all

the modes that can propagate at this frequency and their cutoff

frequencies ? (b) Find the phase velocities of two TM modes with the

lowest cutoff frequencies ? (c) What should be the maximum plate

seperation to insure that only one mode propagates at this frequency?

(Ans: (a) TM₀₀(0), TE/TM₁₀(7.5G), TE/TM₂₀(15G) (b) 3&3.23166*10⁸m/s (c) 0.75cm )

Electromagnetic Fields – Prob – ch_7

P7.3: The dimension a of an air-dielectric parallel-plate waveguide

is 3 cm. Find the values of  for each of the following cases: (a) f =

6000 MHz, TE₁₀mode; (b) f = 15000 MHz, TE₁₀mode ; (c) f =

15000 MHz, TE₂₀mode.

(Ans: (a) 33.56^o(b) 70.53^o(c) 48.19^o)

P7.4: For a parallel-plate waveguide of spacing a = 3 cm and filled

with a dielectric of  = 6.25₀and  = ₀, find the values of the guide

characteristic impedance for each of the following cases: (a) f = 3000

MHz, TE₁₀mode; (b) f = 3000 MHz, TM₁₀mode ; (c) f = 6000 MHz,

TE₁₀mode.

(Ans: (a) 202.3  (b) 112.4  (c) 159.94  )

Electromagnetic Fields – Prob – ch_7

P7.5: Find the spacing a for a parallel-plate waveguide having a

dielectric of  = 9₀and  = ₀such that 6000 MHz is 20% above the

cutoff frequency of the dominant mode , that is , the mode with the

lowest cutoff frequency.

(Ans: 1 cm )

P7.6: The dimension a of a parallel-plate waveguide with a dielectric

of  = 4₀and  = ₀is 3 cm. Determine the propagating modes for a

wave of frequency 6000 MHz ? For each propagating mode, find _c,

f_c, , and v_pz?

Electromagnetic Fields – Prob – ch_7

P7.7:

(Ans: 1.44 GHz, 173.65 rad/m, 0.036m, 1.81*10⁸m/s, 227.3 )

P7.8:

(Ans: (a) 3.225 GHz, 138.55 rad/m, 0.0453m, 2.267*10⁸m/s, 166.32 (b) )

Electromagnetic Fields – Prob – ch_7

P7.9:

(Ans: axb = 2.25cm x 1.3cm )

P7.10: Consider propagation of TM waves of frequency f = 6000

MHz in an air-dielectric waveguide of square cross section (b = a) .

Find the range of a for which the TM₁₁mode propagates with a 20%

safety factor ( f > 1.2f_c) but also such that f is at least 20% below the

f_cof the next higher-order mode .

(Ans: 4.24 cm < a < 4.47 cm )

Electromagnetic Fields – Prob – ch_7

P7.11: A rectangular waveguide of dimensions a = 3 cm and b = 1.5

cm has a dielectric discontinuity as shown in Fig. 7.11. A TE₁₀wave

of frequency 6000 Mhz is incident on the discontinuity from the free

space side. (a) Find the SWR in the free space section (b) Find the

length and the permittivity of a quarter-wave section require to

archieve a match between he two media. Assume  = ₀for the

quarter-wave section.

Section 1

Section 2

(₀, ₀)

(₀, 4₀)

z

Fig. 7.11

Electromagnetic Fields – Prob – ch_7

P7.12: A rectangular waveguide of dimensions a = 4 cm and b = 2

cm has a dielectric discontinuity as shown in Fig. 7.12. A TM₁₁wave

of frequency 10000 Mhz is incident on the discontinuity from the

free space side. (a) Find the SWR in the free space section (b) Find

the length and the permittivity of a quarter-wave section require to

archieve a match between he two media. Assume  = ₀for the

quarter-wave section.

Section 1

Section 2

(₀, ₀)

(₀, 9₀)

z

Fig. 7.11

(Ans: (a) 1.7 (b) 0.366 cm, 4.9₀)

Electromagnetic Fields – Prob – ch_7

P7.13: For a rectangular waveguide of dimensions a = 3.75 cm and b

= 1.25 cm, and having a dielectric of  = 6.25₀and  = ₀. Find all

propagating modes for f = 5000 MHz , and for each mode, find the

values of _z, _g, v_pzand  .

P7.14:

(Ans: a) 6.55 GHz b) 1069 c) 5.46 mW )

Electromagnetic Fields – Prob – ch_7

P7.15:

(Ans: a) 0.835 GHz b) 0.515 Np/m c) 0.67m )

Bài giảng Electromagnetic Fields – Prob - Chapter 7 - Trần Quang Việt