Problem 4 (10 points) (Chap 3) (Learning objective: Wave Propagation in TEM transmission line) A voltage wave Voe- travels along a transmission line. The voltage is maximum at = x/4 and t = 0. The wavelength A is 10 cm. Write an expression for this voltage wave as a function of both position and time. Be sure to indicate numerical values in your solution whereever possible.

3. Coaxial cable is used in applications requiring the propagation of high-frequency signal. Such cable consists of a solid conducting cylinder as the inner conductor and a solid conducting cylindrical shell as the outer conductor. A dielectric fills the region between these conductors. Consider the RG-59/U coaxial cable that is commonly used to connect a television/internet equipment. It has an inner conductor with a diameter of 0.584 mm, dielectric filler with a dielectric constant of K = 1.20, and an outer conductor with an inner diameter of 3.7084 mm. Assuming that these conductors are very long, calculate the capacitance per metre of the RG-59/U coaxial cable. Include a derivation of an equation for the capacitance per unit length of the coaxial cable and then use this equation to calculate your answer. (As discussed in class, assign a charge +Q and voltage V to the inner conductor and a charge -Q and 0 V to the outer conductor, solve for the voltage V, and then compute the…

3) Solve the cutoff frequency for the first mode and second mode of WR975 Wave guide TABLE 7.1 Some Standard Rectangular Waveguides Waveguide de signation a (in) b (in) t (in) fe, (GHz) Frequency range (GHz) WR975 9.750 4.875 0.125 0.605 0.75-1.12 WR650 6.500 3.250 0.080 0.908 1.12–1.70 WR430 4.300 2.150 0.080 1.375 1.70-2.60 WR284 2.840 1.340 0.080 2.08 2.60-3.95 WR187 1.872 0.872 0.064 3.16 3.95-5.85 WR137 1.372 0.622 0.064 4.29 5.85-8.20 WR90 0.900 0.450 0.050 6.56 8.2–12.4 WR62 0.622 0.311 0.040 9.49 12.4–18

Solve the cutoff frequency for the first mode and third mode of WR430 waveguide.

Communication system

We have discussed in class that a wire should be treated as a transmission line when its length exceeds an appreciable fraction of the wavelength. If this fraction is 1%, calculate the maximum frequencies at which you can neglect the transmission line effects for the following (assume the wave velocity is equal to speed of light in free space) and make the comparisons indicated: a. Power line of length 300 km (How does this frequency compare with the line frequency used for AC power?) b. Phone line of length 3 km c. USB cable of length 0.3 m (How does this compare with today's USB data rates?) d. CMOS circuit trace of length 300 μm (How does this compare with today's processor frequencies?)

Answer the following questions with simple answer within few lines only. A. If the probability of error of BPSK is 0.85 then Pe of BFSK is? B. What happens to the radio wave propagation when the refractive index of ionospheric layer becomes low or high? C. If the number of quantization levels are multiplied by four time them how many numbers of bits are added to the actual number? D. What is the disadvantage of wave tilt? E. What is a bipolar line coding technique with phase encoding, and explain why it is named as phase encoding method? F. What is oblique communication circuit? G. What are the differences between DPCM and Delta Modulation? H. What is the change in bandwidth when channel capacity is doubled and two number of bits are increased?

Give a waveguide example that can support a TEM wave.

Q/ The wave impedance of the TE10 mode of an air-filled rectangular waveguide at a frequency of 15 GHz is given to be 480 2. a- Calculate the cutoff frequency for the TE10 mode of this waveguide b- Calculate the 'a' dimension for the waveguide c- Calculate the cutoff frequency for the TE11 mode for this waveguide assuming b-0.4a d- Calculate the wave impedance at the frequency of 15 GHz for the TE10 mode if the above waveguide is filled with a dielectric with &,-2.5

COS (2T10 Problem 4. A voltage wave of the form V+ = (2x 10-4V) cos( t-kz is incident from cable 1 with characteristic impedance 201 = 1200 onto a connection to cable 2 with characteristic impedance Z02=1002. Take the speed of the cable wave in each cable to be 2 x 10 m/s. A) Find the amplitudes of the reflected and transmitted voltages. B) Find the incident, reflected, and transmitted powers.