EE 330: ELECTROMAGNETIC FIELD AND WAVES
Home Work-4
Submission Deadline: 2:00pm 25 Nov 2010
Note: Deadline would not be extended. Late assignments will not be accepted.
Question 1:
A generator with an open-circuit voltage and internal
impedance 40+j30 (Ω) is connected to a 50-ohms distortionless line. The line has a resistance of
0.5(Ω/m), and its lossy dielectric medium has a loss tangent of 0.18%. The line is 50(km) long and is
terminated in a matched load. Find
a) The instantaneous expression for the voltage and current at an arbitrary location on the line,
b) The instantaneous expression for the voltage and current at the load
c) The average power transmitted to the load.
Question 2:
A transmission line of characteristic impedance Ro=50 ohms is to be matched to the load
impedance ZL=40+j10 ohms through a length l’ of another transmission line of characteristic impedance
R’o. Find the required length l’ and R’o for matching.
Question 3:
Obtain an analytical expression for the load impedance ZL connected to a line of
characteristic impedance Zo in terms of standing wave ratio ‘S’ and a distance /λ of the voltage
minimum closest to the load.
Question 4: The open circuit and the short circuit impedances measured at the input terminal of a air
space transmission line 4m long are 250<-50o ohms and 360<20o ohms respectively.
a) Determine Zo, α and β of the line.
b) Determine R, L, G and C.
Question 5: A DC generator of voltage Vg and internal resistance Rg is connected to a lossy transmission
line characterized by a resistance per unit length R and a conductance per unit length G.
a)
b)
c)
d)
Write the governing voltage and current transmission line equations.
Find the general solution for V(z) and I(z).
Specialize the solution in part(b) to those for an infinite line.
Specialize the solution in part(b) to those for a finite line of length l that is terminated in a load
resistance RL
Question 6: Measurements on a 0.6m lossless coaxial cable at 100 kHz show a capacitance of 54pF
when the cable is open circuited and an inductance of 0.3uH when it is short circuited.
a) Determine Zo and the dielectric constant of its insulating medium.
b) Calculate the Xio and Xis at 10MHz.
Question 7: A DC voltage Vo is applied at t=0 directly to the input terminals of a lossless air-dielectric
transmission line of length l. the line has a characteristic resistance Ro and is terminated in a load
resistance RL= 2Ro
a) Draw the voltage and current reflection diagrams
b) Sketch V(l,t) and I(l,t).
c) Sketch V(z,2.5T) and I(z,2.5T), where T=l/u.
Question 8: A 300-Ω twin-lead (TEM) cable is delivering RF power to a heating device with impedance
150(1-j) Ω. A single-stub tuner is to be designed to provide a perfect match to this load. The tuner is
shorted at one end and has length L. The characteristic impedance is also 300 Ω.
a) If the stub tuner were connected in series with the 300-Ω line, what is the closest distance to
the load the stub could be placed to yield a match.
b) Repeat part (a) for the case where the stub is connected in parallel.
c) For part (b), what should be the length of the short-circuited stub?