Page 376 - Engineering Electromagnetics, 8th Edition

358 ENGINEERING ELECTROMAGNETICS

The current through the resistor is most easily obtained by dividing the voltages
in Figure 10.28a by −R g .Asa demonstration, we can also use the current diagram
of Figure 10.22a to obtain this result. Using (120) and (121), we evaluate the current
wavesas follows:

I 1 + = V /Z 0 =−1.2A
+
1
I 1 − =−V /Z 0 =+1.2A
−
1
I 2 + =−I 2 − = V /Z 0 =+0.6A
+
2
I 3 + =−I 3 − = V /Z 0 =−0.30 A
+
3
I 4 + =−I 4 − = V /Z 0 =+0.15 A
+
4
Using these values on the current reflection diagram, Figure 10.22a,we add up
currents in the resistor in time by moving up the left-hand axis, as we did with
the voltage diagram. The result is shown in Figure 10.28b.Asa further check to the
correctness of our diagram construction, we note that current at the open end of the
line (Z = l) must always be zero. Therefore, summing currents up the right-hand
axis must give a zero result for all time. The reader is encouraged to verify this.

REFERENCES
1. White, H. J., P. R. Gillette, and J. V. Lebacqz. “The Pulse-Forming Network.” Chapter 6
in Pulse Generators, edited by G. N, Glasoe and J. V. Lebacqz. New York: Dover, 1965.
2. Brown, R. G., R. A. Sharpe, W. L. Hughes, and R. E. Post. Lines, Waves, and Antennas.
2d ed. New York: The Ronald Press Company, 1973. Transmission lines are covered in
the first six chapters, with numerous examples.
3. Cheng, D. K. Field and Wave Electromagnetics.2d ed. Reading, Mass.: Addison-Wesley,
1989. Provides numerous examples of Smith chart problems and transients.
4. Seshadri, S. R. Fundamentals of Transmission Lines and Electromagnetic Fields.
Reading, Mass.: Addison-Wesley, 1971.

CHAPTER 10 PROBLEMS
10.1 The parameters of a certain transmission line operating at ω = 6 × 10 rad/s
8
are L = 0.35 µH/m, C = 40 pF/m, G = 75 µS/m, and R = 17 /m. Find
γ , α, β, λ, and Z 0 .
10.2 A sinusoidal wave on a transmission line is specified by voltage and current
in phasor form:
αz
αz
V s (z) = V 0 e e jβz and I s (z) = I 0 e e jβz e jφ
where V 0 and I 0 are both real. (a)In which direction does this wave
propagate and why? (b)Itis found that α = 0, Z 0 = 50 , and the wave
8
8 −1
velocity is v p = 2.5 × 10 m/s, with ω = 10 s .Evaluate R, G, L, C, λ,
and φ.