Page 345 - Engineering Electromagnetics, 8th Edition

CHAPTER 10 Transmission Lines 327

Finally, the voltage standing wave ratio is defined as:

V sT (z max ) 1 +| |
s ≡ = (92)
V sT (z min ) 1 −| |
Since the absolute voltage amplitudes have divided out, our measured VSWR permits
the immediate evaluation of | |. The phase of is then found by measuring the
location of the first maximum or minimum with respect to the load, and then using
(86) or (89) as appropriate. Once is known, the load impedance can be found,
assuming Z 0 is known.

D10.3. What voltage standing wave ratio results when =±1/2?

Ans. 3

EXAMPLE 10.7
Slotted line measurements yield a VSWR of 5, a 15-cm spacing between successive
voltage maxima, and the first maximum at a distance of 7.5 cm in front of the load.
Determine the load impedance, assuming a 50- impedance for the slotted line.

Solution. The 15-cm spacing between maxima is λ/2, implying a wavelength of
30 cm. Because the slotted line is air-filled, the frequency is f = c/λ = 1 GHz. The
first maximum at 7.5 cm is thus at a distance of λ/4 from the load, which means that
avoltage minimum occurs at the load. Thus will be real and negative. We use (92)
to write
s − 1 5 − 1 2
| |= = =
s + 1 5 + 1 3
So
2 Z L − Z 0
=− =
3 Z L + Z 0
which we solve for Z L to obtain
1 50
Z L = Z 0 = = 10
5 5

10.11 TRANSMISSION LINES
OF FINITE LENGTH
Anew type of problem emerges when considering the propagation of sinusoidal
voltages on finite-length lines that have loads that are not impedance matched. In
such cases, numerous reflections occur at the load and at the generator, setting up a
multiwave bidirectional voltage distribution in the line. As always, the objective is
to determine the net power transferred to the load in steady state, but we must now
include the effect of the numerous forward- and backward-reflected waves.