Practical_Antenna_Handbook_0071639586

C h a p t e r 4 : T r a n s m i s s i o n L i n e s a n d I m p e d a n c e M a t c h i n g 131
Figures 4.8C through 4.8H show the signal waveform at the input end of the transmission
line resulting from a step-function input for various values of mismatched load
impedance (i.e., Z L not equal to Z 0 ). When the load impedance is less than the line impedance
(in this case, 0.5Z 0 ), the reflected wave is inverted as seen in Fig. 4.8C and sums
with the incident wave along the top of the pulse. The reflection coefficient can be determined
by examining the relative amplitudes of the two waves.
When Z L = 2Z 0 , the waveform of Fig. 4.8D results. In this case, the reflected wave is
in phase with the incident wave, so it adds to the incident wave as shown. Waveforms
for a short-circuited load and an open-circuited load are shown in Figs. 4.8E and 4.8F,
respectively. Finally, examples of waveforms resulting from adding capacitive and inductive
reactance to a 50-Ω load are displayed in Figs. 4.8G and 4.8H, respectively. The
waveform in Fig. 4.8G resulted from a capacitance in series with a 50-Ω (matched) resistance;
the waveform in Fig. 4.8H resulted from a 50-Ω resistance in series with an inductance.
Steady-State Response of the Transmission Line
When a CW RF signal is applied to a transmission line, the excitation is sinusoidal (Fig.
4.9), so investigation of the steady-state ac response of the line is useful. By steady-state
we mean a sine-wave excitation of constant amplitude, phase, and frequency.
Our initial examination of the reflected wave that results when the load impedance
does not match Z 0 of the transmission line used a step function, but the same reflection
occurs when the transmission line is excited with a pure sinusoid at a single frequency.
Here, too, when a transmission line is not matched to its load, some of the energy is
absorbed by the load and some is reflected back up the line toward the source. The in-
L
Z o
Z S
Z L
Figure 4.9 AC-excited transmission line.