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 133 V Z L Z o D 0 4 2 3 4 Load end Toward source Figure 4.10 Continued: (D) Z L not equal to Z 0 . terference of incident (or “forward”) and reflected (or “reverse”) waves creates standing waves on the transmission line. If the voltage or current is measured along the line, it will vary, depending on the load, according to Fig. 4.10. In the absence of special instrumentation, such as a directional coupler, the voltage or current seen at any point will be the vector sum of the forward and reflected waves. Figure 4.10A is a voltage-versus-length curve for a matched line—i.e., where Z L = Z 0 . The line is said to be “flat” because both voltage and current are constant all along the line. But now consider Fig. 4.10B and C. Figure 4.10B shows the voltage distribution over the length of the line when the load end of the line is shorted (i.e., Z L = 0). Of course, at the load end the voltage is zero, which results from the boundary condition of a short circuit. As noted earlier, the same conditions are repeated every half-wavelength along the line back toward the generator. When the line is unterminated or open-circuited (i.e., Z L = ∞), the pattern in Fig. 4.10C results. Note that it is the same shape as Fig. 4.10B for the shorted line, but the phase is shifted 90 degrees, or a quarter-wavelength, along the line. In both cases, the reflection is 100 percent, but the phase relationships in the reflected wave are exactly opposite each other. Of course, if Z L is not equal to Z 0 but is neither zero nor infinite, yet another set of conditions will prevail on the transmission line, as depicted in Fig. 4.10D. In this case, the nodes exhibit some finite voltage, V MIN , instead of zero. Standing Wave Ratio One measure of the impact of load mismatch is the standing wave ratio (SWR) on a line. If the current along the line is measured, the pattern will resemble the patterns of Fig. 4.10. The SWR is then called ISWR, to indicate the fact that it came from a current
134 P a r t I I : F u n d a m e n t a l s measurement. Similarly, if the SWR is derived from voltage measurements it is called VSWR. Perhaps because voltage is easier to measure, VSWR (or just plain SWR) is the term most commonly used in most radio work. VSWR can be specified in any of several equivalent ways: • From incident (or forward) voltage (V FWD ) and reflected voltage (V REF ): V VSWR = V FWD FWD + V – V REF REF (4.29) • From transmission line voltage measurements (Fig. 4.10D): V VSWR = V MAX MIN (4.30) • From load and line characteristic impedances: ( Z > Z )VSWR = Z / Z (4.31) L 0 L 0 ( Z < Z )VSWR = Z / Z (4.32) L 0 0 L • From forward (P FWD ) and reflected (P REF ) power: VSWR = 1+ 1– P P REF REF / P / P FWD FWD (4.33) • From reflection coefficient (G): G VSWR = 1+ 1– G (4.34) Of course, it’s also possible to determine the reflection coefficient G from a knowledge of VSWR: G = VSWR – 1 VSWR + 1 (4.35) VSWR is expressed as a ratio. For example, when Z L is 100 Ω and Z 0 is 50 Ω, the VSWR is Z L /Z 0 = 100 Ω/50 Ω = 2, which is usually expressed as VSWR = 2.0:1. However, VSWR can also be expressed in decibel form: VSWR = 20 log (VSWR) (4.36)
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134 P a r t I I : F u n d a m e n t a l s<br />
measurement. Similarly, if the SWR is derived from voltage measurements it is called<br />
VSWR. Perhaps because voltage is easier to measure, VSWR (or just plain SWR) is the<br />
term most commonly used in most radio work.<br />
VSWR can be specified in any of several equivalent ways:<br />
• From incident (or forward) voltage (V FWD ) and reflected voltage (V REF ):<br />
V<br />
VSWR =<br />
V<br />
FWD<br />
FWD<br />
+ V<br />
– V<br />
REF<br />
REF<br />
(4.29)<br />
• From transmission line voltage measurements (Fig. 4.10D):<br />
V<br />
VSWR =<br />
V<br />
MAX<br />
MIN<br />
(4.30)<br />
• From load and line characteristic impedances:<br />
( Z > Z )VSWR = Z / Z<br />
(4.31)<br />
L 0 L 0<br />
( Z < Z )VSWR = Z / Z<br />
(4.32)<br />
L 0 0 L<br />
• From forward (P FWD ) and reflected (P REF ) power:<br />
VSWR = 1+<br />
1–<br />
P<br />
P<br />
REF<br />
REF<br />
/ P<br />
/ P<br />
FWD<br />
FWD<br />
(4.33)<br />
• From reflection coefficient (G):<br />
G<br />
VSWR = 1+<br />
1– G<br />
(4.34)<br />
Of course, it’s also possible to determine the reflection coefficient G from a knowledge<br />
of VSWR:<br />
G = VSWR – 1<br />
VSWR + 1<br />
(4.35)<br />
VSWR is expressed as a ratio. For example, when Z L is 100 Ω and Z 0 is 50 Ω, the<br />
VSWR is Z L /Z 0 = 100 Ω/50 Ω = 2, which is usually expressed as VSWR = 2.0:1. However,<br />
VSWR can also be expressed in decibel form:<br />
VSWR = 20 log (VSWR) (4.36)
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