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 145 I I max 0 / 4 / 2 Z Length Figure 4.13 Quarter-wavelength shorted stub. Series Matching Section The series matching section—also called the series section transformer—is a generalization of the Q-section that permits us to build an impedance transformer that overcomes the Q-section’s limitations. According to The ARRL Antenna Book, with appropriate choices of transmission lines this form of transformer is capable of matching any load resistance between about 5 and 1200 Ω. In addition, the transformer section does not have to be located at the antenna feedpoint. Figure 4.14 shows the basic layout of the series matching section. Three lengths of coaxial cable, L 1 , L 2 , and L 3 , serve to form the entire feedline connecting the antenna to the transmitter. Lengths L 2 and the line to the transmitter (L 3 , which is any convenient length and doesn’t appear in the equations) have the same characteristic impedance, usually 75 Ω, while section L 1 has a different impedance. Note that only standard, easily obtainable values of impedance are used here. The design procedure for this transformer consists of finding the correct lengths for L 1 and L 2 . You must know the characteristic impedance of the two lines (75 Ω and 50 Ω, respectively, in this example), along with the complex feedpoint impedance of the antenna, Z L = R L + jX L .
146 P a r t I I : F u n d a m e n t a l s L 3 L 1 L 2 Z 0 Z 1 Z 0 R s Z L Figure 4.14 Series matching section. The first task in designing the transformer is to define normalized impedances: N= Z1 Z0 (4.56) R = RL (4.57) Z 0 X = X L (4.58) Z 0 Adopting ARRL notation and defining A = tan L 1 and B = tan L 2 , the following equations can be written: tan L = = 2 B ± 2 2 ( R – 1) + X R{ N – (1/ N ) }– ( R– 1) – X 2 2 2 (4.59) tan N R N × B X L = A = { – ( / )} + 1 R + ( XNB) – 1 (4.60) The lengths of L 1 and L 2 determined from Eqs. (4.59) and (4.60) are in electrical degrees. To find their physical length in feet: L1 (degrees)l L1 (feet) = (4.61) 360 L2 (degrees)l L2(feet) = (4.62) 360
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146 P a r t I I : F u n d a m e n t a l s<br />
L 3<br />
L 1 L 2<br />
Z 0 Z 1 Z 0<br />
R s Z L<br />
Figure 4.14 Series matching section.<br />
The first task in designing the transformer is to define normalized impedances:<br />
N= Z1 Z0<br />
(4.56)<br />
R =<br />
RL (4.57)<br />
Z<br />
0<br />
X =<br />
X L (4.58)<br />
Z 0<br />
Adopting ARRL notation and defining A = tan L 1 and B = tan L 2 , the following equations<br />
can be written:<br />
tan L = =<br />
2<br />
B ±<br />
2 2<br />
( R – 1) + X<br />
R{ N – (1/ N ) }– ( R– 1) – X<br />
2 2 2<br />
(4.59)<br />
tan N R N × B X<br />
L = A = { – ( / )} +<br />
1<br />
R + ( XNB) – 1<br />
(4.60)<br />
The lengths of L 1 and L 2 determined from Eqs. (4.59) and (4.60) are in electrical degrees.<br />
To find their physical length in feet:<br />
L1 (degrees)l<br />
L1<br />
(feet) =<br />
(4.61)<br />
360<br />
L2 (degrees)l<br />
L2(feet)<br />
=<br />
(4.62)<br />
360
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