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466 Impedance-matching in antenna systems
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24-9 Coaxial balun transformer
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Load impedance
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Load impedance Z R jX
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Quarter-wave matching sections
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Figure 24-11 shows the elementary quarter-wavelength transformer section connected between the transmission line and the antenna load This transformer is also sometimes called a Q section When designed correctly, this transmission line transformer is capable of matching the normal feedline impedance Zs to the antenna feedpoint impedance ZR The key factor is to have available a piece of transmission line that has an impedance Zo of Zo = Zs ZR [2424]
Most texts show this circuit for use with coaxial cable Although it is certainly possible, and even practical in some cases, for the most part there is a serious flaw in using coax for this project It seems that the normal range of antenna feedpoint impedances, coupled with the rigidly fixed values of coaxial-cable surge impedance available on the market, combines to yield unavailable values of Zo Although there are certainly situations that yield to this requirement, many times the quarter-wave section is not usable on coaxial-cable antenna systems having standard impedance values On parallel transmission line systems, on the other hand, it is quite easy to achieve the correct impedance for the matching section We use the equation above to find a value for Zo, and then calculate the dimensions of the parallel feeders Be-
468 Impedance-matching in antenna systems
ZL Load impedance
/4 Q section
24-11 Quarter-wavelength Q section
cause we know the impedance, and can more often than not select the conductor diameter from available wire supplies, you can use the equation below to calculate conductor spacing: S=D where S is the spacing D is the conductor diameter Z is the desired surge impedance From there you can calculate the length of the quarter-wave section from the familiar 246/FMHz D and S are in the same units 10(Z/276) [2425]
Series matching section
The quarter-wavelength section, covered in the preceding section, suffers from drawbacks: it must be a quarter-wavelength and it must use a specified (often nonstandard) value of impedance The series matching section is a generalized case of
Transmatch circuit 469 the same idea, and it permits us to build an impedance transformer that overcomes these faults According to The ARRL Antenna Book, this form of transformer is capable of matching any load resistance between about 5 and 1200 In addition, the transformer section is not located at the antenna feedpoint Figure 24-12 shows the basic form of the series matching section There are three lengths of coaxial cable: L1, L2, and the line to the transmitter Length L1 and the line to the transmitter (which is any convenient length) have the same characteristic impedance, usually 75 Section L2 has a different impedance from L1 and the line to the transmitter Note that only standard, easily obtainable values of impedance are used here The design of this transformer consists of finding the correct lengths for L1 and L2 You must know the characteristic impedance of the two lines (50 and 75 given as examples), and the complex antenna impedance In the case where the antenna is non resonant, this impedance is of the form Z = R jX, where R is the resistive portion, X is the reactive portion (inductive or capacitive), and j is the so-called imaginary operator (ie, square root of minus one) If the antenna is resonant, then X = 0, and the impedance is simply R The first chore in designing the transformer is to normalize the impedances: N= ZL1 Zo RL Zo XL Zo [2426]
[2427]
[2428]
The lengths are determined in electrical degrees, and from that determination we can find length in feet or meters If we adopt ARRL notation and define A = tan L1, and B = tan L2, then the following equations can be written: If: ZL = R jXL
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