Matching stubs

A shorted stub can he built to produce almost any value of reactance. This can be used to make an impedance-matching device that cancels the reactive portion of a complex impedance. If you have an impedance of, for example, Z = R + j'30 ft, you need to make a stub with a reactance of ->30 ft to match it. TVo forms of matching stubs are shown in Figs. 19-1 OA and 19-1 OB. These stubs are connected exactly at the feedpoint of the complex load impedance, although they are sometimes placed fijrther baek on the line at a (perhaps) more convenient point. In that case, however, the reactance required will be transformed by the transmission line between the load and the stub.

Quarter-waveleiigth matching sections 339


Transmission Line





Load Impedance


(A) Shorted matching stub made of coaxial cabJe. (B) Schematic representation.

Load Impedance



Quarter-wavelength matching sections

Figure 19-11 shows the elementary quarter-wavelength transformer section connected between the transmission line and the antenna load. This transformer is also sometimes called a Q-secticm. 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 Zu of:

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 Although there are certainly situations that yield to this requirement, many times the quarter wave section is not usable on coaxial-cable antenna systems using standard impedance values.

-Q-Sectkm 4


Quarter-wavelength Q-srrrtion impedance transformer.

On parallel transmission-line systems, on the other hand, it is quite easy to achieve the correct impedance for the matching section. Use Eq,( 19-18) to find a value for Zti then calculate the dimensions of the parallel feeders Because you know the impedance, and can more often than not select the conductor diameter from available wire supplies, you can use the following equation to c alculate conductor spacing:


5 = the spacing

D = the conductor di;imeler (D and S in the same units)

Z = the desired surge impedance.

From there we can calculate the length of the quarter-wave section from the familiar 246IFmi.

Series-matching section

The quarter-wavelength section discussed above suffers front several drawbacks: it must be located at the antenna feedpoint, it must be a quarter-wave length, and it must use a specified (often nonstandard) value of impedance. The series-matching section is a generalized case of the same idea and permits us to build an impedance transformer that overcomes most of these faults. According to The ARRL Antenna Book, this form of transformer is capable of matching any load resistance between about 5 and 1200 ft, in addition, the transformer section is not located at the antenna feedpoint.

Se ries- milch itig section 341

Figure 19 12 show's the basic form of the series-matching section. There are three lengths of coaxial cable: Lt, L2t and the line to the transmitter. Length Li and the line to the transmitter (which is any convenient length) have the same characteristic impedance, usually 75 ft. Section L -> has a different impedance from L\ and the line to the transmitter, usually 75 ft. Notice that only standard, easily obtainable values of impedance are used here.

1 J


! \





19-12 Matching-sectiori Impedance transformer.

The design of this transformer consists of finding the correct, lengths for L] and L2. You must know the characteristic impedance of the two lines (50 and 75 ft are given as examples) and the complex antenna impedance. If 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) anil j is the so-called "imaginary" operator (i.e., V-T). 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:

The lengths are determined in electrical degrees, aiul from that determination you can find length in feet or meters. If you adopt ARRL notation and define A = tan (L|), and B = tan (L-) then the following equations can be written

N =


R -

X =*




Z\ not equal to Zrt.


Physical length in feet: L\* = <L, A)/360 V " (LaA)/360 where

frequency in MHz

The physical length is determined from arctan 04) and arctan (5) divided by 360 and multiplied by the wavelength along the line and the velocity factor Although the sign of B might be selected as either — or +„ the use of + is preferred because a shorter section is obtained. In the event that the sign of A turns out negative, add 180 degrees to the result.

There are constraints on the design of this transformer The impedances of the two sections (¿-i and Li>) cannot be too close together. In general, the following relationships must be observed: Either


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