Impedance-Matching Section of Line Inserted in Antenna Feeder

This program assists with design of a class of impedance-matching transformers formed by inserting a short section of line, of different Zo, into the feedline between transmitter and antenna. It is applicable to both coaxial and balanced-pair lines. To minimise loss due to standing waves the matching section is best located near the antenna end of the feeder. But in principle it may be inserted anywhere along the length. There are 5 basic variables: Zo and length of feeder between matching section and antenna, Zo and length of matching section, and frequency. Antenna feedpoint impedance, Z = Rin+jXin, is input to the program as is the propagation velocity expressed as a percentage of free-space value.

The main practical constraint imposed on transformer design occurs with coaxial construction due to the small number of readily available impedances. There is the theoretical constraint that matching section Zo must NOT BE INSIDE the range of ZoF/Sqrt(SWR) to ZoF*Sqrt(SWR) where ZoF is the feedline impedance and the SWR is that on the section of feedline immediately adjacent to the antenna.

For many years the design of line transformers has been aided by Smith Charts. This program provides a fast and more reliable procedure.

The computed length of feedline between matching section and the antenna load never exceeds 1/2-wavelength. However, if it is more practical to locate the matching section nearer to the transmitter, the section of feedline adjacent to the antenna can be increased in length by an integral number of 1/2-wavelengths. The length of line from transmitter to transformer is immaterial - the purpose of the transformer is to reduce the SWR on this longest part of the line to 1-to-1.

The matching section of line inserted never exceeds 1/4-wavelength. In the case of open wire lines the matching section can be constructed and installed relatively easily for any Zo from about 150 to 650 ohms.

The program does not take into account conductor resistance loss. Any error in computing line lengths will be negligible on this account. Inevitably, the high SWR which may exist on the transformer itself will result in loss but provided computed SWR is less than 15:1 the adverse effects at HF will be very small.

For a given inner conductor diameter the program computes the diameter of the outer coaxial conductor for both the feedline and matching-section impedances. For the same diameter of balanced-pair conductors and impedances, the conductor spacing is computed. The need for both types of line to be used in one transformer never arises. Line dimensions are likely to be of use only at VHF and higher frequencies where self-supporting rods and tubes can be used.

                       o--------------------o
                       ¦                    ¦
   ->------------------o                    o-------------------o
    Feedline from                               Feedline        Antenna
         Transmitter                             to Antenna     Zin=Rin+jXin
   ->------------------o                    o-------------------o
            ZoF        ¦  Matching Section  ¦        ZoF
                       o--------------------o
                                 Zo

                       <-------------- Transformer ------------->

For given values of ZoF and Zo, Rin and jXin, the program computes the lengths, in wavelengths, of the two lines forming the transformer such that the impedance terminating the line from the transmitter is equal to ZoF.

A warning message is displayed if an impedance match is not possible and the user is asked to change the input data. The most obvious parameter to change is the value of the matching section Zo.

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link MatchSec then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.