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# Match Antenna Zin to Feedline Using a Stub-Line Transformer

Author: R.J.Edwards G4FGQ © 24th February 2003
```                                                \
--->-------------------------------o------------o   Antenna
Feedline from xmtr. Impedance = Ro       LineA       Feedpoint
--->---------------------------------o------------o   Zin = R+jX
\

<-- LineB (Stub line)
\
Terminated with open or short --> \
```

LineA and LineB have the same Zo. Both lines are less that 1/2-wavelength. The feedline from the transmitter can have any Ro and be of any length. Velocity factors of LineA and LineB are assumed unity which applies only to air-spaced lines. Physical length of other types must be calculated outside this program.

LineA length is varied until its shunt input resistance equals feedline Ro. The length of LineB is then varied till its shunt input reactance is equal and opposite in sign to the shunt input reactance of LineA. Select the sign of reactance of LineB by terminating it with either a short or an open circuit.

The sign of the reactance can also be reversed by changing length of LineB by crudely 1/4-wavelength. For least loss in transformer prefer shorter lengths.

Transformer Zin is Zin of LineA in shunt with Zin of LineB. The design is complete when transformer Zin equals Ro of the feedline. Line Zin's are displayed as their lengths are varied. Because transformer loss is taken into account the two operations interact and it is necessary to alternate between adjusting Rin of LineA and Xin of LineB to obtain an exact Z-match.

Computed line lengths are in wavelengths. When converting to physical lengths take actual line velocity into account. Also consider whether wide conductor spacing has an effect on electrical length of line - an end effect.

It may be mechanically convenient at VHF and UHF for all three lines to have the same Zo, conductor diameter and spacing. Any two of the three lines may be co-linear, the 3rd line being tapped into the other two. (Three implementations)

Be prepared to change Zo of Lines A and B if first choice does not allow the antenna Zin to be matched to the feedline. The choice is wide and uncritical. Initial choice can be intermediate between Ro of feedline and antenna Zin.

NOTE: THE VALUE OF FEEDLINE IMPEDANCE Ro IS NOT NEEDED BY THIS PROGRAM. INPUT RESISTANCE OF THE TRANSFORMER IS VARIED UNTIL IT IS OBSERVED TO MATCH Ro.