Match is a simple and robust form of matching a lower impedance Yagi to the transmission line.
This calculator allows calculation of shunt match values to match a nominal impedance Ro.
You need to know the equivalent series resistance at the feed point (Rfeedpoint), the calculator will find:
Rfeedpoint must be less than Ro. As Rfeedpoint approaches Ro, Xbeta becomes impractically large.
The calculator assumes the match device is lossless, good enough for a starting point.
The sign of the shunt match reactance (Xbeta) is opposite to that of the feed point reactance (Xfeedpoint), you can choose which combination you use for convenience of implementation. Cleary if you use a shunt coil for Xbeta, then Xfeedpoint must be negative.
In practice, if you measure Rfeedpoint and design with that value, adjusting the driven element to obtain the needed Xfeedpoint will probably change Rfeedpoint a little, so it is an iterative process to converge on the right values allowing for actual loss etc.
The results are valid only for linear circuits.
The calculator does not do a lot of error checking, if you enter nonsense, it will probably produce nonsense.
If you want to use a hairpin or transmission line section for the match device, The Beta or Hairpin Match sets out a method for designing the hairpin.
A certain 3.7MHz mobile whip has minimum VSWR of 1.3 and is to be matched with a shunt coil. The nature of this antenna means that at VSWR minimum Xfeedpoint is approximately zero and Rfeedpoint=50/1.3=39Ω.
If we assume that Rfeedpoint changes much more slowly than Xfeedpoint, we can assume that Rfeedpoint is almost constant and calculate the required Xfeedpoint and Xbeta.
From the calculator above, |Xfeedpoint|=20.71Ω. |Xbeta| then is 94.15Ω which at say 3.7MHz requires an inductance L=94.15/(2*pi*3.7)=4.05µH.
So the antenna is shortened until Xfeedpoint is around -20Ω and the shunt coil connected and adjusted for minimum VSWR. A small change to antenna length and readjustment of the shunt coil can be pursued for a better match, a perfect match should be achievable.
A certain 144MHz Yagi has a ordinary split dipole driven element with Z approximately 25+j0Ω at 144MHz.
The driven element will be transformed to 200+j0Ω to use an ordinary half wave coax balun. Lets design a beta match.
From the calculator above with inputs Rfeedpoint=25Ω and Ro=200Ω; |Xfeedpoint|=66.14Ω, |Xbeta| then is 75.59Ω.
Lets design a short circuit stub of 4mm wire with 63mm spacing using RF Two Wire Transmission Line Loss Calculator. Length of the stub for X=75.59Ω is 60mm. The dipole is shortened to deliver minimum VSWR at which point the dipole impedance is around 25-j66Ω
(This is essentially the matching scheme used on a Hygain VB-214 Yagi.)
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