John Smith wrote:
In other words, what set of formulas would give you length, conductor
spacing, gamma capacitor value, ratio of gamma rod to driven element
diameter, and a starting measurement for the shorting bar between
conductors-- for a given frequency?

EZNEC will give you ballpark answers that require
some adjustments to length and capacitance. The
free version of EZNEC is available at www.eznec.com.

What conditions requiring a match is the gamma best suited for?

When your electrical dipole is one piece of metal,
i.e. a physical monopole. The center of 1/2WL of
one piece of metal has the voltage equal to zero
so you cannot feed it there but you can connect
ground to there. Then feed it some distance away
from center through a parallel element and a series
capacitor.
--
73, Cecil http://www.qsl.net/w5dxp

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