NOTICE THAT THE EXPRESSION
D =3D 2*K*R + (K*R)^2
IS SIMPLY MADE FROM TWO TERMS.
K*(2*R) IS THE GAIN OVER AN ISOTROPIC ANTENNA OF AN ENDFIRE
ARRAY OF LENGTH 2*R, THAT WOULD FIT IN THE SPHERE OF RADIUS
R. FOR EXAMPLE, IT IS THE GAIN OF A LONG YAGI ARRAY.
(K*R)^2 IS THE GAIN OVER AN ISOTROPIC ANTENNA OF A PARABOLOID
OR HORN WHERE R IS THE RADIUS OF THE APERTURE.
IT SEEMS THAT ALL STANDARD ANTENNAS WOULD BE COVERED BY THIS
EQUATION ... AND WE ARE NOT FAR FROM THESE LIMITS SINCE HORNS
AND PARABOLOIDS ARE 45% TO 85% APERTURE EFFICIENT AND LONG
YAGIS ARE USUALLY BETWEEN 80% AND 250% OF THE GAIN PREDICTED
FROM THEIR LENGTH BY 2*K*R.
NOTE THAT FOR ENDFIRE ARRAYS, THERE ARE TWO STANDARD
CONDITIONS. ONE IS THAT THE GAIN IS K*(2*R) OR
K*(BOOMLENGTH). THIS IS THE =D2NORMAL GAIN=D3 CASE. THE OTHER
IS THAT THE GAIN IS 2*K*(2*R) OR 2*K*(BOOMLENGTH), THE
=D2INCREASED GAIN=D3 CASE. BOTH ARE ALLOWED, WITH THE GAIN
DIFFERENCE BEING 3 DB.
PUSHING THE GAIN TO MORE THAN THAT PREDICTED BY THE LENGTH
SHOULD RESULT IN A =D2SUPER-GAIN=D3 ARRAY WITH HIGHER Q REQUIRED
FROM THE ELEMENTS AND A NARROWER BANDWIDTH.
NOTE THAT YAGIS ARE USUALLY MADE OF HALF-WAVE ELEMENTS AND
SHOULD HAVE THE GAIN OF A HALF-WAVE DIPOLE (2.14 DBI) ADDED
TO THE ENDFIRE GAIN (DBI) ... UNLESS THE GAIN IS SPECIFIED AS
OVER A HALF-WAVE DIPOLE (DBD). ( FOR CONVENIENCE, ONLY.)