A 
CALCULATION OF RADIO GAIN 385 
Ey’ = VG, Eo, where Ey is the free-space field 
strength radiated by a doublet. 
When the antenna pattern factors are taken into 
account, the resultant field intensity, following 
equation (30), is 
E = VG, Ey V Fe + Fi2p?D? — 2F\F2pD cos 2. (41) 
Figure 11. Antenna pattern factors F, and F2. 
The factors F; and F2 are functions of the angles 
1 — a and »y+a which the direct and reflected 
rays make with the axis of the beam. Figure 11 is a 
typical antenna pattern. 
GENERAL SOLUTION 
Generalized Reflection Coefficient 
Equation (41) may be simplified by introducing a 
generalized coefficient which includes the effects of 
reflection, divergence, and directivity. The ampli- 
tude of this coefficient will be denoted by K and is 
given by 
K =—pD. (42) 
Substituting fF. = F,K/pD in equation (41) gives 
E =VQFiEyV1+ K?—2Kcos2 (48) 
or 
ip VG. Bs] (1 — K)? + 4K sin? ;: (44) 
If the transmitting antenna is pointed so that the 
direct ray lies in the direction of maximum gain, 
F, = 1, and 
E = VG.E \| (1 — K)'+t 4K sin? 5 (45) 
Gada Va =~ He wee ; (46) 
a) (1 — K)? + 4K sin? ; 
as a function of K for various values of sin 2/2 and 
may be used to calculate E. 
The value of G, to be used in equation (46) may 
and 
Figure 12 shows 
fe 
[sirell= 
z A SK A 7 B ar) 1 
Ficure 12. , E — K)? + 4K sit as a function of 
K and Q. 
be found from the antenna specifications for a given 
set. The free-space field Hy at distance d from a 
transmitting doublet with power output P; is equal to 
3V5 VP. 
Eo = Saas . (47) 
is 
E 120 1o® 
= 
Bis 108 
3 Fy 
2 80 iH ot S 
< TIENT 2 
Sie RH. 2 
2 |_SSOUMIE Seaton 
ao SSS SST soe 
10 50. 100 500 1000 5000 10,000 
d IN METERS 
Ficure 13. Free-space range d as a function of field 
strength Hy and transmitter power Py. 
Figure 13 shows Eo in decibels above 1 microvolt 
per meter as a function of d for various values of 
transmitted power. The free-space field at distance 
of d meters expressed in decibels above 1 microvolt 
per meter for P; watts radiated is 
3V5 VP 
Decibels = 20 login a= | (48) 
PLANE EARTH 
Use of Plane Earth Formula 
The following sectior will show that under cer- 
tain conditions calculations based upon the assump- 
