340 ; PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
strength, equation (20), for any transmitting an- 
tenna, becomes 
E = EVGA). (28) 
In defining gain, the electric doublet is selected 
here as the comparison antenna in place of the iso- 
tropic radiator (that is, a hypothetical antenna 
which radiates equally in all directions) which is 
sometimes used in the literature. Since the gain of 
an isotropic radiator relative to a doublet is 74, the 
gain of any antenna referred to an isotropic radiator 
is 32 the value referred to a doublet antenna. 
G (isotropic) = 1.5Gdoublet). (29) 
The chief objections to the isotropic radiator are 
that it does not occur in practice and cannot be 
produced experimentally, even approximately. 
In experimentally measuring the gain of an an- 
tenna, a half-wave dipole is often used as a reference 
antenna. While the gain of a half-wave dipole rela- 
tive to a doublet is approximately unity, being 1.09 
for a very thin dipole, it depends somewhat on its 
actual dimensions so that it is better to express the 
experimental gain in terms of the doublet antenna 
even though a longer antenna is used as a reference 
antenna in making the measurements. 
When antennas are oriented so that the directions 
of polarization make an angle y with each other 
DIRECTION OF 
MAX RADIATION 
TRANS RE 
sO ee Soe Se PIS 
igaqe ae ee ee OY 
TT mes 
TRANSMITTER DIRECTION OF RECEIVER END VIEW 
MAX RE-RADIATION 
Ficure 4. Relation of antenna axes and wave polariza- 
tion. 
(while the maxima of their angular patterns still 
point toward each other), the formulas for power 
transfer, equations (18), (22), and (27), are multi- 
plied by a factor cos? y (see Figure 4). 
The Reciprocity Principle 
So far in this chapter the radiation and reception 
of power by antennas have been treated separately. 
Actually, many of the properties of an antenna-are 
the same for either reception or radiation; in partic- 
ular, the current distribution, the effective length, 
and the gain are unchanged. The reciprocity prin- 
ciple, from which these propositions may be proved, 
may be stated as follows: If an electromotive force 
V, inserted in antenna 1 at a point 21, causes a cur- 
rent IJ to flow at a point x2 in antenna 2, then the 
voltage V applied at 22 will produce the same cur- 
rent I at 2. 
From this principle the statement of the equiva- 
lence of current distribution, effective length, and 
gain follow readily. 
This theorem does not hold when the propagation 
of a wave takes place in an ionized medium in the 
presence of a magnetic field (the ionosphere), but it 
does hold for all cases of transmission discussed in 
this volume, 
RECEIVER SENSITIVITY 
The sensitivity of a-radio receiver is that charac- 
teristic which determines the minimum strength of 
signal input capable of causing a desired value of 
signal output. In high-frequency receivers the 
limiting factor for reception is usually set noise, 
that is, noise produced in the tubes or other ele- 
ments, such as crystals, of the receiver itself. At 
frequencies below about 100 mc, atmospheric dis- 
turbances sometimes exceed the set noise in intensity, 
but at higher frequencies atmospheric static is 
negligible. Man-made noise (automobiles, etc.) 
may be a source of serious trouble, but such inter- 
ference can often be eliminated by proper siting. 
Consequently, for high-frequency receivers, sensi- 
tivity may be expressed, at least approximately, in 
terms of set noise only. 
Although set noise has an important bearing on 
sensitivity of radar receivers, there are other factors 
which must be considered for this type of equipment. 
There are several types of set noise. Though all 
noise sources in a well-designed receiver are mini- 
mized with the exception of the thermal noise whose 
magnitude is independent of equipment construction, 
the total set noise is usually several times the purely 
thermal noise. 
Thermal Noise 
Thermal noise is generated by the random 
(temperature) motion of electrons in a conductor; 
it is, therefore, a universal property of matter and 
independent of the design features of the receiver. 
The rms thermal-noise voltage that appears across 
the terminals of any circuit element is a function of 
the frequency interval (receiver bandwidth) over 
which the noise is averaged; it is given by 
Vn = V4kTAf - R, (30) 
where R is the resistance across which the noise 
voltage is measured, Af the bandwidth in cycles 
per second, 7 the absolute temperature, and k, 
the Boltzmann constant, is equal to 1.38 X 107% 
watt-second per degree. The noise voltage is inde- 
pendent of the reactance components in the circuit. 
Consider now, for the purpose of definition, a 
receiver without internal noise, that is, let all the 
noise be generated in the receiving antenna of re- 
sistance R,. If R, designates the load resistance 
(that is, the resistance of the receiver exclusive of its 
antenna), the average noise power delivered to the 
