Practical_Antenna_Handbook_0071639586
492 P a r t V I : A n t e n n a s f o r O t h e r F r e q u e n c i e s Degrees kelvin (K) is the international way of defining all temperatures relative to absolute zero. (No degree symbol is used with K.) To express temperature in degrees kelvin (K) we add 273.16 to a temperature expressed in Celsius. The formula is T(K) = T( ° C) + 273.16 (21.2) Of course, temperatures expressed in Fahrenheit (°F) are related to Celsius by so we also have T(Fahrenheit) = 9 T(Celsius) 32 5 + (21.3) T(K) = 5 T( F) 255.38 9 ° + (21.4) Thus, water turns to ice at 32°F, 0°C, or 273.16 K. Water boils at 212°F, 100°C, or 373.15 K. Absolute zero corresponds to –459.67°F, –273.16°C, or 0 K. Another important point on the various temperature scales is room temperature, typically taken to be 27°C (or about 80°F) by some scientific and engineering specialties. This may be higher than what you or I would want our room to be, but it has the advantage of corresponding to 300 K—a nice round number for doing calculations! Finally, by international agreement, T for terrestrial components and system elements is assumed to be 290 K (about 17°C, or 62°F) unless otherwise stated. To improve weak-signal detection at microwave frequencies and above, however, receiver input stages are often cooled by liquid nitrogen. The markedly lower T of those stages results in their contributing a substantially reduced noise power to the overall system noise figure. Example 21.1 A terrestrial receiver with a 1-MHz bandwidth and a 50-Ω input impedance is connected to a 50-Ω resistor. The noise power delivered to the receiver input stage is (1.38 × 10 –Â23 J/K) × (290 K) × (1,000,000 Hz) = 4 × 10 –15 W. This noise is called thermal noise, thermal agitation noise, or Johnson noise. Noise Factor, Noise Figure, and Noise Temperature The noise performance of a receiving system can be defined in three different, but related, ways: noise factor F n , noise figure (NF), and equivalent noise temperature T e ; these properties are definable as a simple ratio, decibel ratio, or kelvin temperature, respectively. Noise Factor (F n ) For components such as resistors, the noise factor is the ratio of the noise produced by a real resistor to the simple thermal noise of an ideal resistor. The noise factor of a
C h a p t e r 2 1 : A n t e n n a N o i s e T e m p e r a t u r e 493 radio receiver (or any system) is the ratio of output noise power P no to input noise power P ni : F n P = P no ni T = 290 K (21.5) In order to make comparisons easier, the noise factor is usually measured at the standard temperature (T 0 ) of 290 K, although in some countries 299 K or 300 K is commonly used (the differences are generally negligible). It is also possible to define noise factor F n in terms of input and output signal-tonoise ratios: Sni Fn = (21.6) S no where S ni = input signal-to-noise ratio S no = output signal-to-noise ratio Noise Figure (NF) The noise figure is a frequently used measure of a receiver’s “goodness”, or its departure from “idealness”. Thus, it is a figure of merit. The noise figure is the noise factor converted to decibel notation: NF = 10 log F n (21.7) where NF = noise figure, in decibels F n = noise factor “log” refers to the system of base-10 logarithms. (See App. A for an explanation of logarithms.) Noise Temperature (T e ) Noise temperature is a means for specifying noise in terms of an equivalent temperature. Examination of Eq. (21.1) shows that the noise power is directly proportional to temperature in kelvins, and also that noise power collapses to zero at the temperature of absolute zero (0 K). Note The equivalent noise temperature T e is not the physical temperature of the amplifier but, rather, a theoretical construct that is an equivalent temperature that would produce the same amount of noise power in a resistor at that temperature. Noise temperature is related to the noise factor by T F T = ( – 1) e n 0 (21.8)
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C h a p t e r 2 1 : A n t e n n a N o i s e T e m p e r a t u r e 493<br />
radio receiver (or any system) is the ratio of output noise power P no to input noise<br />
power P ni :<br />
F<br />
n<br />
P<br />
=<br />
P<br />
no<br />
ni<br />
T = 290 K<br />
(21.5)<br />
In order to make comparisons easier, the noise factor is usually measured at the<br />
standard temperature (T 0 ) of 290 K, although in some countries 299 K or 300 K is commonly<br />
used (the differences are generally negligible).<br />
It is also possible to define noise factor F n in terms of input and output signal-tonoise<br />
ratios:<br />
Sni<br />
Fn<br />
=<br />
(21.6)<br />
S<br />
no<br />
where S ni = input signal-to-noise ratio<br />
S no = output signal-to-noise ratio<br />
Noise Figure (NF)<br />
The noise figure is a frequently used measure of a receiver’s “goodness”, or its departure<br />
from “idealness”. Thus, it is a figure of merit. The noise figure is the noise factor converted<br />
to decibel notation:<br />
NF = 10 log F n<br />
(21.7)<br />
where NF = noise figure, in decibels<br />
F n = noise factor<br />
“log” refers to the system of base-10 logarithms. (See App. A for an explanation of logarithms.)<br />
Noise Temperature (T e )<br />
Noise temperature is a means for specifying noise in terms of an equivalent temperature.<br />
Examination of Eq. (21.1) shows that the noise power is directly proportional to temperature<br />
in kelvins, and also that noise power collapses to zero at the temperature of<br />
absolute zero (0 K).<br />
Note The equivalent noise temperature T e is not the physical temperature of the amplifier but,<br />
rather, a theoretical construct that is an equivalent temperature that would produce the<br />
same amount of noise power in a resistor at that temperature.<br />
Noise temperature is related to the noise factor by<br />
T F T = ( – 1)<br />
e n 0 (21.8)