0195136047.pdf

14.3 INTERFERENCE AND NOISE 653

(a) illustrates a typical thermal noise waveformn(t). In view of the unpredictable behavior, since
the average value ofn(t) may be equal to zero, a more useful quantity is the rms valuenrmsso that
theaverage noise poweris given by

N=n^2 rms/R, ifnrmsis noise voltage (14.3.4)

or

N=n^2 rmsR, ifnrmsis noise current (14.3.5)

The spectrum of thermal noise power is uniformly spread over frequency up to the infrared region
around 10^12 Hz, as shown in Figure 14.3.5(b). Such a distribution indicates thatn(t) contains all
electrical frequencies in equal proportion, and an equal number of electrons is vibrating at every
frequency. By analogy to white light, which contains all visible frequencies in equal proportion,
thermal noise is also referred to aswhite noise.
The constantηin Figure 14.3.5(b) stands for thenoise power spectral density, expressed in
terms of power per unit frequency (W/Hz). Statistical theory shows that

η=kT (14.3.6)

wherekis the Boltzmann constant given by 1. 381 × 10 −^23 J/K andTis the source temperature
in kelvins. Equation (14.3.6) suggests that a hot resistance is noisier than a cool one, which is
compatible with our notion of thermally agitated electrons. At room temperatureT 0 ∼=290 K
(17° C),η 0 works out as 4× 10 −^21 W/Hz.
When we employ amplifiers in communication systems to boost the level of a signal, we are
also amplifying the noise corrupting the signal. Because any amplifier has some finite passband,
we may model an amplifier as a filter with frequency response characteristicH(f). Let us evaluate
the effect of the amplifier on an input thermal noise source.

Noiseless

amplifier

nout(t)

N Nout

n(t)

G, B

R RL

Power

spectrum

B

Bandwidth

fl fu

(c)

0

η

N = ηB

Lower

cutoff

Upper

cutoff

Thermal

noise

source

Amplifier

H(f) Load

(b)

(a)

Matched Matched

Figure 14.3.6Thermal noise converted to amplifier and load.(a)Matched block diagram.(b)Circuit
representing thermal noise at amplifier input.(c)Power spectrum.