0195136047.pdf

654 SIGNAL PROCESSING

Figure 14.3.6(a), in block diagram form, illustrates a thermal noise source connected to

a matched two-port network having frequency responseH(f)and the output of the network

connected to a matched load. Figure 14.3.6(b) shows a thermal noise source represented by a

resistanceRconnected to an amplifier with a matched input resistance. Presuming the amplifier

to be noiseless, with power gainGand bandwidthB, the output noise power is

Nout=GN=GηB (14.3.7)

whereN =ηBrepresents the source noise power [the area under the power-spectrum curve

falling within the passband, as shown in Figure 14.3.6(c)] accepted by the amplifier as input. The

rms noise voltage for a thermal source connected to a matched resistance is then given by

ηrms=

√

RkT B (14.3.8)

The open-circuit voltage would be twice this value.

Amplifier noisearises from both thermal sources (resistances) and nonthermal sources

(semiconductor devices). Although nonthermal noise is not related to physical temperature and

does not necessarily have a uniform spectrum like that of thermal noise, one still refers to an

amplifier’snoise temperature Ta, for convenience, as a measure of noisiness referred to the input.

The model of a noisy amplifier is shown in Figure 14.3.7(a) with input noiseN=ηB=kT B

from a source at temperatureT,and the output power given by

Nout=GN+Na=GN+GkTaB=Gk(T+Ta)B (14.3.9)

whereNa=GkTaBis the output noise power caused only by the amplifier,Gis the power gain

of the amplifier, andBis the bandwidth of the amplifier. Note that the amplifier noiseNais added

to the amplified source noise to yield the output power in Equation (14.3.9). IfT=T 0 (i.e., room

temperature), thenNout∼=Na, and the amplifier noise dominates the source noise, which is a

common occurrence. WhenTa>>T 0 , the amplifier is very noisy, although not physically hot.

Figure 14.3.7(b) depicts the variation of noise temperature with frequency for a nonthermal

source. Several phenomena lumped together under the termone-over-f( 1 /f )noiselead to the

pronounced low-frequency rise in Figure 14.3.7(b). Such 1/f noise is produced by transistors

and certain transducers, such as photodiodes and optical sensors.

Signals in Noise

Let us now consider a weak information signal that is to be amplified by a noisy amplifier.

Thesignal-to-noise ratio(SNR), usually expressed in decibels, becomes an important system

performance measure. It is given by

Nout = GN + Na

= Gk(T + Ta)B

G, B, Ta

Power

spectrum

N = kTB

f

(^1) f noise
(a) (b)
Figure 14.3.7(a)Model of a noisy amplifier.(b)Power spectrum of nonthermal noise.