4.4. RECEIVER NOISE 157
The quantityσsis the root-mean-square (RMS) value of the noise current induced by
shot noise.
Thermal Noise
At a finite temperature, electrons move randomly in any conductor. Random thermal
motion of electrons in a resistor manifests as a fluctuating current even in the absence
of an applied voltage. The load resistor in the front end of an optical receiver (see Fig.
4.12) adds such fluctuations to the current generated by the photodiode. This additional
noise component is referred to as thermal noise. It is also calledJohnson noise[84]
orNyquist noise[85] after the two scientists who first studied it experimentally and
theoretically. Thermal noise can be included by modifying Eq. (4.4.1) as
I(t)=Ip+is(t)+iT(t), (4.4.6)whereiT(t)is a current fluctuation induced by thermal noise. Mathematically,iT(t)
is modeled as a stationary Gaussian random process with a spectral density that is
frequency independent up tof∼1 THz (nearly white noise) and is given by
ST(f)= 2 kBT/RL, (4.4.7)wherekBis theBoltzmann constant,Tis the absolute temperature, andRLis the load
resistor. As mentioned before,ST(f)is the two-sided spectral density.
The autocorrelation function ofiT(t)is given by Eq. (4.4.2) if we replace the sub-
scriptsbyT. The noise variance is obtained by settingτ=0 and becomes
σT^2 =〈i^2 T(t)〉=∫∞−∞ST(f)df=( 4 kBT/RL)∆f, (4.4.8)where∆fis the effective noise bandwidth. The same bandwidth appears in the case of
both shot and thermal noises. Note thatσT^2 does not depend on the average currentIp,
whereasσs^2 does.
Equation (4.4.8) includes thermal noise generated in the load resistor. An actual re-
ceiver contains many other electrical components, some of which add additional noise.
For example, noise is invariably added by electrical amplifiers. The amount of noise
added depends on the front-end design (see Fig. 4.12) and the type of amplifiers used.
In particular, the thermal noise is different for field-effect and bipolar transistors. Con-
siderable work has been done to estimate the amplifier noise for different front-end
designs [5]. A simple approach accounts for the amplifier noise by introducing a quan-
tityFn, referred to as theamplifier noise figure, and modifying Eq. (4.4.8) as
σT^2 =( 4 kBT/RL)Fn∆f. (4.4.9)Physically,Fnrepresents the factor by which thermal noise is enhanced by various
resistors used in pre- and main amplifiers.
The total current noise can be obtained by adding the contributions of shot noise and
thermal noise. Sinceis(t)andiT(t)in Eq. (4.4.6) are independent random processes