### Overview

The noise of a system or network can be defined in three different but related ways: noise factor (Fn), noise figure (NF) and equivalent noise temperature (Te); these properties are definable as a simple ratio, decibel ratio or temperature, respectively.

## Noise factor

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 system is the ratio of output noise power (P_{no}) to input noise power (P

_{ni}):

To make comparisons easier, the noise factor is always measured at the standard temperature (T

_{o}) 290°K (standardized room temperature).

The input noise power P

_{ni}is defined as the product of the source noise at standard temperature (T

_{o}) and the amplifier gain (G):

_{ni}= GKBT

_{0}(5-16)

It is also possible to define noise factor F

_{n}in terms of output and input S/N ratio:which is also:where

S

_{ni}is the input signal-to-noise ratio

S

_{no}is the output signal-to-noise ratio

P

_{no}is the output noise power

K is Boltzmann's constant

(1.38 X 10

^{-23}J/°K)

T

_{o}is 290°K

B is the network bandwidth in hertz (Hz)

G is the amplifier gain

The noise factor can be evaluated in a model that considers the amplifier ideal and therefore amplifies only through gain

*G*the noise produced by the input noise source:orwhere

N is the noise added by the network or amplifier

(Other terms as previously defined)

## Noise figure

The noise figure is a frequently used measure of an amplifier's

*goodness,*or its departure from the ideal. Thus it is

*a figure of merit*

*.*The noise figure is the noise factor converted to decibel notation:

**=**10 LOG F

_{n}(5-21)

where

NF is the noise figure in decibels (dB)

F

_{n}is the noise factor

LOG refers to the system of base-10 logarithms

## Noise temperature

The noise temperature is a means for specifying noise in terms of an equivalent temperature. Evaluating Equation 5-18 shows that the noise power is directly proportional to temperature in degrees Kelvin and that noise power collapses to zero at absolute zero (0°K).

Note that the equivalent noise temperature

*T*

*is not the physical temperature of the amplifier, but rather a theoretical construct that is an*

_{e}*equivalent*temperature that produces that amount of noise power. The noise temperature is related to the noise factor by:

_{e}= (F

_{n}- 1) T

_{o}(5-22)

and to noise figure by:

Now that we have noise temperature T

_{e}, we can also define noise factor and noise figure in terms of noise temperature:

and

The total noise in any amplifier or network is the sum of internally and externally generated noise. In terms of noise temperature:

**P**

_{n(total)}

**= GKB(T**

_{o}+ T

_{e}) (5-26)

where

P

_{n(total)}is the total noise power

(other terms as previously defined)

## Noise in cascade amplifiiers

A noise signal is seen by a following amplifier as a valid input signal. Thus, in a cascade amplifier the final stage sees an input signal that consists of the original signal and noise amplified by each successive stage. Each stage in the cascade chain amplifies signals and noise from previous stages and contributes some noise of its own. The overall noise factor for a cascade amplifier can be calculated from the

*Friis noise equation:*

where

F

_{N}is the overall noise factor of N stages in cascade

F

_{1}is the noise factor of stage 1

**F**

_{2}

**is the noise factor of stage 2**

F

_{n}is the noise factor of the nth stage

G1 is the gain of stage 1

G2 is the gain of stage 2

G

_{n-1}is the gain of stage (n-1).

As you can see from Equation 5-27, the noise factor of the entire cascade chain is dominated by the noise contribution of the first stage or two. High-gain, low-noise amplifiers (such as electroencephalograph [EEG] preamplifiers) typically use a low-noise amplifier circuit for only the first stage or two in the cascade chain.

### Reader Comments | Submit a comment »

how can u put the value of Fn how wil came k
in 5-23 eqn

- sabitha15m@gmail.com - Feb 9, 2012

there s no error in 5.20.. +1 is just
neglected for approximation..

- May 17, 2011

in equation 5-23, it is written as KTo, but
it should be KPni.

- Oct 31, 2008

What will happen if noise sources are
correlated??

- Oct 4, 2007

Equations contains errors!!
How (5-19) can be reduced into (5-20), +1 is
missing
Equation (5-23) contains K?, I think "K" to
be removed unless we can't make the equation
(5-24), please correct these.

- Oct 21, 2006

**equation error**

There's an error in Friis' formula (5.27).
The last denominator should be G1
G2 ... Gn-1, not Gn (this can be
explained intuitively, because the last
gain has no influence on cascaded
noise figure).

- Oct 16, 2006

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