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.
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 (Pno) to input noise power (Pni):
To make comparisons easier, the noise factor is always measured at the standard temperature (To) 290°K (standardized room temperature).
The input noise power Pni is defined as the product of the source noise at standard temperature (To) and the amplifier gain (G):
It is also possible to define noise factor Fn in terms of output and input S/N ratio:
Sni is the input signal-to-noise ratio
Sno is the output signal-to-noise ratio
Pno is the output noise power
K is Boltzmann's constant
(1.38 X 10-23 J/°K)
To 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:
N is the noise added by the network or amplifier
(Other terms as previously defined)
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:
NF is the noise figure in decibels (dB)
Fn is the noise factor
LOG refers to the system of base-10 logarithms
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 Te is not the physical temperature of the amplifier, but rather a theoretical construct that is an equivalent temperature that produces that amount of noise power. The noise temperature is related to the noise factor by:
and to noise figure by:
Now that we have noise temperature Te, we can also define noise factor and noise figure in terms of noise temperature:
The total noise in any amplifier or network is the sum of internally and externally generated noise. In terms of noise temperature:
Pn(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:
FN is the overall noise factor of N stages in cascade
F1 is the noise factor of stage 1
F2 is the noise factor of stage 2
Fn is the noise factor of the nth stage
G1 is the gain of stage 1
G2 is the gain of stage 2
Gn-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.
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how can u put the value of Fn how wil came k
in 5-23 eqn
- email@example.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
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
Excerpt from the book published by Prentice Hall Professional (http://www.phptr.com).
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