Download Noise Caculations (I) Thermal Noise Calculations. In

Noise Caculations
(I)
Thermal Noise Calculations.
In thermodynamics, Kinetic theory shows that the temperature of a
particle is a way of expressing its internal kinetic energy and hence the
power on it. The resistor determines amount of current on the circuit
and hence the noise on it. Therefore the noise generated by a resistor is
proportional to its absolute temperature and the bandwidth, over which
the noise is to be measured.
Ie The maximum noise power Pn generated by the resistor is given as:
Pn=kTBw
Where: k= Boltzmann`s constant=1.38x10^-23
T=Temperature in Kelvin
Bw= Bandwidth
Pn=Maximum noise power output generated by the resistor.
But this power on the resistor may be considered to be noise generator,
consider the noise generator circuit below:
Where: R Is the noise generating Resistor and RL is the output
Resistor.
The voltage across RL is V
Maximum Noise Power Received by RL, Pn= V^2 /RL = V^2
/R (Where, RL=R).
Pn=V^2 /R
Vn= VR + VRL
If
R=RL then VR = VRL =V.
Vn = 2V, V=Vn/2.
Thus Pn= ((Vn/2)^2 )/R = Vn^2/4R.
But, Pn=kTBw and thus
Vn^2/4R= kTBw
,
Vn^2 =4kTBwR
Where; Vn is the noise equivalent voltage generated by the resistor
(II) NOISE FIGURE AND SIGNAL TO NOISE RATIO
The noise of a system or network can be defined in three different but
related ways:


noise factor (Fn),
noise figure (NF) and
these properties are definable as a simple ratio, decibel ratio
respectively.
Noise Factor
The Noise Factor (Fn), of a device specifies how much additional noise
the device will contribute to the noise already from the source. The
noise factor at a specified input frequency, is defined as the ratio of
available output noise power
Fn =
available output noise due to source
(1)
The noise factor is expressed as a dimensionless ratio.
 “The noise factor, at a specified input frequency, is defined as the
ratio of the total noise power per unit bandwidth available at the
output port when noise temperature of the input termination is
standard (290 K) to that portion produced at the input frequency
by the input termination.”
 Quantitative measure of receiver performance with respect to
noise for a given bandwidth
 The noise factor can also be defined as:
Where: SNRin and SNRout are the input and output power signalto-noise ratios, respectively
Noise Figure
Noise Figure (NF) is the Noise factor expressed in Decibels,
NF  10 log( F )
Where: SNRin,dB and SNRout,dB are in decibels (dB). The noise
figure is the noise factor, given in dB:
Signal to noise ratio (SNR)
Signal-to-noise ratio (often abbreviated SNR or S/N)defined as the
ratio of a signal power to the noise power corrupting the signal. A ratio
higher than 1:1 indicates more signal than noise.
In less technical terms, signal-to-noise ratio compares the level of a
desired signal (such as music) to the level of background noise. The
higher the ratio, the less obtrusive the background noise is.
SNR 
S ( f ) average  signal  power

N ( f ) average  noise  power
where P is average power. Both signal and noise power must be
measured at the same or equivalent points in a system, and within
the same system bandwidth. If the signal and the noise are measured
across the same impedance, then the SNR can be obtained by
calculating the square of the amplitude ratio:
where A is root mean square (RMS) amplitude (for example, typically,
RMS voltage). Because many signals have a very wide dynamic range,
SNRs are usually expressed in terms of the logarithmic decibel scale.
In decibels, the SNR is, by definition, 10 times the logarithm of the
power ratio:
References: Wikipedia Noise, Wikipedia Noise figure