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 theresistor.
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
Fn= / available output noise power / (1)available output noise due to source
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 signal-to-noise ratios, respectively
Noise Figure
Noise Figure (NF) is the Noise factor expressed in Decibels,
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.
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 logarithmicdecibel scale. In decibels, the SNR is, by definition, 10 times the logarithm of the power ratio:
References: Wikipedia Noise, Wikipedia Noise figure