Noise Notes
Noise - Noise is any signal present in your system that you do not want to be in the system.
Signal-to-Noise Ratio
The signal to noise ratio is the most important statistic in any communication system. Intelligibility is dependent upon having a good signal to noise ratio.
SNR = 10 x log10 = 20 x log10
Noise Sources
External:
Natural:
Atmospheric ( mostly lightning ) - 1/f
Solar
Cosmic
Man-Made:
Welders
Ignition
60 Hz and harmonics
Radio
TV
etc.
Internal Noise Sources
White noise - also known as Johnson or thermal noise
Discovered by J.B. Johnson in 1928
Caused by thermal interaction of free electrons and vibrating ions
Random in nature
Varies in amplitude
Equal power throughout the spectrum
The equation for white noise in a metal resistor is given by:
Pn = kTf
en =
Where:
Pn = noise power in watts
en = noise voltage in volts rms
k = 1.38 x 10-23 J/°K
T = temperature in °K
f = bandwidth of circuit/system in Hz
Pink noise - also known as 1/f noise
Amplitude is 1/f
Of little consequence except at low frequencies
Should be infinite @ an infinite period - "big bang"
Shot noise - also known as transistor noise
Shot noise is caused by random movement of electrons within semiconductor devices. The equation for shot noise in a diode is:
in =
Where:
q = 1.6 x 10-19 coulombs (C)
Idc = dc current in amps
f = bandwidth of circuit/system in Hz
There is no exact formula for shot noise in a transistor. Shot noise generally increases with an increase in bias current except in MOSFET's where it is relatively independent.
Noise Figure
The noise figure of an amplifier is a relative indication of the ability of an amplifier to amplify signals without amplifying noise. It is given by the following:
NF = 10 x log10 = 10 x log10 NR
NR =
Equivalent Noise Bandwidth
feq = f
Real filters do not have square bandpasses. Rather bandwidth is defined by the 3 db points. Noise beyond the 3 db points contributes to noise but at a reduced rate. These effects may be accounted for by using an equivalent bandwidth called the noise equivalent bandwidth. It is given by:
Friss' Formula
NR = NR1 + + ...+
Low Noise Amplifiers
1.The formula for white noise is only true for metal resistors; other materials are worse.
2.Noise effects may be minimized by cooling.
3.Noise effects may be minimized by limiting the bandwidth of the circuit/system.
4.Noise amplification may be minimized by impedance matching to transfer the maximumnoise possible out of the circuit/system.
5.Noise minimization is most important in the first stage of amplification.
Coherent Noise
Definition: - Coherent noise is noise that is in phase with the signal. If there is no signal, there is no noise.
Amplitude Distortion: - Distortions in a signal are referred to as amplitude distortion if we are working in the time domain.
Harmonic Distortion: - Distortions in a signal are referred to as harmonic distortion if we are working in the frequency domain.
harmonic distortion = x 100%
total harmonic distortion = x 100%