Download noise

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.
 signal power 
 signal voltage 
 = 20 x log10 

 noise power 
 noise voltage 
SNR = 10 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 = kTf
e =
n
4kTfR
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 =
2qI dc f
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:
 Si/Ni 
NF = 10 x log10 S /N  = 10 x log10 NR
 o o
 Si/Ni 
NR = S /N 
 o o
Equivalent Noise Bandwidth

feq =
f
2
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 -1
NR - 1
2
n
NR = NR1 + Pg
+ ...+ Pg x Pg x Pg
1
1
2
(n-1)
Low Noise Amplifiers
1.
2.
3.
4.
5.
The formula for white noise is only true for metal resistors; other materials are
worse.
Noise effects may be minimized by cooling.
Noise effects may be minimized by limiting the bandwidth of the circuit/system.
Noise amplification may be minimized by impedance matching to transfer the
maximum noise possible out of the circuit/system.
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.
vnoise
harmonic distortion = v
x 100%
signal
total harmonic distortion =
v + v + ... + v 
2
n
 1
x 100%
vsignal
Example Problem
A three stage amplifier has a 3-db system bandwith of 200 kHz determined by an LC
tuned circuit at it's input, and operates at 22 °C. The first stage has a power gain of 14 db
and a NF of 3 db. The second and third stages are identical, with power gains of 20 db
and NF = 8 db. The output is 300 Ω. The input noise is generated by a 10 kΩ resistor.
Calculate:
a.
The noise and power at the input and output of the system assuming
noiseless amplifiers
The overall noise figure for the system
The actual noise voltage and power.
b.
c.
(a)


feq =
f =
200 kHz = 3.14 x 105 Hz
2
2
Pn = kTf = 1.38 x 10-23 x (273 +22) x 3.14 x 105 = 1.28 x 10-15 W
en =
4kTfR =
4 x 1.28 x 10-15 x 10 x 103 = 7.15 µV
Total power gain = 14 db + 20 db + 20db = 54 db = 2.51 x 105
For noisless amplifiers:
Pnoise out = 2.51 x 105 x 1.28 x 10-15 = 3.22 x 10-10 W
enoise out)
(
10
3.22 x 10 x 10 W =
300 Ω
enoise out = 0.311 mV
(b)
With noisy amplifiers:
Pg1 = 14 db = 25.1
Pg2 = Pg3 = 20 db = 100
NF1 = 3 db
NR1 = 2
NF2 = NF3 = 8 db
NR2 = NR3 = 6.31
2
NR2-1
NRn - 1
NR = NR1 + Pg
+ ... + Pg x Pg x Pg
1
1
2
(n-1)
6.31-1
6.31-1
NR = 2 + 25.1 + 25.1x 100 = 2.212
NF = 10 x log10 NR = 10 x log10 (2.212) = 3.45 db
(c)
 Si/Ni 
 = 2.212
NR = 
So/No


So
Pg = S = 2.51 x 105
i
Si/Ni
No

 





2.212 =
=
2.51 x 105 x S /N  2.51 x 105 x N 
i o 
i

No




2.212 = 
5
-15
2.51 x 10 x 1.28 x 10 
No = 7.11 x 10-10 W
enoise out)
(
-10
7.11 x 10
W=
300 Ω
enoise out = 0.462 mV
2