Electrical Noise

Wang C. Ng

Nature of electrical noise

• Noise is caused by the small current and voltage fluctuations that are generated internally.

• Noise is basically due to the discrete nature of electrical charges.

• Externally generated noise is not considered here.

Why study noise?

• It sets the lower limit for the detectable signals.

• It sets the upper limit for system gains.

• Develop mathematical models to take the effects of noise into account when analyzing electrical circuits/systems.

• Find ways to reduce noise.

Thermal noise

• Due to random motion of electrons.

• It is ubiquitous (resistors, speakers, microphones, antennas, …)

• It is directly proportional to absolute temperature.

• White noise - Frequency independent up to 1013 Hz.

Thermal noise modeling

• The noise amplitude is represented by the rms value:

C-V 201066.14 where

4

kT

fkTRnv

Thermal noise modeling

• The rms noise voltage for a 1-K resistor is about 4 nV/Hz1/2.

• The amplitude distribution is Gaussian with = 0 and = vn .

• A series voltage source (vn) can be added to a resistor to account for the thermal noise.

Thermal noise modeling

• Examples:– A 1-K resistor in a system with a bandwidth

of 100 MHz generates about 40 V of noise voltage.

– A 1-M resistor in this system generates about 40 mV of noise voltage.

– 10 1-M resistor in this system generates about 0.4 V of noise voltage.

Shot noise

• Shot noise is due to the random arrivals of electron packets at the potential barrier of forward biased P/N junctions.

• It is always associated the a dc current flow in diodes and BJTs.

• It is frequency independent (white noise) well into the GHz region.

Shot noise modeling

• The noise amplitude is represented by the rms value:

C 106.1 where

219

q

fqIi Dn

Shot noise modeling

• The rms noise current for a diode current of 1 mA is about 20 pA/Hz1/2.

• The amplitude distribution is Gaussian with = ID and = in .

• A parallel current source (in) can be added to a diode to account for the shot noise.

Shot noise modeling

• Examples:– For a diode current of 1 mA in a bandwidth of 1

MHz shot noise generates about 20 nA of noise current.

– For a diode current of 10 mA in a bandwidth of 100 MHz shot noise generates about 2 A of noise current.

– 100 diodes would generate .2 mA of noise current.

Flicker noise• Flicker noise is due to contamination and

crystal defects.

• It is found in all active devices.

• It is inversely proportional to frequency (also called 1/f noise) .

• DC current in carbon resistors cause flicker noise.

• Metal film resistors have no flicker noise.

Flicker noise modeling

• The noise amplitude is represented by the rms value:

1 and 2 to5.0 where

1

ba

ff

IKi

b

a

n

Flicker noise modeling

• The constant K1 is device dependent and must be determined experimentally.

• The amplitude distribution is non-Gaussian.

• It is often the dominating noise factor in the low-frequency region.

• It can be described in more details with fractal theory.

Other noise types

• Burst noise (popcorn noise):

System Noise Analysis

Wang Ng

Introduction

• Noise sources can be added to a device models to represent the effect of noise.

• We need a means to characterize the noise performance of a system (black box).

• Noise figure

• Noise temperature

Noise figure

• Used for resistive source impedance.

• Most communication systems have a 50- source impedance (Thevenin equivalent).

• Signal-to-noise (S/N) ratio

• Noise figure: F = (S/N)in / (S/N)out

• F is a direct measure of the S/N ratio degradation caused by the system.

Noise figure calculations

• For an ideal (noiseless) amplifier:

Sout = G Sin

Nout = G Nin

• For a real system:

F = (Sin/Nin)(Nout/Sout) = Nout/GNin

or F = (Total noise)/(Noise due to input)

• F in in general frequency dependent.

System noise

• Internally generated noise can be computed from:

Nsys = (F - 1)GNin

since Nout = Nsys + GNin

Cascade systems

• Gain: Gtotal = G1 G2 … GN

• Noise figure:

Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/G1G2 + … + (FN - 1)/G1G2 … GN

• What does this tell us?

We should pay most attention to the reduce the noise of the first system (Why???)

Noise temperature

• It is the temperature at which the noise generated from the source resistance equals to the system noise.

• The noise temperature of a system is a better measure when F is close to 1 (low-noise system)

• Noise temperature: Tn = T(F-1)

Radiometer

• A modern radiometer can measure noise temperature variation down to 100th or even less in K.

• This instrument can be used for remote sensing/imaging.

• Possible extra credit presentation.

Summary

• System noise measure: Noise figure and noise temperature

• Internal noise calculation

• Cascade system noise

• First stage noise