Electrical noise arises from small fluctuations in current and voltage internally generated in electronic components. There are several types of noise including thermal noise due to random electron motion, shot noise from random electron arrival at junctions, and flicker noise from defects. Noise sets fundamental limits on signal detection and system gain. Noise is modeled by adding independent current and voltage sources to circuit elements. System noise performance is characterized by noise figure and noise temperature, with lower noise earlier in a signal chain providing better overall performance.

1. Electrical Noise
Wang C. Ng

2. 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.

3. 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.

4. 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.

5. Thermal noise modeling
• The noise amplitude is represented by the
rms value:
C-V201066.14where
4
−×=
∆=
kT
fkTRnv

6. Thermal noise modeling
• The rms noise voltage for a 1-KΩ resistor is
about 4 nV/Hz1/2
.
• The amplitude distribution is Gaussian with
µ = 0 and σ = vn.
• A series voltage source (vn) can be added to
a resistor to account for the thermal noise.

7. Thermal noise modeling
• Examples:
– A 1-KΩ resistor in a system with a bandwidth
of 100 MHz generates about 40 µV of noise
voltage.
– A 1-MΩ resistor in this system generates about
40 mV of noise voltage.
– 10 1-MΩ resistor in this system generates about
0.4 V of noise voltage.

8. 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.

9. Shot noise modeling
• The noise amplitude is represented by the
rms value:
C106.1where
2
19−
×=
∆=
q
fqIi Dn

10. 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
µ = ID and σ = in.
• A parallel current source (in) can be added
to a diode to account for the shot noise.

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

12. 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.

13. Flicker noise modeling
• The noise amplitude is represented by the
rms value:
1and2to5.0where
1
≅≅
∆=
ba
f
f
I
Ki b
a
n

14. 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.

15. Other noise types
• Burst noise (popcorn noise):

16. System Noise Analysis
Wang Ng

17. 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

18. Noise figure
• Used for resistive source impedance.
• Most communication systems have a 50-Ω
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.

19. 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.

20. System noise
• Internally generated noise can be computed
from:
Nsys = (F - 1)GNin
since Nout = Nsys + GNin

21. 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???)

22. 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)

23. 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.

24. Summary
• System noise measure: Noise figure and
noise temperature
• Internal noise calculation
• Cascade system noise
• First stage noise