noise intro

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