Electrical Noise

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Electrical Noise

• Wang C. Ng

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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.

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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.

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Thermal noise modeling

• The noise amplitude is represented by the rms
  value

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Thermal noise modeling

• The rms noise voltage for a 1-KW resistor is
  about 4 nV/Hz1/2.
• The amplitude distribution is Gaussian with m 0
  and s vn .
• A series voltage source (vn) can be added to a
  resistor to account for the thermal noise.

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Thermal noise modeling

• Examples
• A 1-KW resistor in a system with a bandwidth of
  100 MHz generates about 40 mV of noise voltage.
• A 1-MW resistor in this system generates about 40
  mV of noise voltage.
• 10 1-MW 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.

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Shot noise modeling

• The noise amplitude is represented by the rms
  value

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

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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 mA 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.

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Flicker noise modeling

• The noise amplitude is represented by the rms
  value

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.

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Other noise types

• Burst noise (popcorn noise)

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System Noise Analysis

• Wang Ng

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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

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Noise figure

• Used for resistive source impedance.
• Most communication systems have a 50-W 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.

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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.

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System noise

• Internally generated noise can be computed from
• Nsys (F - 1)GNin
• since Nout Nsys GNin

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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)

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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.

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Summary

• System noise measure Noise figure and noise
  temperature
• Internal noise calculation
• Cascade system noise
• First stage noise