Ruido

1
Ruido

• Dispositivos Semiconductores

2
Basics

• RMS value
• Mean value
• Variance s2 (standar dev. s)

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Basics

• Gaussian distribution
• Has a probability density function

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Motivation Flash AD Converter

• A 3-volts 16 bits ADC (analog to digital
  converter)
• One bit is equivalent to
• Noise has to be less than half LSB (less
  significant bit)

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Noise definition and sources

• Noise random noise of a physical (often thermal)
  origin
• Types
• Johnson (white)
• Shot noise
• Flicker noise (1/f)

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Johnson (thermal) noise

• Product of thermal energy kT
• Flat frequency spectrum
• Same noise power in each hertz of bandwith White
• Gaussian distribution
• In a resistance
• Where k is Boltzmanns constant (4kT1.62 x
  10e-20 V2/Hz-O)
• Example a 10K resistor in a 10Khz bandwith has
  1.3uV

k1.38e-23 V2/ (Hz-O-K)
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Shot Noise

• Due to the discrete nature of charge flow
• q 1.6 e-19
• Shot noise is Gaussian and White
• Formula assumes no correlation in charges (good
  for diodes, not for metallic conductors)

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Shot Noise

• Relative percentage of noise increases when
  current decreases
• Example
• Idc1A, In57nA (0.000006)
• Idc1uA, In3.42pA (0.006)
• Idc1pA, In56fA (5.6)
• B10Khz

Percentage of In with respect to current
(normalized to B1)
I amps
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Flicker Noise

• Excess noise found in many occasions in nature
• Flow of Nile
• Speed of ocean currents
• Intensity of classical music
• Wind blow
• Spectrum 1/f
• For resistor, depends heavily on materials,
  geometry, etc.
• Carbon comp. 0.1µV 3.0µV
• Carbon film 0.05µV 0.3µV
• Metal 0.02µV 0.2µV
• Wire wound 0.01µV 0.2µV
• (rms µV over 1 decade)

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Interference

• Interfering signal or stray pickup is also noise
• Spectrum and characteristics depend on
  interfering signal
• Ex. 50Hz pickup has constant amplitude and fixed
  frequency
• Car ignition noise have broad spectrum
• Radio and TV signals
• Mechanical vibrations
• Effect minimized by shielding and filtering

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Noise Density

• Measured noise depends on bandwith
• RMS Noise density vn
• For a resistor
• Two uncorrelated noise sources are added

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Example

• R11M, R2100K in series
• vn1 0.12µV
• vn2 40nV
• vnt 0.135 µV

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Signal to noise ratio (SNR)

• Relation between signal and noise in db
• Noise figure of an amplifier
• Ratio of the output of a real amplifier to a
  perfect amplifier

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Example

• Two series resistors and source signal 1mV
• SNR ?
• Amplifier (2N6483 Jfet, Id100µA) with en
  7nV/vHz
• NF ?

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Motivation Flash AD Converter

• Suppose a Bandwith B10Khz
• Single resistance noise is
• Maximum resistor value for 22.5µV noise is

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Noise model of an amplifier

• Noiseless transistor
• Noise is modelled with
• current noise source
• voltage noise source
• Input-referred equivalent noise

• Circuits are solved using small-signal models
• The noise sources depend on the transistor type,
  model and bias conditions
• Bipolar
• JFET
• MOS

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Bipolar transistor noise 2N5087

• Johnson noise in the base resistance
• Collector current shot noise across the
  base-emitter junction equivalent resistance
  (Ic/Vt)
• Some 1/f of Ib through rbb (noticeable at high
  currents)

• Shot noise in Ib
• 1/f noise in rbb also manifest

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Bipolar transistor noise

• Total values of noise are determined from the
  small signal model
• Dominant source of noise depends on Rs

• Equivalent input voltage and current noise for
  an npn 2N5087 transistor

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Motivation Flash AD Converter

• Suppose a Bandwith B10Khz
• Using a bipolar input amplifier with I1mA
• Input voltage noise
• Input current noise

(12 bits)
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JFET transistor noise

• voltage noise is the Johnson noise of the
  channel resistance

• Shot noise from leakage current
• This current and the noise increase with temp
  and VDG

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Motivation Flash AD Converter

• Suppose a Bandwith B10Khz
• Using a 2N3954 FET input amplifier with I1mA
• Input voltage noise
• Input current noise

(21 bits)
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Comparison of discrete devices
Current noise
Voltage noise
Bip
Bip
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MOS noise

• Thermal noise
• Channel resistance
• Flicker noise
• Effects of Si-SiO2 interface traps on carriers
• Proportional to area

Total input noise. Orbit 1.2µm process
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References

• Horowitz and Hill, The Art of Electronics, 1989,
  Cambridge Univ. Press
• Randall L. Geiger, Phillip E. Allen, N. Strader,
  VLSI. McGraw Hill, 1990.
• Paul R. Gray, Robert G. Meyer, Analyis and Design
  of Analog Integrated Circuits. John Wiley and
  Sons, 3rd edition, 1993.
• M. Adlerstein, Andreas G. Andreou, Noise
  Measurement, Internal Report, Johns Hopkins
  University, 2005.