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Ruido

Ruido. Dispositivos Semiconductores. Basics. RMS value: Mean value: Variance σ 2 (standar dev. σ ). Basics. Gaussian distribution Has a probability density function: . Motivation: Flash AD Converter. A 3-volts 16 bits ADC (analog to digital converter) One bit is equivalent to

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  1. Ruido Dispositivos Semiconductores Dispositivos Semicoductores - DIEC/UNS

  2. Basics • RMS value: • Mean value: • Variance σ2 (standar dev. σ) Dispositivos Semicoductores - DIEC/UNS

  3. Basics • Gaussian distribution • Has a probability density function: Dispositivos Semicoductores - DIEC/UNS

  4. 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) Dispositivos Semicoductores - DIEC/UNS

  5. Noise definition and sources • Noise: random noise of a physical (often thermal) origin • Types: • Johnson (white) • Shot noise • Flicker noise (1/f) Dispositivos Semicoductores - DIEC/UNS

  6. 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 Boltzmann’s constant (4kT=1.62 x 10e-20 V^2/Hz-Ω) • Example: a 10K resistor in a 10Khz bandwith has 1.3uV k=1.38e-23 V2/ (Hz-Ω-K) Dispositivos Semicoductores - DIEC/UNS

  7. 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) Dispositivos Semicoductores - DIEC/UNS

  8. Shot Noise • Relative percentage of noise increases when current decreases • Example: • Idc=1A, In=57nA (0.000006%) • Idc=1uA, In=3.42pA (0.006%) • Idc=1pA, In=56fA (5.6%) • B=10Khz Percentage of In with respect to current (normalized to B=1) I [amps] Dispositivos Semicoductores - DIEC/UNS

  9. 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) Dispositivos Semicoductores - DIEC/UNS

  10. 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 Dispositivos Semicoductores - DIEC/UNS

  11. Noise Density • Measured noise depends on bandwith • RMS Noise density vn • For a resistor • Two uncorrelated noise sources are added: Dispositivos Semicoductores - DIEC/UNS

  12. Example • R1=1M, R2=100K in series • vn1= 0.12μV • vn2= 40nV • vnt= 0.135 μV Dispositivos Semicoductores - DIEC/UNS

  13. 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 Dispositivos Semicoductores - DIEC/UNS

  14. Example • Two series resistors and source signal 1mV • SNR = ? • Amplifier (2N6483 Jfet, Id=100μA) with en= 7nV/√Hz • NF = ? Dispositivos Semicoductores - DIEC/UNS

  15. Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Single resistance noise is: • Maximum resistor value for 22.5µV noise is: Dispositivos Semicoductores - DIEC/UNS

  16. 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 Dispositivos Semicoductores - DIEC/UNS

  17. 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 Dispositivos Semicoductores - DIEC/UNS

  18. 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 Dispositivos Semicoductores - DIEC/UNS

  19. Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Using a bipolar input amplifier with I=1mA: • Input voltage noise: • Input current noise: (12 bits) Dispositivos Semicoductores - DIEC/UNS

  20. 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 Dispositivos Semicoductores - DIEC/UNS

  21. Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Using a 2N3954 FET input amplifier with I=1mA: • Input voltage noise: • Input current noise: (21 bits) Dispositivos Semicoductores - DIEC/UNS

  22. Comparison of discrete devices Current noise Voltage noise Bip Bip Dispositivos Semicoductores - DIEC/UNS

  23. 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 Dispositivos Semicoductores - DIEC/UNS

  24. 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. Dispositivos Semicoductores - DIEC/UNS

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