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Dispositivos Semicoductores - DIEC/UNS Ruido Dispositivos Semiconductores

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

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Dispositivos Semicoductores - DIEC/UNS Basics Gaussian distribution –Has a probability density function:

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Dispositivos Semicoductores - DIEC/UNS 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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Dispositivos Semicoductores - DIEC/UNS 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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Dispositivos Semicoductores - DIEC/UNS 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 (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 V 2 / (Hz-Ω-K)

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Dispositivos Semicoductores - DIEC/UNS 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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Dispositivos Semicoductores - DIEC/UNS 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 Shot Noise Percentage of In with respect to current (normalized to B=1) I [amps]

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

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Dispositivos Semicoductores - DIEC/UNS Example R1=1M, R2=100K in series –v n1 = 0.12μV –v n2 = 40nV –v nt = 0.135 μV

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

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

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Dispositivos Semicoductores - DIEC/UNS Circuits are solved using small-signal models The noise sources depend on the transistor type, model and bias conditions –Bipolar –JFET –MOS Noise model of an amplifier Noiseless transistor Noise is modelled with: –current noise source –voltage noise source Input-referred equivalent noise:

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Dispositivos Semicoductores - DIEC/UNS 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 r bb (noticeable at high currents) Shot noise in Ib 1/f noise in rbb also manifest

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Dispositivos Semicoductores - DIEC/UNS Bipolar transistor noise Equivalent input voltage and current noise for an npn 2N5087 transistor Total values of noise are determined from the small signal model Dominant source of noise depends on Rs

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Dispositivos Semicoductores - DIEC/UNS 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)

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Dispositivos Semicoductores - DIEC/UNS 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 V DG

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Dispositivos Semicoductores - DIEC/UNS 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)

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Dispositivos Semicoductores - DIEC/UNS Comparison of discrete devices Current noiseVoltage noise Bip

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Dispositivos Semicoductores - DIEC/UNS MOS noise Thermal noise –Channel resistance Flicker noise –Effects of Si-SiO 2 interface traps on carriers –Proportional to area Total input noise. Orbit 1.2µm process

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Dispositivos Semicoductores - DIEC/UNS 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, 3 rd edition, 1993. M. Adlerstein, Andreas G. Andreou, Noise Measurement, Internal Report, Johns Hopkins University, 2005.

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