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Ruido Dispositivos Semiconductores Dispositivos Semicoductores - DIEC/UNS Basics • RMS value: T 1 2 2 2 Vn (rms ) E (v ) v ( t ) dt T1 T2 T1 • Mean value: T 1 2 V E (v ) v(t )dt T1 T2 T1 • Variance σ2 (standar dev. σ) 2 E (v 2 ) E ( v ) Dispositivos Semicoductores - DIEC/UNS Basics • Gaussian distribution – Has a probability density function: Dispositivos Semicoductores - DIEC/UNS Motivation: Flash AD Converter • A 3-volts 16 bits ADC (analog to digital converter) – One bit is equivalent to 3V 45V 216 – Noise has to be less than half LSB (less significant bit) 22.5V 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) 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 Vn (rms) 4kTRB – 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 Shot Noise • Due to the discrete nature of charge flow I n (rms) 2 q I DC B – 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 Shot Noise • Relative percentage of noise increases when current decreases I n (rms) 2 q I DC B Percentage of In with respect to current (normalized to B=1) -2 10 • Example: -3 10 – Idc=1A, In=57nA (0.000006%) – Idc=1uA, In=3.42pA (0.006%) – Idc=1pA, In=56fA (5.6%) -4 10 – B=10Khz -5 10 -6 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 I [amps] 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) 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 Dispositivos Semicoductores - DIEC/UNS Noise Density • Measured noise depends on bandwith • RMS Noise density vn Vn (rms) vn B • For a resistor vn (rms ) 4kTR V / Hz v 2 n (rms ) 4kTR V 2 / Hz • Two uncorrelated noise sources are added: v va2 vb2 Dispositivos Semicoductores - DIEC/UNS Example • R1=1M, R2=100K in series – vn1= 0.12μV – vn2= 40nV – vnt= 0.135 μV Dispositivos Semicoductores - DIEC/UNS Signal to noise ratio (SNR) • Relation between signal and noise in db VS2 SNR 10log10 2 Vn • Noise figure of an amplifier – Ratio of the output of a real amplifier to a perfect amplifier 4kTRS vn2 vn2 NF 10log10 10log10 1 4 kTR 4 kTR S S Dispositivos Semicoductores - DIEC/UNS Example • Two series resistors and source signal 1mV – SNR = ? • Amplifier (2N6483 Jfet, Id=100μA) with en= 7nV/√Hz – NF = ? Dispositivos Semicoductores - DIEC/UNS Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Single resistance noise is: Vn (rms) 4kTRB • Maximum resistor value for 22.5µV noise is: Rmax 3.1M Dispositivos Semicoductores - DIEC/UNS Noise model of an amplifier • Noiseless transistor • Noise is modelled with: – current noise source – voltage noise source • Input-referred equivalent noise: ea (rms) en2 (in Rs )2 • 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 Bipolar transistor noise 2(kT )2 en 4kTrbb 2qI r 4kTrbb qI c 2 2N5087 in I b 2 2 c e Johnson noise in the base resistance Shot noise in Ib Collector current shot noise across the base-emitter junction equivalent resistance (Ic/Vt) 1/f noise in rbb also manifest Some 1/f of Ib through rbb (noticeable at high currents) Dispositivos Semicoductores - DIEC/UNS 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 Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Using a bipolar input amplifier with I=1mA: – Input voltage noise: Vn (rms) 2 nV 10 Khz 0.2V Hz – Input current noise: Vn (rms) 2 pA 3.6M 10 Khz 600V Hz (12 bits) Dispositivos Semicoductores - DIEC/UNS JFET transistor noise voltage noise is the Johnson noise of the channel resistance en 4 KT 2 2 ; gm I D 3g m Shot noise from leakage current This current and the noise increase with temp and VDG in 3.2 1019 I G B Dispositivos Semicoductores - DIEC/UNS 2 Motivation: Flash AD Converter • Suppose a Bandwith B=10Khz • Using a 2N3954 FET input amplifier with I=1mA: – Input voltage noise: Vn (rms) 10 nV 10 Khz 1V Hz – Input current noise: Vn (rms) 0.5 fA 3.6M 10 Khz 0.15V Hz (21 bits) Dispositivos Semicoductores - DIEC/UNS Comparison of discrete devices Current noise Voltage noise Bip Bip Dispositivos Semicoductores - DIEC/UNS MOS noise • Thermal noise – Channel resistance en 2 4 KT 2 ; gm I D 3g m • Flicker noise – Effects of Si-SiO2 interface traps on carriers – Proportional to area Total input noise. Orbit 1.2µm process Kf 1 en C W L ox f 2 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, 3rd edition, 1993. M. Adlerstein, Andreas G. Andreou, “Noise Measurement, Internal Report,” Johns Hopkins University, 2005. Dispositivos Semicoductores - DIEC/UNS