Analog Integrated Circuits (Jieh Tsorng Wu)

84 105 nv2 f 103 pn2 noise 20 d f 20 2 102 2 103 f

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Unformatted text preview: creased by adding the M6 common-source stage. Output Stages 10-27 Analog ICs; Jieh-Tsorng Wu Parallel Common-Source Configuration EP1 VOS VDD M1 VDD V2 V3 EP2 M11 Io Vo Vi M2 VOS RL EN2 M12 VSS VSS EN1 VDD IB2 VDD M5 M3 M4 V1 Output Stages M21 M22 V3 VB M23 EP2 Amplifier VSS 10-28 VB M24 M25 IB1 EP1 Amplifier V2 V2 V2 V2 V1 IB2 M6 M26 VSS Analog ICs; Jieh-Tsorng Wu Parallel Common-Source Configuration • Want turn off M11 and M12 when Vo ≈ Vi = 0, so that AE P 2 and AE N 2 have high gain, and AE P 1 and AE N 1 have low gain. • VOS of EP1 is introduced by making (W/L)3 ID3 = IB1 · AE P 1 = 0.8(W/L)4 . When Vo ≈ Vi = 0, (W/L)3 ID1 = (ID3 − IB2 ) · (W/L)3 + (W/L)4 gm3 = gm5 ID3 kn (W/L)3 · · kp (W/L)5 ID3 − IB2 (W/L)1 (W/L)3 AE P 2 ≈ gm22ro22 • When |Vi | is small, and M11 and M12 are not turned on, the output is Vo = Output Stages Vi 1 + 1/(A1gm1RL) 10-29 Analog ICs; Jieh-Tsorng Wu Parallel Common-Source Configuration • When Vi is large, M11 can be turned on, and the output becomes Vo ≈ Vi − VOS if AE P 2 → ∞ • When V2+ = V2− at EP2, define V3 = Vov 25 + Vt25 + VSS = VK + VSS . Then V3 = [Vo − (Vi − VOS )]AE P 1AE P 2 + VK + VSS Define Vi (mi n) as the minimum input to turn on M11. Let V3 = VDD − |Vtp11|, we have Vi (mi n) = VOS (1 + AE P 1gm1RL) − (VDD − VSS − VK − |Vtp11 |)(1 + AE P 1gm1RL) AE P 1AE P 2 Vi (mi n) = VOS (1 + AE P 1gm1RL) if AE P 2 → ∞ M11 and M12 remain off for only a small range of input voltages. Output Stages 10-30 Analog ICs; Jieh-Tsorng Wu Noise Analysis and Modeling Jieh-Tsorng Wu ES A December 5, 2002 1896 National Chiao-Tung University Department of Electronics Engineering Noise in Time Domain n(t) PDF t 0 n 0 1 Mean = n = T T n(t )d t = 0 0 1 Noise Power = n2 = T Root Mean Square = nrms = n2 T n 2 (t )d t 0 1/2 • T is a suitable averaging time interval. Typically, a longer T gives a more accurate measurement. Noise 11-2 Analog ICs; Jieh-Tsorng Wu Probability Density Function • The probability that the noise lies between values n and n + d n at any time is given by P (n)d n. P (n) is the probability density function (PDF). • The PDF of a random noise is usually Gaussian, i.e., 1 P (n) = √ 2πσ 2 − n2 e 2σ We have +∞ −∞ PDF(n)d n = 1 and Variance = Noise +∞ −∞ n2 · PDF(n)d n = n2 = σ 2 11-3 Analog ICs; Jieh-Tsorng Wu Noise in Frequency Domain BPF One-sided power spectral density n f f n2(f ) SD(f ) = lim ∆f →0 ∆f Power Meter Spectral Density One-sided root spectral density 2 V Hz RD(f ) = (SD)1/2 log f The total noise power is Root Spectral Density ∞ V √ Hz SDn(f )d f = n2 0 log f Noise 11-4 Analog ICs; Jieh-Tsorng Wu Filtered Noise ni no H(s) SDno (f ) = SDni (f ) × |H (j 2πf )|2 If SDni (f ) = N is a constant (white noise), then n2 o = ∞ 0 SDni (f ) · |H (j 2πf )| d f = N · 2 ∞ |H (j 2πf )|2d f = N · Bn 0 • Bn is called the noise bandwidth of the filter. • For a single-pole filter H (s) = Bn = ∞ 1 , 1+s/ωo |H (j 2πf )|2d f = 0 Noise ∞ 0 11-5 1 1+ f fo 2 df = π ·f 2o Analog ICs; Jieh-Tsorng Wu Noise Summation n i1 H 1 (s) n i2 H 2 (s) n i3 H 3 (s) n i1 n o1 n o2 n i2 If two noises, ni and nj , are uncorrelated then, i.e., ni · nj = 0. Then n21 = (ni 1 + ni 2)2 = n21 + n22 + 2 · ni 1ni 2 = n21 + n22 o i i i i SDno2 (f ) = |H1(j 2πf )|2SDni 1 + |H2(j 2πf )|2SDni 2 + |H3(j 2πf )|2 SDni 3 Noise 11-6 Analog ICs; Jieh-Tsorng Wu Piecewise Integration of Noise 200 (nV)2 Hz 20 2 2 2 ∝ 2 0 10 1 10 2 10 N1 f 3 10 N2 1 f 4 10 N3 5 10 6 10 7 10 N4 The noise power in each frequency region is 102 PN1 = 100 2 200 102 2 d f = 200 ln(f )|100 = 1.84 × 105 (nV)2 f 103 PN2 = Noise 20 d f = 20 2 102 2 103 f |102 11-7 = 3.6 × 105 (nV)2 Analog ICs; Jieh-Tsorng Wu Piecewise Integration of Noise 104 PN3 = PN4 103 = = 20 103 ∞ 104 200 2 f df = 1+ 2 20 103 2 200 2 f 105 2 2 = ∞ 0 13 f 3 200 1+ 104 = 1.33 × 108 (nV)2 103 10 4 2 f 105 2 df − 2002d f 0 π 105 − 2002 · 104 = 5.88 × 109 (nV)2 2 Total rms of the noise is nrms = PN1 + PN2 + PN3 + PN4 1/2 = 77.5 µV rms • 1/f noise tangent principle: Lower a 1/f line until it touches the spectral density curve; the total noise can be approximated by the noise in the vicinity of the 1/f line. Noise 11-8 Analog ICs; Jieh-Tsorng Wu Thermal Noise R R R i2 v2 v2 = 4kT R ∆f 1 i2 = 4kT ∆f R f =0∼∞ T = Absolute Temperature in Kelvins k = 1.38 × 10−23 watt/K-Hz (Boltzmann’s Constant) ∆f = Bandwidth per Hertz • Thermal noise is a white noise, i.e., its power spectral density v 2/∆f is independent of frequency, and its amplitude distribution is Gaussian. ◦ • For a 1 kΩ resistor at 300 K, Noise v 2/∆f √ 2 ≈ (4 nV/ Hz) . 11-9 Analog ICs; Jieh-Tsorng Wu Thermal Noise with Loading 2 vo Pn R R RL v2 C v2 • The RL load receives the maximum power if RL = R . Thus the available noise power for RL is 1 · v 2 · Bn = kT Bn Bn = Noise Bandwidth Pn = 4R • For the RC low-pass network 1 1 π = Bn = · 2 2πRC 4RC ◦ 2 vo kT 1 = = 4kT R · 4RC C 2 2 If C = 1 pF a...
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This note was uploaded on 03/26/2013 for the course EE 260 taught by Professor Choma during the Winter '09 term at USC.

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