G opamp feedback network insensitive to absolute

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Unformatted text preview: g. contacts) – Run-to-run variations – Random variations between devices • Absolute resistor value – E.g. filter time constant, bias current (BG reference) – ~ 15 percent variations (or more) • Resistor ratios – E.g. opamp feedback network – Insensitive to absolute resistor value – “unit-element” approach rejects systematic variations (large area for non-integer ratios) – Process gradients – 0.1 … 1 percent matching possible with careful layout EECS 240 Lecture 2: CMOS - passive devices © 2006 A. M. Niknejad and B. Boser 15 Resistor Layout Example: R1 : R2 = 1 : 2 gradient Dummy 0.5 * R2 + ∆R R1 0.5 * R2 - ∆R Dummy EECS 240 Lecture 2: CMOS - passive devices © 2006 A. M. Niknejad and B. Boser 16 Resistor Layout (cont.) Serpentine layout for large values: Better layout (mitigates offset due to thermoelectric effects): See Hastings, “The art of analog layout,” Prentice Hall, 2001. EECS 240 Lecture 2: CMOS - passive devices © 2006 A. M. Niknejad and B. Boser 17 MOSFETs as Resistors • Triode region (“square law”): I D = µCox • W L V VGS − VTH − DS VDS 2 for VGS − VTH > VDS Small signal resistance: W 1 ∂I = D = µCox (VGS − VTH − VDS ) L R ∂VDS R≈ • 1 W µCox (VGS − VTH ) L for VGS − VTH >> VDS Voltage coefficient: VC = 1 ∂R 1 = R ∂VDS VGS − VTH − VDS EECS 240 Lecture 2: CMOS - passive devices © 2006 A. M. Niknejad and B. Boser 18 MOS Resistors Example: R = 1 MΩ R≈ • • • 1 W (VGS − VTH ) L 1 W = L µCox R (VGS − VTH ) µCox 1 = 100 VC V DS = 0V µA × 1MΩ × 2 V V2 1 = VGS − VTH = 1 = 0.5V −1 2V = 1 200 Large R-values realizable in small area Very large voltage coefficient Applications: – MOSFET-C filters: (linearization) Ref: Tsividis et al, “Continuous-Time MOSFET-C Filters in VLSI,” JSSC, pp. 15-30, Feb. 1986. – Biasing: (>1GΩ) Ref: Geen et al, “Single-Chip SurfaceMicromachined Integrated Gyroscope with 50o/hour Root Allen Variance,” ISSCC, pp. 426-7, Feb. 2002. EECS 240 Lecture 2: CMOS - passive devices © 2006 A. M. Niknejad and B. Boser 19 Resistor Summary • No or limited support in standard CM...
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This note was uploaded on 03/18/2014 for the course EECS 240 taught by Professor Boser during the Spring '04 term at Berkeley.

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