Four Voltage References, an ADC and MSP430

Similar documents
Bipolar Emitter-Follower: Riso w/dual Feedback

EE247 Analog-Digital Interface Integrated Circuits

Sample-and-Holds David Johns and Ken Martin University of Toronto

Homework Assignment 08

Switched Capacitor: Sampled Data Systems

SHM-14 Ultra-Fast, 14-Bit Linear Monolithic Sample-Hold Amplifiers

Final Exam. 55:041 Electronic Circuits. The University of Iowa. Fall 2013.

Homework Assignment 11

EXAMPLE DESIGN PART 2

Switched-Capacitor Circuits David Johns and Ken Martin University of Toronto

DESIGN MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OP-AMP CMOS CIRCUIT. Dr. Eman Azab Assistant Professor Office: C

E40M. Op Amps. M. Horowitz, J. Plummer, R. Howe 1

Chapter 10 Feedback. PART C: Stability and Compensation

Operational Amplifiers

ELECTRONIC SYSTEMS. Basic operational amplifier circuits. Electronic Systems - C3 13/05/ DDC Storey 1

Maxim Integrated Products 1

Advanced Current Mirrors and Opamps

Lecture 10, ATIK. Data converters 3

Time Varying Circuit Analysis

Precision, Micropower, Low-Dropout, High- Output-Current, SO-8 Voltage References

UNIVERSITÀ DEGLI STUDI DI CATANIA. Dottorato di Ricerca in Ingegneria Elettronica, Automatica e del Controllo di Sistemi Complessi, XXII ciclo

Systematic Design of Operational Amplifiers

Fig. 2.0: SPICE Loop Gain Test

Monolithic N-Channel JFET Dual

OPERATIONAL AMPLIFIER APPLICATIONS

D/A Converters. D/A Examples

EECE 2150 Circuits and Signals, Biomedical Applications Final Exam Section 3

Lecture 340 Characterization of DACs and Current Scaling DACs (5/1/10) Page 340-1

Lecture 4: Feedback and Op-Amps

Georgia Institute of Technology School of Electrical and Computer Engineering. Midterm-1 Exam (Solution)

Monolithic N-Channel JFET Duals

System on a Chip. Prof. Dr. Michael Kraft

D is the voltage difference = (V + - V - ).

CE/CS Amplifier Response at High Frequencies

Electronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory

KH600. 1GHz, Differential Input/Output Amplifier. Features. Description. Applications. Typical Application

EXAMPLE DESIGN PART 2

Application Report. Mixed Signal Products SLOA021

LASER PULSE DETECTION: The Tradeoff between Pulse Resolution and Responsivity

SGM nA, Non-Unity Gain, Dual Rail-to-Rail Input/Output Operational Amplifier

Lab #4 Capacitors and Inductors. Capacitor Transient and Steady State Response

Design Engineering MEng EXAMINATIONS 2016

H(s) = 2(s+10)(s+100) (s+1)(s+1000)

Low-Sensitivity, Highpass Filter Design with Parasitic Compensation

NCS1002A. Constant Voltage / Constant Current Secondary Side Controller

EMC Considerations for DC Power Design

ESE319 Introduction to Microelectronics. Feedback Basics

Guest Lectures for Dr. MacFarlane s EE3350

MAX14753 V DD INA0 INA1 INA2 INA3 OUT INB0 INB1 INB2 INB3

High-Supply-Voltage, Precision Voltage Reference in SOT23 MAX6035

SGM nA, Non-Unity Gain, Quad Rail-to-Rail Input/Output Operational Amplifier

ECEN 610 Mixed-Signal Interfaces

SC70, 1.6V, Nanopower, Beyond-the-Rails Comparators With/Without Reference

Electronic Circuits Summary

EXAMPLE DESIGN PART 1

Lecture 6, ATIK. Switched-capacitor circuits 2 S/H, Some nonideal effects Continuous-time filters

Lecture 37: Frequency response. Context

General Purpose Transistors

2N5545/46/47/JANTX/JANTXV

Homework Assignment 09

55:041 Electronic Circuits The University of Iowa Fall Final Exam

ENGN3227 Analogue Electronics. Problem Sets V1.0. Dr. Salman Durrani

1/13/12 V DS. I d V GS. C ox ( = f (V GS ,V DS ,V SB = I D. + i d + I ΔV + I ΔV BS V BS. 19 January 2012

SGM nA, Dual Rail-to-Rail I/O Operational Amplifier

Section 4. Nonlinear Circuits

Low Drift, Low Power Instrumentation Amplifier AD621

Pipelined multi step A/D converters

Lecture 310 Open-Loop Comparators (3/28/10) Page 310-1

Stability and Frequency Compensation

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences

Summary Last Lecture

Quick Review. ESE319 Introduction to Microelectronics. and Q1 = Q2, what is the value of V O-dm. If R C1 = R C2. s.t. R C1. Let Q1 = Q2 and R C1

LM108/LM108AQML Operational Amplifiers

ECE 304: Design Issues for Voltage Follower as Output Stage S&S Chapter 14, pp

Figure Circuit for Question 1. Figure Circuit for Question 2

LD A high PSRR ultra low drop linear regulator with reverse current protection. Datasheet. Features. Applications.

Microelectronic Circuit Design 4th Edition Errata - Updated 4/4/14

PT5108. High-PSRR 500mA LDO GENERAL DESCRIPTION FEATURES APPLICATIONS TYPICAL APPLICATIONS. Ripple Rejection vs Frequency. Ripple Rejection (db)

Lecture 4, Noise. Noise and distortion

Bandwidth of op amps. R 1 R 2 1 k! 250 k!

Errata of CMOS Analog Circuit Design 2 nd Edition By Phillip E. Allen and Douglas R. Holberg

Switched-Capacitor Filters

DAC10* PRODUCT PAGE QUICK LINKS Last Content Update: 02/23/2017

SGM nA, Single Rail-to-Rail I/O Operational Amplifier

EXAMPLE DESIGN PART 1

Current feedback operational amplifiers as fast charge sensitive preamplifiers for

ENGR-4300 Spring 2009 Test 2. Name: SOLUTION. Section: 1(MR 8:00) 2(TF 2:00) 3(MR 6:00) (circle one) Question I (20 points): Question II (20 points):

( s) N( s) ( ) The transfer function will take the form. = s = 2. giving ωo = sqrt(1/lc) = 1E7 [rad/s] ω 01 := R 1. α 1 2 L 1.

Ultra-Low-Power Series Voltage Reference

Ω μ. PKG CODE M AX 5128E LA+ -40 C to +85 C 8 μdfn AAF L822-1 TEMP RANGE PIN - PA C K A G E TOP MARK PART. Maxim Integrated Products 1

Cast of Characters. Some Symbols, Functions, and Variables Used in the Book

EE247 Lecture 16. Serial Charge Redistribution DAC

AN019. A Better Approach of Dealing with Ripple Noise of LDO. Introduction. The influence of inductor effect over LDO

RP mA, Ultra-Low Noise, Ultra-Fast CMOS LDO Regulator. General Description. Features. Applications. Ordering Information. Marking Information

Ultra-Low-Power Precision Series Voltage Reference MAX6029. Features. General Description. Ordering Information. Applications.

SERIALLY PROGRAMMABLE CLOCK SOURCE. Features

Frequency Dependent Aspects of Op-amps

Laboratory III: Operational Amplifiers

ADC Bit, 50MHz Video A/D Converter

Experiment Guide for RC Circuits

Transcription:

Four Voltage References, an ADC and MSP430 Tadija Janjic HPL Tucson Michael Ashton DAP

Motivation u Total Solution Concept u Application section of datasheets u New REF products from TI u Greed Product Recognition Increased Revenue 2

Experiment u Verify setup/measurements u Evaluate TI REFs with ADS1256 u Compare different TI REF results u Suggest the optimal circuitry 3

Basic Setup Vss 5 + + R2 R2 1k To ADS Vref R1 R1 1k -!OPAMP Vref C1 1u C1 C2 1u C2 ADS1256, PGA=1, Vref=2.5V 4

Board 5

Board (side view) 6

Considerations u Low Noise u Long term stability Time Temperature 7

Experiment Design R1 C1 OPA R2 C2 RMS noise free bits.... 335 100 10u 227 100 10u Additional considerations: Vin amplitude, f s (data output rate) 8

Confirm the Setup REF R1 C1 OPA R2 C2 RMSnfb 1004 10k 47u 227 100 10u 23.8 VIn=0V, shorted inputs, 9

Results REF R1 C1 OPA R2 C2 RMSnfb 1004 ------ ------ OPA335 100 10u 20.7 1004 10k 220u same same same 22.3 1004 10k 47u same same same 22.4 3025 same same same same same 20.8 3125 same same same same same 20 1112 * same same same same same 22.1 1004 same same OPA227 same same 22.4 Vin=2.5V, data output rate = 60Hz, * OPA in a gain of 2 10

Conclusions u On ADS1256 one needs external buffer Input impedance 18k u Noise-wise OPA227 and OPA335 equal However, we tried at T=25 C u REF1004 and REF1112 similar results u REF3xxx family good for lower precision u RC (settling time vs. noise) trade off 11

MSP430 u Has 12 bit ADC (ADC12) u Has Vref (2.5V or 1.5V) 800uA max 100ppm/ C max 4% initial accuracy TI REFs: 8uA -110 ua max current 15-100ppm/ C 2.048/2.5/3.0V/3.3V 0.2% 12

Results REF R1 C1 Noise RMS bits Internal (2.5V) ------ ------ ~3.1 1004 2.5V 100 47u ~3.0 3025 10k 47u ~2.7 3125 same same ~2.7 1004 same same ~2.7 3125 100 same ~3.0 3025 same same ~3.0 1112 same same 5.5 13

Conclusions Part II u External REFs improve performance Lower noise Lower supply current u REF1112 can not be used with MSP430 VeRef is 1.4V min!!!!! 14

Summary u Built tools for evaluations u Got preliminary results u Will work on other ADCs and MSP430 SARs, Delta-Sigma u Will improve datasheets u Support customers with optimal solution Thank You 15

Amplifier to A/D Interface Study Or that short task that will not go away Generated by Foxit PDF Creator Foxit Software Bill Klein Senior Applications Engineer Miro Oljaca Strategic Marketing: Motor Control With major contributions from: Tom Hendrick, Tim Green, Rick Downs, Rod Burt, Bob Benjamin, Bernd Rundel, Bruce Trump, Dennis Goeke, Pat Highton 16

The Interface Circuit R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv Op Amp Filter A/D CMV Range, V OS vs CMV Charge Bucket Acquisition Time RR Out-Swing to the rail Filtering, Input Circuit Parameters Slew Rate, Signal BW, C load Isolation, Initial Voltage on C SH Load Transient, Settling Time, Output Impedance, 17

LSB Size usignal range: +/-10V is a 20V range 12 bits: 20V/4,096 = 4.88mV per LSB 16 bits: 20V/65,536 = 305µV per LSB +5V range 12 bits: 5V/4,096 = 1.22mV per LSB 16 bits: 5V/65,536 = 76.2µV per LSB 24 bits: 5V/16,777,216 = 298nV per LSB +3.3V range 12 bits: 3.3V/4,096 = 806µV per LSB 16 bits: 3.3V/65,536 = 50.4µV per LSB 24 bits: 3.3V/16,777,216 = 196nV per LSB 18

Op Amp Input Concerns See Appendix R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv Rail-to-Rail Input 19

Output Stage Concerns See Appendix R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv Rail-to-Rail Output 20

How Fast does that Op Amp Settle R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv 21

What Settling Time? uthink of a linear voltage regulator, there are TWO Settling Times. Line Transient Load Transient usame applies here. udata sheets report settling time to 0.01% at best. 22

The Test Circuit C fb REF1004 +15V-1 +15V-1 OPA227-15V-1 1 2 0.4V 2.0K 10K +5V DUT R fil C fil Ref ADS8361 2.0K 10K 2.5V ADS CMD Acquire Convert 30usec T Conv Acq Conv Increment in 20nsec steps 4.0V DUT Out 0.5V 23

OPA300 32640 32620 32600 Bits 32580 32560 32540 32520 32500 Series1 Series2 Series3 Series4 0 100 200 300 400 500 600 700 800 900 1000 Time (nsec) 24

OPA340 32700 32600 32500 32400 32300 32200 32100 32000 Series1 Series2 0 200 400 600 800 1000 25

OPA350 32600 32590 32580 32570 32560 32550 32540 32530 32520 32510 32500 0 200 400 600 800 1000 26

Line Transient Becomes uresponse to change in input signal uincludes Slew Rate. uop Amp data sheets MAY address Settling Time to 0.01% ubut we need 0.0007629% for a 16 bit system 27

Required Settling Time Number of bits 0.5LSB 10 0.0488281% 12 0.0122070% 14 0.0030518% 16 0.0007629% 18 0.0001907% 20 0.0000477% 22 0.0000119% 24 0.0000030% See appendix for calculations 28

Load Transient is UNKNOWN uwe know the load is the input capacitance of the A/D uwe do NOT know the starting voltage. Possible voltages: GND, Mid-Rail, Random Not given in data sheet uthe Op Amp data sheet does NOT even mention this settling time. 29

SAR A/D < 500kHz u 70% Applications Slow Moving Real World Process Signals Fast Acquisition & Conversion Allows More System Time For Processing, Computation, Decision Making Multiplexed, Scanning Systems for Slow Moving Signals u 30% Applications AC Fast Moving Dynamic Signals Real Time Processing of Input Signals 30

Look at the Charge Transients 31

Capacitor Type is Critical R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv 32

THD+N vs. Frequency for Various Capacitor types -60-65 -70-75 -80 d B -85-90 -95-100 -105-110 100 200 500 1k 2k 5k 10k 20k 50k 100k 200k Hz Sweep Trace Color Line Style Thick Data Axis Comment 1 1 Yellow Solid 1 Anlr.THD+N Ratio Left C = 0 2 1 Red Solid 1 Anlr.THD+N Ratio Left C1 3 1 Blue Solid 1 Anlr.THD+N Ratio Left C2 4 1 Cyan Solid 1 Anlr.THD+N Ratio Left C3 5 1 Green Solid 1 Anlr.THD+N Ratio Left C4 R = 100 ohm, C = 3.3 nf, Vp-p = 5V f(-3db) = 482 khz 33

THD+N vs. Voltage for Various Capacitor Types -60-65 -70-75 -80 d B -85-90 -95-100 -105-110 1 2 3 4 5 6 7 8 9 10 11 12 Vrms Sweep Trace Color Line Style Thick Data Axis Comment 1 1 Yellow Solid 1 Anlr.THD+N Ratio Left C = 0 2 1 Red Solid 1 Anlr.THD+N Ratio Left C1 3 1 Blue Solid 1 Anlr.THD+N Ratio Left C2 4 1 Cyan Solid 1 Anlr.THD+N Ratio Left C3 5 1 Green Solid 1 Anlr.THD+N Ratio Left C4 R = 100 ohm, C = 3.3 nf, f = 10 khz, f(-3db) = 482 khz 34

Conclusions on C Type ubest performance: Sliver Mica or COG(NPO) uavoid all other uothers may cost less and be smaller but can distort signal 35

Selecting the Fly-wheel Values R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv 36

Fly Wheel Component Selection u Pick C =20*C SH (See Appendix for proof) u R Calculation t _settle = t SAMPL = 12 τ FLT Theoretical Minimum Practical results Use t =18τ FLT Margin for: Op Amp Output Load Transient Op Amp Output Small Signal Settling Time R = t SAMPL /18 C 37

ADC Sampling Considerations Voltage on the sampling capacitor during sampling period V C ( t) = V0 + ( E V0 ) (1 e t τ ) 1) E V V t C ( t ) AQ 1 2 LSB 1 ) E (1 2 C ( AQ 17 t AQ τ E V ln( E 0 2 17 ) ) 38

ADC Sampling Considerations Suggested input sampling switch transient-immunity RC filter R SW R SW V C C C S V 0 τ E ln( t AQ V E 0 2 17 ) 39

Required Settling Time Number of bits 0.5LSB Time Constants 10 0.0488281% 8 12 0.0122070% 9 14 0.0030518% 11 16 0.0007629% 12 18 0.0001907% 13 20 0.0000477% 15 22 0.0000119% 17 24 0.0000030% 18 See appendix for calculations 40

Establish Op Amp Specs Determine Op Amp specs needed based on system values set in design. Op Amp specs to be determined: uugbw uslew Rate ui out 41

Impact on UGBW u Modified A ol due to R FLT & C FLT f PX = 1/[2 Π(R O + R FLT )C FLT ] f ZX = 1/[2 Π R FLT C FLT ] u Stability Check At f cl Rate-of-closure is 20dB/decade f ZX cancels f PX before f cl f PX and f ZX are < decade apart Phase of pole will be cancelled by phase of zero This implies: R FLT < 9 R O u Impact on UGBW UGBW mod = UGBW orig -(f ZX - f PX ) 42

Impact on UGBW-cont 43

Op Amp Specs to Check uugbw mod >2* 1/[2 Π R FLT C FLT ] uop Amp Transient Output Drive to R FLT & C FLT I Opk max = (5% V REF )/(R FLT ) 44

Interface Design Check List uop Amp Common Mode Voltage uop Amp Output Swing to Rail uop Amp Settling Time ufilter Capacitor Type ufilter Component Values uop Amp Specifications 45

Appendix Calculation Details 1.C as a Function of C sh 2.Open Loop Output Resistance vs. Closed Loop Output Resistance 3.Modified A ol Calculations 4.Time to Charge Capacitor 46

Op Amp Input Concerns R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv Rail-to-Rail Input 47

Input Stage-Parallel P-ch & N-ch +V SUPPLY V IN - Q 1 Q 2 V IN + Q 3 Q 4 -V SUPPLY 48

Looking at Input Stage Performance 1.0kΩ 1.0kΩ - + 100kΩ 100kΩ Gain=100 49

Single Supply RRI Plot-V OS vs CMV (Most RRI Op Amps Except OPA363/OPA364) OPA2340 (Dual: V OUT1 & V OUT2 from different halves) CMV V OUT1 V OUT2 50

Performance Requirements The simple buffer stage. Most accurate unity gain. V IN - + V+ V OUT Bits (mv) (db) 10 2.44 66.2 12 0.61 78.3 16 0.0382 102.3 51

OPA350 Data Sheet THD+N 52

Possible Input Schemes - V+ V OUT V B - V+ V OUT V IN + (A) Good V IN + (B) Better V IN - V+ V OUT V B + (C) Best 53

OPA350 THD+N vs Frequency -50-55 -60-65 -70-75 d B -80-85 -90-95 -100-105 -110 100 200 500 1k 2k 5k 10k 20k 50k 100k 200k Hz Sweep Trace Color Line Style Thick Data Axis Comment 1 1 Yellow Solid 1 Anlr.THD+N Ratio Left OPA350 High CMRR G=-1 2 1 Red Solid 1 Anlr.THD+N Ratio Left OPA350 High CMRR G=+1 3 1 Blue Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR G=+1 4 1 Cyan Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR G=-1 OPA 350, R = 0 ohm, C = 0 nf, Vp-p = 4 V, G = +1or -1 54

OPA350 with RC, THD+N vs Frequency -50-55 -60-65 -70-75 d B -80-85 -90-95 -100-105 -110 100 200 500 1k 2k 5k 10k 20k 50k 100k 200k Hz Sweep Trace Color Line Style Thick Data Axis Comment 1 1 Yellow Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR G=+1 C1 2 1 Red Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR G=-1 C4 OPA 350, R = 100 ohm, C = 3.3 nf, Vp-p = 4 V, f(-3db) = 482 khz, G = +1or -1 55

OPA350 THD+N vs Input Voltage -50-55 -60-65 -70-75 d B -80-85 -90-95 -100-105 -110 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 Vpp Sweep Trace Color Line Style Thick Data Axis Comment 1 1 Yellow Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR 1kHz 2 1 Red Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR 10kHz 3 1 Cyan Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR 50kHz 4 1 Green Solid 1 Anlr.THD+N Ratio Left OPA350 Low CMRR 100kHz OPA 350, R = 0 ohm, C = 0 nf, G = -1 56

Output Stage Concerns R C sw samp R sw C SH (20pF to 50pF) V int (V cc, 0.5V cc, or GND) sw conv Rail-to-Rail Output 57

OPA300-30 -40 1KHz 10KHz -50 THD+N -60-70 -80-90 -100 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 V(out) 58

OPA350-30 -40 1KHz 10KHz -50 THD+N -60-70 -80-90 -100 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.85 4.9 4.95 5 5.05 5.1 V(out) 59

Solution Circuit - + +In ADS8361 usince Op Amp can only swing 4.8Vp-p uset ADS FSR to 4.8V by reducing Ref in to 2.4V. 2.5V -In Ref Out Ref In 2.4V 60

Filter Design Example u R SW = 100Ω (Not needed for Buffer & Filter Calculations) u C SH = 50pF [for ADS8361] u Worst case ΔV across C SH is V REF V REF = +5V u t SAMPL = 1.88μs [for ADS8361] 61

Filter Design Example(cont) u Charge Transfer Equation: Q = CV u Charge required to charge C SH to V REF Q SH = C SH V REF Q SH = 50pF 5V = 250pC u IDEAL C FLT Charge Bucket to fill C SH with only a 76μV (1/2LSB) droop on C FLT Q FLT =Q SH Q FLT = C FLT (38μV) 250pC = C FLT (38μV) C FLT = 6.6μF u IDEAL C FLT = 6.6μF Not a good, small, cheap high frequency ceramic capacitor Not practical for Op Amp to drive directly (stability, transient current) Isolation resistor likely not large enough to help isolate Cload and still meet necessary filter time constant 62

Filter Design Example(cont) u Partition the Charge Bucket 95% from C FLT 5% from Op Amp u C FLT value required to provide Q SH with <5% droop on C FLT Q FLT = Q SH Q FLT = C FLT (0.05V REF ) 250pC = C FLT (0.05 5V) C FLT = 1nF u During t SAMPL the Op Amp must provide 5% V REF to C FLT Ensure C FLT is at least 10X > C SH This implies dominant load for Op Amp Buffer is C FLT 1nF = 20 X 50pF C FLT = 20X C SH 63

Op Amp Model for Derivation of R OUT 64

Derivation of R OUT (Closed Loop Output Resistance) β = V FB /V OUT = [V OUT (R I / {R F + R I })]/V OUT = R I / (R F + R I ) R OUT = V OUT /I OUT V O = -V E Aol V E = V OUT [R I /(R F + R I )] V OUT = V O + I OUT R O V OUT = -V E Aol + I OUT R O V OUT = -V OUT [R I /(R F + R I )] Aol+ I OUT R O V OUT + V OUT [R I /(R F + R I )] Aol = I OUT R O V OUT = I OUT R O / {1+[R I Aol/(R F +R I )]} R OUT = V OUT /I OUT = I OUT R O / {1+[R I A OL /(R F +R I )]} R OUT = R O / (1+Aolβ)

OPA353 Specifications R O = 40Ω R OUT (@1MHz, G=10) = 10Ω Aol @1MHz = 29.54dB = x30 66

OPA353 R OUT Calculation R O = 40Ω R OUT (@1MHz, G=10) = 10Ω Aol @10mHz = 29.54dB = x30 67

R OUT vs R O u R O does not change when feedback is used to close the loop u Closed loop feedback forces V O to increase/decrease u The increase/decrease in V O appears at V OUT as a reduction in R O u R OUT is the net effect of R O and closed loop feedback controlling V O 68

Op Amp Model for AC Stability Analysis R O is constant over the Op Amp s bandwidth R O is defined as the Op Amp s Open Loop Output Resistance R O is measured at I OUT = 0 Amps, f = 1MHz R O is included in β calculation 69

Aol Modified by Filter 80 70 60 Original Aol f P 50 40 30 20 f Z 10 0-10 -20 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 70

Modified Aol-The Math V OUT = V R O O R + R 1 + sc 1 + sc V OUT V O = K = 1 R + sc 1 RO + R + sc V OUT V O = K = sc sc + 1 ( R + R ) + 1 O R V OUT V O = K = C ( R + R ) C O s + C R 1 R s + C 1 R 71

72 Modified Aol-The Math cont. ( ) ( ) + + + + = = O f f O O OUT R R C R C R C s R R C R C R C s K V V 1 1 ( ) ( ) + + + + = = O O O OUT R R R R C s R R R R C s K V V 1 1 ( ) ( ) + + + + = = O O O OUT R R C s R C s R R R K V V 1 1 ( ) z O p R C f R R C f Π = + Π = 2 1 ; 2 1 Generated by Foxit PDF Creator Foxit Software

Voltage on the sampling capacitor during sampling period VC ( t) = V0 + ( E V0 ) (1 e 1 E VC ( taq) LSB 2 V 1 ) E (1 2 C ( t AQ 17 t AQ τ E V ln( E 0 2 17 ) ) t τ ) 73