EE 435 ecture 5 Sprin 06 Fully Differential Sinle-Stae Amplifier Desin Common-mode operation Desin of basic differential op amp Slew Rate The Reference Op Amp
Review from last lecture: Where we are at: Basic Op Amp Desin Fundamental Amplifier Desin Issues Sinle-Stae ow Gain Op Amps Sinle-Stae Hih Gain Op Amps Two-Stae Op Amp Other Basic Gain Enhancement Approaches
Review from last lecture: General Differential Analysis 5T Op Amp from simple quarter circuit Biasin with CMFB circuit Common-mode and differential-mode analysis Common Mode Gain Overall Transfer Characteristics 3
Review from last lecture: Determination of op amp characteristics from quarter circuit characteristics -- The differential ain -- Small sinal Quarter Circuit Small sinal differential amplifier DD I XX IN F OUT OUT d F BB d OUT A OQC BW GB SS G G C G G M M A Odif f G GB C GM G G M I BIAS G G BW C or SS Note: Factor of 4 reduction of ain 4
Review from last lecture: Sinle-stae low-ain differential op amp -- The differential ain -- DD B M 3 M 4 OUT SS IN M M IN Quarter Circuit Sinle-Ended Output : Differential Input Gain A(s) sc m A O O m O O3 m GB C B M 5 Need a CMFB circuit to establish b O3 5
Review from last lecture: Common-Mode and Differential-Mode Analysis Consider any output voltae for any linear circuit with two inputs inear Circuit A B OUT A c =A +A OUT=A +A A OUT = ca c + dad -A A d= A -A OUT = c A A + d Implication: Can solve a linear two-input circuit by applyin superposition with and as inputs or by applyin c and d as inputs Implication: In a circuit with A = - A, A C =0 we obtain = A OUT d d 6
Review from last lecture: Common-Mode and Differential-Mode Analysis Extension to differential outputs and symmetric circuits OUT inear Circuit OUT E E A B A B Differential Output Symmetric Circuit with Symmetric Differential Output Theorem: The differential output for any linear network can be expressed equivalently as OUT=A +A or as OUT = ca c + dad and superposition can be applied to either and to obtain A and A or to c and d to obtain A c and A d Theorem: The symmetric differential output voltae for any symmetric linear network excited at symmetric nodes can be expressed as OUT =A d d where A d is the differential voltae ain and the voltae d = - 7
Today s Outline Common-mode operation Desin of basic differential op amp Slew Rate The Reference Op Amp 8
Common-Mode and Differential-Mode Analysis Consider any output voltae for any linear circuit with two inputs inear Circuit OUT A B OUT=A +A OUT = ca c + dad A inear Circuit B OUT d A inear Circuit B OUT d inear Circuit A B OUT c A inear Circuit B OUT c Sinle-Ended Superposition Difference-Mode/Common-Mode Superposition 9
Common-Mode and Differential-Mode Analysis Consider an output voltae for any linear circuit with two inputs inear Circuit OUT A B OUT = ca c + dad Difference-Mode/Common-Mode Superposition is almost exclusively used for characterizin Amplifiers that are desined to have a lare differential ain and a small common-mode ain Analysis to this point have focused only on the circuit on the left d A inear Circuit B OUT inear Circuit d c A B OUT c Note: revious analysis was correct, just did not address whether the circuit had any common mode ain. Will now et the total output of an amplifier circuit! 0
Common-Mode and Differential-Mode Analysis Consider an output voltae for any linear circuit with two inputs inear Circuit OUT A B OUT = ca c + dad Does Conventional Wisdom Address the Common Mode Gain Issue?
Does Conventional Wisdom Address the Common Mode Gain Issue? Yes Common-Mode Gain was Addressed
Does Conventional Wisdom Address the Common Mode Gain Issue? Yes Common-Mode Gain was Addressed 3
How is Common-Mode Gain Modeled? If Op Amp is a oltae Amplifier with infinite input impedance, zero output impedance, and one terminal of the output is rounded d A d OUT d A d A C c OUT Ideal Differential oltae Amplifier - d Ideal oltae Amplifier d - c 4
General Differential Analysis 5T Op Amp from simple quarter circuit Biasin with CMFB circuit Common-mode and differential-mode analysis Common Mode Gain Overall Transfer Characteristics 5
erformance with Common-Mode Input DD DD OUTC c F BB c OUTC OUTC c F BB c OUTC I BIAS SS Sinle-Ended Outputs Tail-Current Bias DD Sinle-Ended Outputs Tail-oltae Bias DD OUT c F BB ODC c OUT OUT c F BB ODC c OUT I BIAS SS Differential Output Tail Current Bias Differential Output Tail oltae Bias 6
erformance with Common-Mode Input Consider tail-current bias amplifier DD DD OUTC c F BB c OUTC OUTC BB I BIAS c F DD OUTC BB OUTC I BIAS / c F c Common-Mode Half-Circuit I BIAS I SYM I BIAS 7
erformance with Common-Mode Input Consider tail-current bias amplifier with i c =0 DD G BB OUTC OUTC C G M G c i c F I BIAS / sc+g +G +G = G OUTC M x = + C X G - G = G X M OUTC X Solvin, we obtain Common-Mode Half-Circuit OUTC =0 thus A C =0 (Note: Have assumed an ideal tail current source in this analysis A C will be small but may not vanish if tail current source is not ideal) 8
erformance with Common-Mode Input Consider tail-voltae bias amplifier with i c =0 DD DD OUTC c F BB c OUTC OUTC BB SS c F DD SS OUTC c F BB c OUTC Common-Mode Half-Circuit SS I SYM SS 9
erformance with Common-Mode Input Consider tail-voltae bias amplifier with i c =0 DD G OUTC BB C G M G OUTC c i c F OUTC M = C sc+g +G +G = 0 SS Common-Mode Half-Circuit Solvin, we obtain OUTC -G =A M C= C sc+g +G This circuit has a rather lare common-mode ain and will not reject common-mode sinals Not a very ood differential amplifier But of no concern in applications where C =0 0
General Differential Analysis 5T Op Amp from simple quarter circuit Biasin with CMFB circuit Common-mode and differential-mode analysis Common Mode Gain Overall Transfer Characteristics
Overall Small-Sinal Analysis As stated earlier, with common-mode ain and difference-mode ains available inear Circuit A B OUT OUT = ca c + dad
Today s Outline Common-mode operation Desin of basic differential op amp Slew Rate The Reference Op Amp 3
Recall Sinle-stae low-ain differential op amp DD B M 3 M 4 OUT SS IN M M IN Quarter Circuit Sinle-Ended Output : Differential Input Gain A(s) sc m A O O m O O3 m GB C B M 5 Need a CMFB circuit to establish B O3 4
Desin of Basic Sinle-stae low-ain differential op amp A(s) sc A O O m O m O3 O3 DD B M 3 M 4 OUT IN M M IN GB m C What are the number of derees of freedom? (assume DD, fixed, Symmetry) Natural arameters (assumin symmetry): W W3 W,, 5, B,B 3 5 B M 5 Need a CMFB circuit to establish B Constraints: I D5 ;I D3 Net Derees of Freedom: 4 Expressions for A 0 and GB were obtained from quarter-circuit Expressions for A 0 and GB in terms of natural parameters for quarter circuit were messy Can be shown that expressions for A 0 and GB in terms of natural parameters are also messy Can a set of practical desin parameters be identified? 5
Desin of Basic Sinle-stae low-ain differential op amp A(s) sc A O O m O m O3 O3 DD B M 3 M 4 OUT IN M M IN GB m C What are the number of derees of freedom? (assume DD, fixed, Symmetry) B M 5 Natural arameters: W W3 W,, 5, B,B 3 5 ractical arameters:,,, EB EB3 EB5 Need a CMFB circuit to establish B Constraints: I D5 ;I D3 Net Derees of Freedom: 4 Will now express performance characteristics in terms of ractical arameters 6
Desin of Basic Sinle-stae low-ain differential op amp DD B M 3 M 4 OUT SS Quarter Circuit Sinle-Ended Output : Differential Input Gain m A(s) sc O O3 m A O O m GB C ractical arameters:,,, O3 EB EB3 EB5 A 0 λ IN M M IN λ 3 B EB M 5 Need a CMFB circuit to establish B GB C DD Have 4 derees of freedom but only two practical variables impact A 0 and GB so still have DOF after meet A 0 and GB requirements 7 EB
Sinle-stae low-ain differential I/O op amp Quarter Circuit OD O O DD B M 3 M 4 OUT OUTD OUT IN M M IN A(s) sc m A O O m GB C SS Differential Output : Differential Input Gain O3 m O O3 A 0 λ λ 3 EB GB Need a CMFB circuit to establish B or B B C Have 4 derees of freedom but only two practical variables impact A 0 and GB so still have DOF after meet A 0 and GB requirements DD M 5 EB 8
Expressions valid for both tail-current and tail-voltae op amp Recall: OUT DD B M 3 M 4 IN M M IN OUT OUT DD B M 3 M 4 OUT IN M M IN W W, 3, B 3 So which one should be used? Common-mode input rane lare for tail current bias Improved rejection of common-mode sinals for tail current bias Two extra desin deree of freedom for tail current bias Improved output sinal swin for tail voltae bias (will show later) B M 5 W W3 W,, 5, B,B3 3 5 30
Today s Outline Common-mode operation Desin of basic differential op amp Slew Rate The Reference Op Amp 3
Slew Rate Definition: The slew rate of an amplifier is the maximum rate of chane that can occur at an output node IN (t) Amplifier OUT (t) IN (t) IN (t) t t OUT (t) OUT (t) Slope = SR - t Slope = SR + SR is a nonlinear lare-sinal characteristic Input is over-driven (some devices in amplifier usually leave normal operatin reion) Hard input overdrive depicted in this fiure Manitude of SR + and SR - usually same and called SR (else SR + and SR - must be iven) t 3
Slew Rate DD B M 3 M 4 OUT OUT IN M M IN B M 5 With step input on IN+, all tail current (I T ) will o to M thus turnin off M thus current throuh M 4 which is ½ of I T will o to load capacitor The I- characteristics of any capacitor is d I=C dt Substitutin I=I T /, = OUT+ and C= obtain a voltae ramp at the output thus + + dout IT SR dt C C DD ractical parameter domain 33
Slew Rate DD B M 3 M 4 OUT OUT IN M M IN B M 5 It can be similarly shown that puttin a neative step on the input steer all current to M thus the current to the capacitor will be I T minus the current from M which is still I T /. This will cause a neative ramp voltae on OUT+ of value + - dout IT SR dt C C DD Since the manitude of SR + and SR - are the same, obtain a sinle SR for the amplifier of value SR C DD 34
Today s Outline Common-mode operation Desin of basic differential op amp Slew Rate The Reference Op Amp 35
IT SR C Sinle-stae low-ain differential op amp Consider sinle-ended output performance : Will term this the reference op amp Will make performance comparisons of other op amps relative to this A(s) sc mixed parameters A m O= O + O3 C m GB m O A O3 0 GB practical parameters λ SR λ C DD DD 3 EB EB IN OUT DD B M 3 M 4 M M B The Reference Op Amp (CMFB not shown) IN IN M 9 OUT OUT 36 IN
Reference Op Amp sinle-ended output IN OUT DD B M 3 M 4 M M OUT IN A(s) sc mixed parameters A m O= O + O3 m GB C A m O O3 practical parameters 0 GB λ λ C DD 3 EB EB B M 9 IT SR C SR DD The Reference Op Amp (CMFB not shown) This is probably the simplest differential input op amp and is widely used Will o to more complicated structures only if better performance is required 37
Amplifier Structure Summary Common Source Small Sinal arameter Domain A O m O GB C m ractical arameter Domain Common Source A O λ EB GB C DD EB Small Sinal arameter Domain Reference Op Amp A O O m O3 C m GB SR λc 0 ractical arameter Domain Reference Op Amp A 0 λ λ 3 EB GB C DD EB SR DD 38
Reference Op Amp sinle-ended output What basic type of amplifier is this op amp? DD B M 3 M 4 OUT OUT IN M M IN oltae Transconductance I T B M 5 Transresistance Current A(s) sc m O O3 39
Reference Op Amp sinle-ended output What basic type of amplifier is this op amp? Does it really matter? Transconductance DD B M 3 M 4 OUT OUT IN M M IN oltae Transconductance I T B M 5 A(s) sc m O O3 Transresistance Current 40
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