EE 435. Lecture 18. Two-Stage Op Amp with LHP Zero Loop Gain - Breaking the Loop

Transcription

1 EE 435 Lecture 8 Two-Stae Op Amp with LHP Zero Loop Gain - Breakin the Loop

2 Review from last lecture Nyquist and Gain-Phase Plots Nyquist and Gain-Phase Plots convey identical information but ain-phase plots often easier to work with Ma ω = Im Ma Phase ω Re ω -+j0 ω = - ω = ω Phase Note: The two plots do not correspond to the same system in this slide

3 Anle in derees Manitude in db Review from last lecture Gain and Phase Marin Examples β T(s) ω 58 s s ω -50 Phase Marin

4 Review from last lecture Relationship between pole Q and phase marin In eneral, the relationship between the phase marin and the pole Q is dependent upon the order of the transfer function and on the location of the zeros In the special case that the open loop amplifier is second-order lowpass, a closed form analytical relationship between pole Q and phase marin exists and this is independent of A 0 and β.. Q cos(φ sin(φ M M ) ) φ M cos 4Q 4 Q The reion of interest is invariable only for < Q < 0.7 larer Q introduces unacceptable rinin and settlin smaller Q slows the amplifier down too much

5 Review from last lecture Phase Marin vs Q Second-order low-pass Amplifier Pole Q Phase Marin

6 Review from last lecture Phase Marin vs Q Second-order low-pass Amplifier Pole Q Phase Marin

7 Review from last lecture Manitude Response of nd -order Lowpass Function Q MAX for no peakin =. 707 Q From Laker-Sansen Text

8 Review from last lecture Step Response of nd -order Lowpass Function Q Q MAX for no overshoot = / From Laker-Sansen Text

9 Review from last lecture ompensation Summary Gain and phase marin performance often stronly dependent upon architecture Relationship between overshoot and rinin and phase marin were developed only for nd -order lowpass ain characteristics and differ dramatically for hiher-order structures Absolute ain and phase marin criteria are not robust to chanes in architecture or order It is often difficult to correctly break the loop to determine the loop ain Aβ with the correct loadin on the loop (will discuss this more later)

10 Desin of Two-Stae Op Amps ompensation is critical in two-stae op amps General approach to desinin two-stae op amps is common even thouh sinificant differences in performance for different architectures Will consider initially the most basic two-stae op amp with internal compensation

11 Natural Parameter Space for the Two-Stae Amplifier Desin DD M 3 M 4 M 5 OUT IN M M IN L I T B M 7 B3 M 6 SS S NATURAL = {W, L, W 3, L 3, W 5, L 5, W 6, L 6, W 7, L 7, I T, I D6, c }

12 Desin Derees of Freedom Total independent variables: 3 Derees of Freedom: 3 If phase marin is considered a constraint 3 independent variables constraint derees of freedom

13 Observation: W,L appear as W/L ratio in almost all characterizin equations Implication: Derees of Freedom are Reduced S NATURAL-REDUED = {(W/L),(W/L) 3,(W/L) 5,(W/L) 6,(W/L) 7,I D6,I T, } With phase marin constraint, Derees of freedom: 7

14 ommon Performance Parameters of Operational Amplifiers Parameter Description Ao Open-loop D Gain GB Gain-Bandwidth Product Φm(or Q) Phase Marin (or pole Q) SR Slew Rate T SETTLE Settlin Time A T Total Area A A Total Active Area P Power Dissipation OS Standard Deviation of Input Referred Offset oltae (often termed the input offset voltae) MRR ommon Mode Rejection Ratio PSRR Power Supply Rejection Ratio imax Maximum ommon Mode Input oltae imin Minimum ommon Mode Output oltae omax Maximum Output oltae Swin omin Minimum Output oltae Swin noise Input Referred RMS Noise oltae Sv Input Referred Noise Spectral Density

15 Performance Parameters Total: 7

16 Performance parameters: 7 Derees of freedom: 7 System is Generally Hihly Over onstrained!

17 Typical Parameter Space for a Two-Stae Amplifier + OUT - d md d Od mo OO L Small sinal model of the two-stae operational amplifier Small sinal desin parameters: S SMALL SIGNAL = { oo, od, mo, md,, o, o4, o5, o6 }

18 Sinal Swin of Two-Stae Op Amp DD M 3 M 4 M 5 OUT IN M M IN L I T B SS M7 B3 M 6 M6: M5: M: i OUT OUT DD SS DD EB6 EB5 T T3 EB3 M: M7: i ic DD T T5 EB5 T EB EB 7 SS S swin/bias Related = {, EBQ, EB3Q, EB5Q, EB6Q, EB7Q, I T }

19 Sinal Swin of Two-Stae Op Amp OUT DD EB5 T EB EB7 max{( ( EB3 EB5 T3 T5 T T ), )} SS DD ic OUT DD EB5 OUT SS EB6 EB6 SS ic T EB EB 7 SS i DD T T3 EB3 i DD T T5 EB5

20 Sinal Swin of Two-Stae Op Amp OUT DD EB5 T EB EB7 max{( ( EB3 EB5 T3 T5 T T ), )} SS DD ic EB6 SS

21 Typical Parameter Space for a Two-Stae Amplifier DD M 3 M 4 M 5 OUT IN M M IN L I T B M7 B3 M 6 SS + OUT - d md d Od mo OO L Aumented set of desin parameters: S AUGMENTED = { oo, od, mo, md,, EBQ, EB3Q, EB5Q, EB6Q, EB7Q, I T, o, o4, o5, o6 } Parameters in this set are hihly inter-related

22 ommon Expressions for the Performance Parameters A O GB SR md oo I md T mo od

23 ommon Expressions for the Performance Parameters (cont) OMAX OMIN DD SS EB5 EB6 inmin T EB EB 7 SS max{( inmax DD EB3 T3 T EB5 T5 T ),( )}

24 Parameter Inter-dependence A O md GB oo mo od md I T affects SR I T W md OX T μ I L

25 A Set of Independent Desin Parameters is Needed onsider the Natural Reduced Parameter Set W W3 W5 W6 W 7,,,,,I T, θ L L3 L L 5 6 L7 A A = O I θ= O D6Q OX I T md oo μμ n p mo od WW LL WL n p IT WL 7 6 λ +λ

26 md GB n p p n L L W β L L L W W W W L L L W W W L Q β n OX T μ W I L GB For a iven pole Q and a feedback factor, it can be shown that:

27 inmin T EB EB7 SS I L I L T T 7 imin T SS μnox W μnox W7 Expressions for sinal swins are particularly complicated!

28 Observation Even the most elementary performance parameters require very complicated expressions when the natural desin parameter space is used Stron simultaneous dependence on multiple natural desin parameters Interdependence and notational complexity obscures insiht into performance and optimization

29 Practical Set of Desin Parameters S PRATIAL = {P, θ, EB, EB3, EB5, EB6, EB7 } 7 derees of freedom! P : total power dissipation q = IDQ5/I T, current split factor EBK=GSQK-TK, excess bias voltae for the k th transistor Phase marin constraint assumed (so not shown in DoF)

30 Basic Two-Stae Op Amp DD M 3 M 4 M 5 OUT IN M M IN L I T B M 7 B3 M 6 SS 7 Derees of Freedom {P, θ, EB, EB3, EB5, EB6, EB7 } W W3 W5 W6 W 7,,,,,I T, θ L L3 L L 5 6 L7

31 Relationship Between the Practical Parameters and the Natural Desin Parameters {P, θ, EB, EB3, EB5, EB6, EB7 } W W3 W5 W6 W 7,,,,,I T, θ L L3 L L 5 6 L7 I T P +θ DD I I I,,θI T DQi T T W I DQi L i μ i OX EBi

32 Relationship Between the Practical Desin Parameters and the Performance Parameters (Assumin Q ) A O 4 λ λ n P Pθ EB β EB5 GB θ 4 θβ θ p EB EB5 DD EB L DD EB EB5 Pθ EB β EB5 SR EBGB 4 L θβ DD θ EB EB5 c 4 θβ L EB EB5 θ β EB EB5

33 Relationship Between the Proposed Desin Parameters and the Performance Parameters OMAX OMIN DD SS EB5 EB6 inmin T EB EB 7 SS max{( inmax DD EB3 T3 T EB5 T5 T ),( )}

34 haracteristics of the Practical Desin Parameter Space Minimum set of independent parameters Results in major simplification of the key performance parameters Provides valuable insiht which makes performance optimization more practical

35 Desin Assumptions Assume the followin system parameters: DD = 3.3 L = pf Typical 0.35um MOS process Simulation corner: typ/55/3.3

36 Example for Desin Procedure Given specifications: A 0 : 66dB GB: 5MHz OMIN = OMAX =3. INMIN =. INMAX =3 P=0.7mw = Assume: TN = 0.6, TP = 0.7, n =0.04, p =0.8 7 constraints (in addition to φ m ) and 7 derees of freedom

37 Example for Desin Procedure. hoose channel lenth. EB3, EB5, EB6 {P, θ, EB, EB3, EB5, EB6, EB7 } 3. EB imax = DD + EB3 + T + T3 omax = DD + EB5 omin = EB6 A = 4. EB7 imin=eb + EB7 + T O 4 λ +λ n p EB EB5 {P, θ, EB, EB3, EB5, EB6, EB7 } {P, θ, EB, EB3, EB5, EB6, EB7 } 5. hoose P to satisfy power constraint {P, q, EB, EB3, EB5, EB6, EB7 } I T P +θ DD

38 Example for Desin Procedure 6. hoose q to meet GB constraint GB 7. ompensation capacitance c DD 4 L q EB EB 5 q EB 8. alculate all transistor sizes I = T P +θ DD EB 5 EB5 q P P q EB q EB 4LqDD EB EB5 Wk L k I μ Dk OXEBk {P, q, EB, EB3, EB5, EB6, EB7 } 9. Implement structure, simulate, and make modifications if necessary uided by where deviations may occur Note: It may be necessary or preferable to make some constraints an inequality Note: Specifications may be over-constrained or have no solution k (Assumin Q )

39 Example for Desin Procedure Desin results: M, W/L M 3,4 W/L M 5 W/L M 6 W/L M 7 W/L P θ 3/ 4.5/ 54/ 7.4/ 7.4/ 0.7mW pF Simulation results: A0 GB P Phase marin 65dB 5.MHz.7mW 45.4 derees

40 Spreadsheet for Desin Space Exploration Settlin haracteristics of Two-Stae Operational Amplifier Process Parameters 0.0 Power 0.0 ln 9E-05 uoxn E- T 0. lp 5E-05 uoxp 4 dd tn tp Dev ice Sizin Output Rane Input Rane Performance haracteristics Desin Parameters W/L5 W/L W/L max min max min ISS(mA) GB Ao EB7 EB6 EB5 EB EB E E E E E E E E E E E E ERR.67 ERR E E E E ERR.67 ERR E E E E E E ERR.67 ERR 39 W/L7 W/L6 W/L Dev ice Sizin W/L7 W/L6 W/L5 W/L

41 Summary. Determination of Desin Space and Derees of Freedom Often Useful for Understandin the Desin Problem. Analytical Expressions for Key Performance Parameters ive onsiderable Insiht Into Desin Potential 3. Natural Desin Parameters Often Not Most Useful for Providin Insiht or Facilitatin Optimization 4. oncepts Readily Extend to other Widely Used Structures

42 Basic Two-Stae Op Amp DD M 3 M 4 M 5 OUT IN M M IN L I T B M 7 B3 M 6 A FB (s) SS s L s md m0 sc mo β md β mdmo Riht Half-Plane Zero Limits Performance Why does the RHP zero limit performance? an anythin be done about this problem?

43 Why does the RHP zero limit performance? Gain Manitude in db β All Pole RHP Zero Phase in Derees 0.00E E E E E E+0 -.0E E E E E+0 RHP Zero All Pole p =, p =000, z x ={none,50} In this example: accumulate phase shift and slow ain drop with RHP zeros effects are dramatic

44 Why does the RHP zero limit performance? Gain Manitude in db β All Pole LHP and RHP Zero Phase in Derees 0.00E E E E E E+0 -.0E E E E E+0 RHP Zero LHP Zero All Pole p =, p =000, z x ={none,50,-50} In this example: accumulate phase shift and slow ain drop with RHP zeros loose phase shift and slow ain drop with RHP zeros effects are dramatic

45 Two-stae amplifier (with RHP Zero ompensation) What causes the Miller compensation capacitor to create a RHP zero? DD M 3 M 4 M 5 s+p s+p A = A p p 0 OUT IN M M IN L with Miller ompensation I T B SS M7 B3 + - d=in-in M 6 A = A 0 pp -s+z z s+p s+p At low frequencies, OUT / d is neative but at hih frequencies it becomes positive Alternately, provides a feed-forward noninvertin sinal from the output of the first stae to the output of the second stae

46 Two-stae amplifier (with RHP Zero ompensation) What can be done to remove the RHP zero? DD M 3 M 4 M 5 s+p s+p A = A p p 0 IN M M IN L OUT with Miller ompensation B I T M7 B3 M 6 A = A 0 pp -s+z z s+p s+p SS + - d=in-in Alternately, provides a feed-forward noninvertin sinal from the output of the first stae to the output of the second stae Break the feed-forward path from the output of the first stae to the output of the second stae at hih frequencies

47 Two-stae amplifier with LHP Zero ompensation DD DD M 3 M 4 M 5 M 3 M 4 M 5 IN M M IN L OUT A B R OUT I T IN M M IN L B M7 B3 M 6 SS B M 7 B M 6 Riht Half-Plane Zero Limits Performance Zero can be moved to Left Half-Plane R realized with sinle triode reion device

48 Two-stae amplifier with LHP Zero ompensation DD IN M 3 M 4 M 5 A B R M M IN OUT L A(s) md s m5 m5 sc c L s m5 oo od B M 7 B M 6 z m5 m5 z location can be prorammed by R If c > m5, z in RHP and if c < m5, z in LHP R has almost no effect on p and p

49 Two-stae amplifier with LHP Zero ompensation o m o o p od oo m L c m c m md s s s A(s) m m z L m p 5 p p X X z where should z be placed?

50 Two-stae amplifier with LHP Zero ompensation where should z be placed? X X p p X X p p X X p p z z z z p Would make situation worse (because m5 m5 o 05 o5 m5 m5 p ratio between two dominant poles would be reduced! L o6 X X z p p X X p z p

51 Two-stae amplifier with LHP Zero ompensation where should z be placed? Would make situation worse (because ratio between two dominant poles would be reduced! X X p p z Other parasitic poles, at hiher frequencies are present and not too much larer than p! X X X X p 4 p 3 p p z

52 Two-stae amplifier with LHP Zero ompensation X X z p p z m5 m5 z often used to cancel p an reduce size of required compensation capacitor a) eliminates RHP zero b) increases spread between p and p 3 Improves phase marin Desin formulations easily extend to this structure

53 Two-stae amplifier with LHP Zero ompensation X p 3 X X p p z z m5 m5 Analytical formulation for compensation requirements not easy to obtain (must consider at least 3 rd order poles and both T(s) and poles not mathematically tractable) often chosen to meet phase marin (or settlin/overshoot) requirements after all other derees of freedom used with computer simulation from manitude and phase plots

54 Basic Two-Stae Op Amp with LHP zero DD M 3 M 4 M 5 A B R OUT IN M M IN L B M 7 B M 6 8 Derees of Freedom with zero cancellation of p {P, θ, EB, EB3, EB5, EB6, EB7,R, } constraint (phase marin) 7 Derees of Freedom {P, θ, EB, EB3, EB5, EB6, EB7,R, } constraints (phase marin), z = p = - m5 m5 -

55 Basic Two-Stae Op Amp with LHP zero DD M 3 M 4 M 5 with zero cancellation of p IN A B M M R IN OUT L 7 Derees of Freedom B M 7 B M 6 {P, θ, EB, EB3, EB5, EB6, EB7,R, } - constraints (phase marin), z m5 = p = m5 - Desin Flow:. Inore R and desin as if RHP zero is present. Pick R to cancel p 3. Adjust p (i.e. chane/reduce ) to achieve desired phase marin

56 Basic Two-Stae Op Amp with LHP zero DD M 3 M 4 M 5 A B R OUT IN M M IN L B M 7 B M 6 XX Realization of R R = μ OX L W EB R OR YY Transistors in triode reion ery little current will flow throuh transistors (and no dc current) DD or GND often used for XX or YY BQ well-established since it determines I Q5 Usin an actual resistor not a ood idea (will not track m5 over process and temp)

57 Two-Stae Amplifiers Practical onsiderations Loop Gain Loadin of A and β networks Breakin the Loop (with appropriate terminations) Biasin of Loop Simulation of Loop Gain Open-loop ain simulations Systematic Offset Embeddin in closed loop

58 End of Lecture 8