EE 435 ecture 2: Basic Op Amp Design - Single Stage ow Gain Op Amps 1
Review from last lecture: How does an amplifier differ from an operational amplifier?? Op Amp Amplifier Amplifier used in open-loop applications Operational Amplifier used in feedback applications 2
Review from last lecture: Conventional Wisdom Does Not Always Provide Correct Perspective even in some of the most basic or fundamental areas!! Just because its published doesn t mean its correct Just because famous people convey information as fact doesn t mean they are right Keep an open mind about everything that is done and always ask whether approach others are following is leading you in the right direction 3
Review from last lecture: What is an Operational Amplifier? Textbook Definition: Voltage Amplifier with Very arge Gain Very High Input Impedance Very ow Output Impedance Differential Input and Single-Ended Output 4
Review from last lecture: What is an Operational Amplifier? Amplifier with Very arge Gain 5
Review from last lecture: Are differential input and singleended outputs needed? Consider Basic Amplifiers R 2 R 1 V 1 V IN R 1 R 2 V 1 A V Inverting Amplifier V IN A V Noninverting Amplifier Only single-ended input is needed for Inverting Amplifier! Many applications only need single-ended inputs! 6
Review from last lecture: Basic Inverting Amplifier Using Single-Ended Op Amp R 2 R 1 V 1 V IN R 2 V IN R 1 A V Inverting Amplifier with Single-Ended Op Amp 7
Review from last lecture: Fully Differential Amplifier R 1 R 2 V IN R 1 R 2 Widely (almost exclusively) used in integrated amplif Seldom available in catalog parts 8
What is an Operational Amplifier? ets see what the experts say! X IN A X OUT β Conventional Wisdom does not provide good guidance on what an amplifier or an operational amplifier should be! What are the implications of this observation? 9
Basic Op Amp Design Outline Fundamental Amplifier Design Issues Single-Stage ow Gain Op Amps Single-Stage High Gain Op Amps Two-Stage Op Amp Other Basic Gain Enhancement Approaches 10
Single-Stage ow-gain Op Amps Single-ended input Differential Input (Symbol not intended to distinguish between different amplifier types) 11
Single-ended Op Amp Inverting Amplifier Consider: V YQ V YQ Slope = -A Slope = -A V XQ V IN V XQ V IN Assume Q-point at {V XQ,V YQ } V f OUT V IN V A V V V OUT IN xq YQ When operating near the Q-point, the linear and nonlinear model of the amplifier are nearly the same If the gain of the amplifier is large, V XQ is a characteristic of the amplifier 12
V IN R 1 Single-ended Op Amp Inverting Amplifier V 1 R 2 A V V = -A V -V +V O 1 XQ YQ R R V = V + V 1 2 1 O IN R 1+R2 R 1+R2 V YQ Eliminating V 1 we obtain: R 1 R V = -A V + 2 V -V +V 0 0 IN XQ YQ R 1+R2 R 1+R2 Slope = -A If we define V iss by V IN =V INQ +V iss V XQ V IN R2 -A R 1 R 2 A 1 V = V +V V V R 1 1 R1 R A 1+A 1 A 1 R1 R2 R 1+R2 R1 R2 0 iss INQ XQ YQ 13
Single-ended Op Amp Inverting Amplifier R 2 V IN R 1 V 1 A V R2 -A R 1 R 2 A 1 V = V + V V V R 1 1 R1 R A 1+A 1 A 1 R1 R2 R 1+ R2 R1 R2 0 iss INQ XQ YQ But if A is large, this reduces to R R V = - V + V + V -V 2 2 O inss XQ XQ inq R1 R1 Note that as long as A is large, if V inq is close to V XQ R V - V + V 2 O inss XQ R1 14
Single-ended Op Amp Inverting Amplifier V IN R 1 V 1 R 2 A V V = -A V -V +V O 1 XQ YQ R R V = V + V 1 2 1 O IN R 1+R2 R 1+R2 Summary: V YQ R R V = - V + V + V -V 2 2 O inss XQ XQ inq R1 R1 Slope = -A V XQ V IN What type of circuits have the transfer characteristic shown? 15
Single-stage single-input low-gain op amp V DD V DD V XX I DQ M 2 V in M 1 C V in M 1 C V SS V SS Basic Structure Practical Implementation Have added the load capacitance to include frequency dependence of the amplifier gain 16
This is not a new idea! 17
Review of ss steady-state analysis Standard Approach to Circuit Analysis X i (t) Time Domain Circuit Circuit Analysis KV, KC Set of Differential Equations Solution of Differential Equations X OUT (t) 18
Review of ss steady-state analysis Time, Phasor, and s- Domain Analysis X i (t) X i (S) s Transform Phasor Transform X i (jω) s-domain Circuit Time Domain Circuit Phasor Domain Circuit Circuit Analysis KV, KC Circuit Analysis KV, KC Circuit Analysis KV, KC Set of inear equations in s Set of Differential Equations Set of inear equations in jω Solution of inear Equations Solution of Differential Equations Solution of inear Equations X OUT (S) Inverse s Transform Inverse Phasor Transform X OUT (jω) X OUT (t) 19
Review of ss steady-state analysis Time and s- Domain Analysis X i (t) X i (S) s-transform s-domain Circuit Time Domain Circuit Circuit Analysis KV, KC Circuit Analysis KV, KC Set of inear equations in s Set of Differential Equations Solution of inear Equations Solution of Differential Equations X OUT (S) Inverse s Transform X OUT (t) 20
Review of ss steady-state analysis s- Domain Analysis X i (t) X i (S) s- Transform s- Domain Circuit Time Domain Circuit Circuit Analysis KV, KC Set of inear equations in s Solution of inear Equations X OUT (S) Inverse s Transform X OUT (t) 21
Review of ss steady-state analysis Dc and small-signal equivalent elements Element ss equivalent dc equivalnet dc Voltage Source V DC V DC ac Voltage Source V AC V AC dc Current Source I DC I DC ac Current Source I AC I AC Resistor R R R 22
Review of ss steady-state analysis Dc and small-signal equivalent elements Element ss equivalent dc equivalnet Capacitors C arge C Small C arge Inductors Small Diodes Simplified MOS transistors Simplified Simplified 23
Review of ss steady-state analysis Dc and small-signal equivalent elements Element ss equivalent dc equivalnet Bipolar Transistors Simplified Simplified Dependent Sources 24
Review of ss steady-state analysis Summary of Sinusoidal Steady-State Analysis Methods for inear Networks Time-Domain Circuit Circuit Analysis Differential Equations aplace Transform inear s-domain Equations s V OUT s =T sv s IN Transfer Function of Time-Domain Circuit: Key Theorem: V Ts = V OUT IN s s If a sinusoidal input V IN =V M sin(ωt+θ) is applied to a linear system that has transfer function T(s), then the steady-state output is given by the expression V T jω sin ωt+θ+ Tjω v t out M 25
Single-stage single-input low-gain op amp V DD V DD I DQ V XX M 2 V in M 1 C V in M 1 C V SS V SS Small Signal Models g o C V IN V gs g m V gs V gs1 g m1 V gs1 g 01 +g 02 V IN V O C A v sc g m g o dc Voltage gain is ratio of overall transconductance gain to output conductance A v sc g g m1 o1 g o2 26
Single-stage single-input low-gain op amp V DD V DD I DQ M 1 C V XX M 2 C V in V in M 1 Observe in either case the small signal equivalent circuit is a two-port of the form: V in V SS I 2 V SS V 1 G M V 1 G V 2 All properties of the circuit are determined by G M and G 27
Single-stage single-input low-gain op amp Small Signal Model of the op amp I 2 V in V 1 G M V 1 G V 2 Alternate equivalent small signal model obtained by Norton to Thevenin transformation V 1 A V V 1 G I 2 V 2 A M V = - G All properties of the circuit are determined by A V and G G 28
Single-stage single-input low-gain op amp V IN V 1 G M V 1 G C -G A M v = sc +G A = v0 -G G M G BW = C A V G G G GB = = G C C M M GB and A VO are two of the most important parameters in an op amp 29
Single-stage single-input low-gain op amp V IN V 1 G M V 1 G C -g A m v = sc +g 0 for notational convenience -g A m v0 = g 0 g BW = C 0 V IN V 1 g m V 1 g 0 C gm g0 g GB = = g C C m 0 Op Amp The parameters g m and g o give little insight into design 30
How do we design an amplifier with a given architecture in general or this architecture in particular? What is the design space? V DD I DQ M 1 C Generally V SS, V DD,C (and possibly Q )will be fixed Must determine { W 1, 1,I DQ and V INQ } Thus there are 4 design variables But W 1 and 1 appear as a ratio in almost all performance characteristics of interest V in and I DQ is related to V INQ, W 1 and 1 V SS Thus the design space generally has only two independent variables or two degrees of freedom W 1 1 Thus design or synthesis with this architecture involves exploring the two-dimensional design space 31 W 1,I DQ 1,I DQ
How do we design an amplifier with a given architecture in general or this architecture in particular? What is the design space? Generally V SS, V DD,C (and possibly Q )will be fixed Must determine { W 1, 1,I DQ and V INQ } Thus there are 4 design variables But W 1 and 1 appear as a ratio in almost all performance characteristics of interest and I DQ is related to V INQ, W 1 and 1 Thus the design space generally has only two independent variables or two degrees of freedom W 1 Thus design or synthesis with this architecture involves exploring the two-dimensional design space W 1 1,I DQ 1,I DQ 1. Determine the design space 2. Identify the constraints 3. Determine the entire set of unknown variables and the Degrees of Freedom 4. Determine an appropriate parameter domain (Parameter domains for characterizing the design space are not unique!) 5. Explore the resultant design space with the identified number of Degrees of Freedom 32
How do we design an amplifier with a given architecture? 1. Determine the design space 2. Identify the constraints 3. Determine the entire set of unknown variables and the Degrees of Freedom 4. Determine an appropriate parameter domain 5. Explore the resultant design space with the identified number of Degrees of Freedom 33
Parameter Domains for Characterizing Amplifier Performance Should give insight into design Variables should be independent Should be of minimal size Should result in simple design expressions Most authors give little consideration to either the parameter domain or the degrees of freedom that constrain the designer 34
Parameter Domains for Characterizing Amplifier Performance Consider basic op amp structure V in V DD I DQ M 1 V SS C -g A m v = sc +g 0 -g A m v0 = g 0 g GB = C Small signal parameter domain : g m, g0 m Degrees of Freedom: 2 Small signal parameter domain obscures implementation issues 35
Parameter Domains for Characterizing Amplifier Performance Consider basic op amp structure V in V DD V SS I DQ M 1 C -g A m v = sc +g 0 -g A m v0 = g 0 g GB = C What parameters does the designer really have to work with? W,IDQ Degrees of Freedom: 2 Call this the natural parameter domain m 36
V in g m Parameter Domains for Characterizing Amplifier Performance Consider basic op amp structure 2I V DQ EB V DD V SS I DQ M 1 C μc OXW V EB C OX Natural parameter domain W I DQ W,IDQ g GB = C How do performance metrics A VO and GB relate to the natural domain parameters? m -g A m v0 = g 0 g λi o DQ 37
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -g A = m gm g v0 0 GB = C Natural design parameter domain: A V0 = W 2μCOX λidq GB = {g m,g 0 } W 2μCOX C -g A m v = sc +g 0 W,IDQ IDQ Expressions very complicated Both A V0 and GB depend upon both design paramaters Natural parameter domain gives little insight into design and has complicated expressions 38
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -g A = m gm g v0 Natural design parameter domain: 0 W 2μCOX A V0= λ IDQ GB = GB = C {g m,g 0 } W,IDQ 2μCOX W IDQ C Process Dependent Architecture Dependent Process Dependent Architecture Dependent 39
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -gm gm A v0 = g 0 Natural design parameter domain: W 2μCOX A V0= λ IDQ Alternate parameter domain: GB = C {g m,g 0 } GB = W,IDQ 2μCOX W IDQ C P,V EB P=power=V DD I DQ V EB =excess bias =V GSQ -V T g 2I 1 2 A V0 = = = g V λi λv M DQ 0 EB DQ EB gm 2IDQ 1 2 P GB = = = C V C V C V EB DD EB 40
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -g g m m A v0 = g 0 Natural design parameter domain: W 2μCOX A V0= λ IDQ GB = C {g m,g 0 } W,IDQ Alternate parameter domain: A = V0 2 1 λ V EB GB = 2μCOX W IDQ C 2 P GB= V DD C V EB P,V EB Process Dependent 41
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -g A = m gm g Natural design parameter domain: A v0 VO 2 C OX W I DQ Alternate parameter domain: A = V0 0 EB GB GB = C {g m,g 0 } 2C C OX W 2 1 2 P λ V GB= V DD C V EB I DQ W,IDQ P,V EB Architecture Dependent 42
Parameter Domains for Characterizing Amplifier Performance Degrees of Freedom: 2 Small signal parameter domain : -g A = m gm g v0 Natural design parameter domain: A VO 2 C OX W I DQ Alternate parameter domain: A = V0 0 EB GB = C {g m,g 0 } GB 2C Alternate parameter domain gives considerable insight into design Alternate parameter domain provides modest parameter decoupling 43 Term in box figure of merit for comparing architectures C OX W 2 1 2 P λ V GB= V DD C V EB I DQ W,IDQ P,V EB
Parameter Domains for Characterizing Amplifier Performance Design often easier if approached in the alternate parameter domain How does one really get the design done, though? That is, how does one get back from the alternate parameter domain to the natural parameter domain? Alternate parameter domain: P,V EB V DD V in V SS I DQ M 1 C W =? =? I DQ =? V INQ =? 44
Parameter Domains for Characterizing Amplifier Performance Design often easier if approached in the alternate parameter domain How does one really get the design done, though? That is, how does one get back from the alternate parameter domain to the natural parameter domain? Alternate parameter domain: P,V EB Natural design parameter domain: W,IDQ I DQ P = V DD W P = V μc V 2 DD OX EB V =V V I INQ SS T DQ 2 C W OX 45
How do we design an amplifier with a given architecture? 1. Determine the design space 2. Identify the constraints 3. Determine the entire set of unknown variables and the Degrees of Freedom 4. Determine an appropriate parameter domain 5. Explore the resultant design space with the identified number of Degrees of Freedom 46
Design With the Basic Amplifier Structure Consider basic op amp structure V DD I DQ Alternate parameter domain: Degrees of Freedom: 2 A = V0 2 1 λ V EB P,V EB V in V SS M 1 C P W P I = = 2 V DQ DD 2 P GB= V DD C V EB V μc V INQ SS T DQ DD OX EB V =V V I 2 C W OX But what if the design requirement dictates that V INQ =0? Increase the number of constraints from 2 to 3 Decrease the Degrees of Freedom from 2 to 1 Question: How can one meet two or more performance requirements with one design degree of freedom with this circuit? 50
Design With the Basic Amplifier Structure Consider basic op amp structure V DD I DQ Alternate parameter domain: Degrees of Freedom: 2 A = V0 2 1 λ V EB P,V EB V in V SS M 1 C P W P I = = 2 V DQ DD 2 P GB= V DD C V EB V μc V INQ SS T DQ DD OX EB V =V V I 2 C W OX But what if the design requirement dictates that V INQ =0? Question: How can one meet two or more performance requirements with one design degree of freedom with this circuit? Degrees of Freedom: 1 uck or Can t 51