EE 435. Lecture 4 Spring Fully Differential Single-Stage Amplifier Design

Transcription

1 EE 435 Lecture 4 Spring 018 ully Differential Single-Stage Amplifier Design eneral Differential Analysis 5T Op Amp from simple quarter circuit Biasing with CMB circuit Common-mode and differential-mode analysis Common Mode ain Overall Transfer Characteristics 1

2 Review from last lecture: Where we are at: Basic Op Amp Design undamental Amplifier Design Issues Single-Stage Low ain Op Amps Single-Stage High ain Op Amps Two-Stage Op Amp Other Basic ain Enhancement Approaches

3 Review from last lecture: Where we are at: Single-Stage Low-ain Op Amps Single-ended input Differential Input (Symbol does not distinguish between different amplifier types) 3

4 Review from last lecture: Differential Input Low ain Op Amps Will Next Show That : Differential input op amps can be readily obtained from single-ended op amps erformance characteristics of differential op amps can be directly determined from those of the single-ended counterparts 4

5 Review from last lecture: Counterpart Networks Definition: The counterpart network of a network is obtained by replacing all n- channel devices with p- channel devices, replacing all p-channel devices with n- channel devices, replacing SS biases with DD biases, and replacing all DD biases with SS biases. 5

6 Review from last lecture: Counterpart Networks Theorem: The parametric expressions for all small-signal characteristics, such as voltage gain, output impedance, and transconductance of a network and its counterpart network are the same. 6

7 Review from last lecture: Synthesis of fully-differential op amps from symmetric networks and counterpart networks Theorem: If is any network with a single input and is its counterpart network, then the following circuits are fully differential circuits --- op amps. BB OUT d DD BB OUT d d 1 1 BB OUT DD BB OUT d I BIAS SS d 1 7

8 Review from last lecture: Synthesis of fully-differential op amps from symmetric networks and counterpart networks Terminology DD BB OUT BB OUT Quarter Circuit Counterpart Circuit d d I BIAS d 1 Half Circuit Symmetric Half Circuit 8

9 Review from last lecture: Synthesis of fully-differential op amps from symmetric networks and counterpart networks A fully differential op amp is derived from any quarter circuit by combining it with its counterpart to obtain a half-circuit, combining two half-circuits to form a differential symmetric circuit and then biasing the symmetric differential circuit on the axis of symmetry. DD BB OUT BB OUT Quarter Circuit d d I BIAS urther, most of the properties of the operational amplifier can be obtained by inspection, from those of the quarter circuit. 9

10 Review from last lecture: Synthesis of fully-differential op amps from symmetric networks and counterpart networks A fully differential op amp is derived from any quarter circuit by combining it with its counterpart to obtain a half-circuit, combining two half-circuits to form a differential symmetric circuit and then biasing the symmetric differential circuit on the axis of symmetry. urther, most of the properties of the operational amplifier can be obtained by inspection, from those of the quarter circuit. Implications: Much Op Amp design can be reduced to designing much simpler quarter-circuits where it is much easier to get insight into circuit performance Quarter Circuit 10

11 eneral Differential Analysis 5T Op Amp from simple quarter circuit Biasing with CMB circuit Common-mode and differential-mode analysis Common Mode ain Overall Transfer Characteristics 11

12 Characterization of Quarter Circuit If the input impedance is infinite, the two-port network only has two characterizing parameters : M and I XX I OUT OUT IN IN 1 M 1 SS Two-ort Model of Quarter Circuit OUT IN 1 sc L M 1 0 A QC ( s) M sc L A OQC M BW B C M L 1

13 Characterization of Quarter Circuit (or Counterpart Circuit) with input port terminated in short circuit I I XX IN OUT 1 M 1 SS If the input port of a two-port has an ac short, then the two-port reduces to a oneport characterized by the conductance I I XX 13

14 Determination of op amp characteristics from quarter circuit characteristics DD -- The differential gain -- Small signal differential half-circuit OUT BB OUT d d O I BIAS d M or SS Derivation: from KCL and KL: o 1 L M1 1 1 sc + = 0 d A o M1 sc d L 1 Note: actor of reduction of gain since only half of the differential input is applied to the half-circuit Note: More reduction of gain since denominator increases 14

15 Determination of op amp characteristics from quarter circuit characteristics DD -- The differential gain -- Small signal differential half-circuit OUT d BB d OUT d M O I BIAS or SS A o M1 sc d L 1 A 0 =? BW=? B=? A O BW B M1 C M1 L 1 1 C L 15

16 Determination of op amp characteristics from quarter circuit characteristics -- The differential gain -- Small signal Quarter Circuit IN 1 M 1 I OUT A QC ( s) M sc L Two-ort Model of Quarter Circuit Small signal differential half-circuit (repeated from last slide) O M1 M 1 I out d M d 1 M 1 A M1 o d scl 1 A QC Two-ort Model of Half Circuit ( s) M sc L 16

17 Determination of op amp characteristics from quarter circuit characteristics -- The differential gain -- Small signal Quarter Circuit Small signal differential amplifier DD I XX OUT OUT BB OUT IN d d SS I BIAS or SS A QC ( s) M sc L A o M1 sc d L 1 17

18 Determination of op amp characteristics from quarter circuit characteristics -- The differential gain -- Small signal Quarter Circuit Small signal differential amplifier I XX DD IN OUT OUT d BB d A BW OQC SS Note: actor of 4 reduction of gain if 1 = Note: actor of increase of BW if 1 = M B C Note: actor of reduction of B if 1 = M L (this often occurs) (this often occurs) (this often occurs) Remember this is applicable to ANY quarter circuit! I BIAS M1 or SS OUT A 0 d 1 BW C B C L L M

19 Comparison of Tail oltage and Tail Current Source Structures -- The differential gain -- DD DD BB OUT BB OUT BB OUT BB OUT d d d d I BIAS SS Small signal half-circuits are identical so voltage gains, BW, and B are all the same 19

20 Biasing Issues for Differential Amplifier Tail voltage bias not suitable for large common-mode (CM) input range but does offer good output swing Tail current bias provides good CM input range but at the expense of a modest reduction in output signal swing 0

21 Differential Output Amplifiers -- The differential gain -- DD DD OUT BB OUT OUT BB OD OUT d d d d I BIAS or SS I BIAS or SS Single-Ended Outputs Differential Output Theorem: or a symmetric circuit with symmetric outputs and differential excitations: Differential oltage ain Double that of Single-Ended Structure BW is the same B Doubles for the Differential Output Structure 1

22 eneral Differential Analysis 5T Op Amp from simple quarter circuit Biasing with CMB circuit Common-mode and differential-mode analysis Common Mode ain Overall Transfer Characteristics

23 Applications of Quarter-Circuit Concept to Op Amp Design consider initially the basic single-ended amplifier DD I DQ Quarter Circuit OUT IN SS 3

24 Single-stage single-input lowgain op amp DD DD I DQ OUT XX M Counterpart Circuit OUT IN IN M 1 SS SS Basic Structure Quarter Circuit ractical Implementation 4

25 Small signal model of half-circuit DD I OUT XX M IN 1 M 1 OUT OUT Two-port model of half-circuit IN SS M 1 M 1 M1 5

26 Single-stage low-gain differential op amp -- The differential gain -- DD B1 M 3 M 4 OUT SS Quarter Circuit Single-Ended Output : Differential Input ain As A 0 BW B g g C OUT d L o1 o3 o1 o3 o1 o3 m1 gm1 g g L g C L gm1 sc g g IN M 1 M IN B Circuit is ery Sensitive to B1 and B!! Have synthesized fully differential op amp from quarter circuit! Have obtained analysis of fully differential op amp directly from quarter circuit! Still need to determine what happens if input is not differential! M 5 6

27 eneral Differential Analysis 5T Op Amp from simple quarter circuit Biasing with CMB circuit Common-mode and differential-mode analysis Common Mode ain Overall Transfer Characteristics 7

28 Single-stage low-gain differential op amp DD -- The differential gain -- DD B1 M 3 M 4 OUT B1 M 3 M 4 IN M 1 M IN CMB Circuit OUT B M 5 IN M 1 M DQ-DES IN CL Need CMB circuit to establish B1 or B!! B M 5 CMB circuit determines average value of the drain voltages Compares the average to the desired quiescent drain voltages Established a feedback signal B1 to set the right Q-point Shown for B1 but could alternately be applied to B Details about CMB circuits will be discussed later 8

29 OUT Single-stage low-gain differential op amp d DD BB -- The differential gain -- Need CMB circuit d OUT DD B1 M 3 M 4 OUT IN M 1 M IN As A 0 BW B C OUT 1 1 M1 L d M 1 C L L I BIAS M sc 1 or SS B M 5 A(s) sc A O L g g g O1 m1 O1 gm1 B C Have obtained differential gain of 5T Op Amp by inspection from quarter circuit L gm1 g g O3 O3 9

30 eneral Differential Analysis 5T Op Amp from simple quarter circuit Biasing with CMB circuit Common-mode and differential-mode analysis Common Mode ain Overall Transfer Characteristics 30

31 Common-Mode and Differential-Mode Analysis Consider an output voltage for any linear circuit with two inputs Linear Circuit 1 A B OUT By superposition OUT=A 1 1+A where A 1 and A are the gains (transfer functions) from inputs 1 and to the output respectively Define the common-mode and difference-mode inputs by c = = - 1 d 1 These two equations can be solved for 1 and to obtain d 1 = c + d = c - 31

32 Common-Mode and Differential-Mode Analysis Consider an output voltage for any linear circuit with two inputs Linear Circuit 1 A B OUT OUT=A 1 1+A Substituting into the expression for OUT, we obtain d d OUT =A 1 c +A c Rearranging terms we obtain A1-A = A A + OUT c 1 d If we define A c and A d by A1-A A c =A 1+A A d= Can express OUT as OUT = ca c + dad 3

33 Common-Mode and Differential-Mode Analysis Consider any output voltage for any linear circuit with two inputs Linear Circuit 1 A B OUT OUT=A 1 1+A Implication: Can solve a linear two-input circuit by applying superposition with 1 and as inputs or by applying c and d as inputs Implication: In a circuit with A = - A 1, A C =0 we obtain = A OUT d d A c =A 1+A A OUT = ca c + dad 1-A A d= A 1-A OUT = c A1 A + d Analysis of op amps up to this point have assumed differential excitatation 33

34 Common-Mode and Differential-Mode Analysis Depiction of singe-ended inputs and common/difference mode inputs 1 A Linear Circuit B OUT Linear Circuit A B d OUT d c c OUT=A 1 1+A OUT = ca c + dad Applicable to any linear circuit with two inputs and a single output Op amps often have symmetry and this symmetry further simplifies analysis 34

35 Common-Mode and Differential-Mode Analysis Extension to differential outputs and symmetric circuits OUT Linear Circuit OUT E E 1 A B 1 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 1 1+A or as OUT = ca c + dad and superposition can be applied to either 1 and to obtain A 1 and A or to c and d to obtain A c and A d Theorem: The symmetric differential output voltage for any symmetric linear network excited at symmetric nodes can be expressed as OUT =A d d where A d is the differential voltage gain and the voltage d = 1-35

36 Common-Mode and Differential-Mode Analysis roof for Symmetric Circuit with Symmetric Differential Output: By superposition, the single-ended outputs can be expressed as + = T + T OUT 0A 1 0B - = T + T OUT 0NA 1 0NB where T 0A, T 0B, T 0NA and T 0NB are the transfer functions from the A and B inputs to the single-ended + and - outputs OUT+ E OUT E OUT- 1 A B taking the difference of these two equations we obtain = - = T -T + T -T OUT OUT+ OUT- 0A 0NA 1 0B 0NB by symmetry, we have T OA =T ONB and T ONA =T OB thus can be express OUT as or as OUT OUT = T0A -T 0NA 1 - =A d d where A d = T OA -T ONA and where d = 1-36

37 End of Lecture 4 37