1 High-Voltage High Slew-Rate Op-Amp Design Team Tucson: Erik Mentze Jenny Phillips Project Sponsor: Apex Microtechnology Project Advisors: Dave Cox Herb Hess

2 Project Overview Deliverables: –PCB Prototype –Amplifier Performance Analysis –PSPICE Model Design a high voltage (+/- 200 V) and high slew rate (1000 V/us) discrete op-amp

3 Specific Design Challenges Power Limitation (P=IV) High Voltage required Slew Rate = I/C c Output Voltage Limitations

4 Dr. Jekyll & Mr. Hyde “ Circuit theory has a dual character; it is a Dr. Jekyll – Mr. Hyde sort of thing; it is two-faced, if you please. There are two aspects to this subject: the physical and the theoretical. The physical aspects are represented by Mr. Hyde – a smooth character who isn’t what he seems to be and can’t be trusted. The mathematical aspects are represented by Dr. Jekyll – a dependable, extremely precise individual who always responds according to established custom. Dr. Jekyll is the circuit theory that we work with on paper, involving only pure elements and only the ones specifically included. Mr. Hyde is the circuit theory we meet in the laboratory or in the field. He is always hiding parasitic elements under his jacket and pulling them out to spoil our fun at the wrong time. We can learn all about Dr. Jekyll’s orderly habits in a reasonable period, but Mr. Hyde will continue to fool and confound us until the end of time. In order to be able to tackle Mr. Hyde at all, we must first become well acquainted with Dr. Jekyll and his orderly ways.” -Ernst A. Guillemin Taken from the preface to his 1953 book Introductory Circuit Theory.

5 Project Breakdown –Dr. Jekyll – General Amplifier Topologies Find topology candidates Throw out those that are obviously deficient Analytically compare the “finalists” to make the best choice –Mr. Hyde – Hardware Implementation Find components that meet our design requirements Adapt chosen topology to meet physical requirements Simulate Implementation, comparing to Dr. Jekyll’s analytic models Implement design, comparing results to simulation and analytic models

6 Dr. Jekyll Two Theoretical Techniques to Improve Slew-Rate: 1. Reduce Capacitance - Passive Frequency Compensation - Active Frequency Compensation 2. Increase Current - Non-Saturated Differential Amplifier - Class AB Push-Pull Gain Stages

7 Two Topologies Two-Stage Amplifier using Miller Compensation –Simple Topology –Uses Passive Frequency Compensation –Brute Force Solution to Slew-Rate by Driving Large Currents into the Compensation Capacitor Three-Stage Dual-Path Amplifier –Complex Topology –Uses Active Frequency Compensation –More Elegant Solution to Slew-Rate by Significantly Reducing Size of Compensation Capacitors, while Maintaining the Ability to Drive Large Currents

8 Two-Stage Amplifier

9 The real issue at hand here is slew-rate. Because the two-stage amplifier (and it’s higher order cousins) use miller capacitors for compensation, the pole locations, and as such the size of the compensating caps are proportional to the ratio of the transconductance.

10 Two-Stage Amplifier: Governing Equations Open Loop Gain: Pole Locations: Compensation Capacitor Sizing:

11 Two-Stage Amplifier: Governing Equations (Continued) This can be further simplified for comparison if we “cut off” the final term under the radical: The Compensation Capacitor is proportional to: - twice the arithmetic mean of the capacitances - the ratio of transconductances

12 Three-Stage Dual-Path Amplifier Input Differential Amplifier Upper Signal Path Lower Signal Path Damping-Factor Control Block Active Feedback Network Output Buffer

13 Three-Stage Dual-Path Amplifier Uses two Active Compensation techniques: –Damping-Factor Control block Removes a compensation capacitor from the output Replaces it with an Active-C block that uses a significantly smaller capacitor. Introduces a high degree of controllability of the non- dominate poles. –Active-Capacitive-Feedback network Adds a positive gain stage in series with the dominate compensation capacitor, reducing the required cap size. Gives an enormous amount of flexibility in determining the amplifier’s dominate poles.

14 Three-Stage Dual-Path Amplifier Because active feedback adds a gain block to each compensating capacitor, we are able to simultaneously: - reduce capacitance - increase current drive The active nature of the feedback allows us to model the frequency and phase response of the amplifier according to any frequency response function we choose. A good choice for maximum bandwidth and good phase margin is a third-order Butterworth response:

15 Three-Stage Dual-Path Amplifier The dimensional values of the active feedback transconductance stages and capacitors are set according to this response:

16 Three-Stage Dual-Path Amplifier Note that for this amplifier topology the slew-rate is going to be defined as: Where I b and I a are independently controllable currents available to charge and discharge the compensating capacitors.

17 Three-Stage Dual-Path Amplifier This can be further simplified for comparison if we consider gm3=gm5. This is a desirable performance choice for AB operation in the output The Compensation Capacitor is proportional to: - the geometric mean of the capacitances - the root of the ratio of transconductances - a constant that is less than one

18 Performance Comparison Two-Stage AmplifierDual-Path Amplifier Greater than the product of twice the arithmetic mean of the lumped parasitic capacitances and the ratio of the transconductances. Equal to the product of the geometric mean of the lumped parasitic capacitances, the root of the ratio of the transconductances, and a constant less than one.

19 Performance Comparison We can show that the following is guaranteed : In fact Ca and Cb will be MUCH smaller than Cc!

20 Comparison Two Stage Amplifier with Miller Compensation Three Stage Dual Path Amplifier 1.Simple Topology 2.Reduced Bandwidth 3.Larger Compensating Caps 4.Able to drive large currents to charge and discharge caps 1.Complex Topology 2.Extended Bandwidth 3.Smaller Compensating Caps 4.Able to drive large currents to charge and discharge caps. 5.Can independently size gain stages that drive caps.

21 Specific Gain Stages

22 Differential Amplifier Both topologies use a differential amplifier as the input stage. As such, a detailed analysis of the available differential amplifier topologies is needed.

23 Source coupled differential pairs are limited to sourcing and sinking their biasing current. By moving the biasing current source out of the signal path this limitation can be overcome. Such diff-pair topologies form a class of diff-pairs referred to as “non- saturating differential pairs”. Source Coupled Diff-Amp

24 Nonsaturating Differential Pairs Operates the same as a source-coupled diff-pair over a given range of differential input values. Unlike the source coupled diff-pair however, outside of these values the output current does not saturate. The output current continues to increases proportional to the square of the input differential voltage. This results in a diff-amp that does not exhibit slew-rate limitations.

25 ID1 ID2 Iout = ID1-ID2 ID1 ID2 ID1ID2 Iout = ID1-ID2 Source Cross-Coupled Differential Amplifier Nonsaturated Differential Amplifier

26 Source Cross-Coupled Differential Amplifier ID1 ID2 Iout = ID1-ID2 ID1 ID2 Governing Equations: Boundary Conditions for AB Operation: Vbias

27 ID1ID2 Nonsaturated Differential Amplifier Governing Equations: Boundary Conditions for AB Operation: ISS

28 Summary of Critical Points of Transfer Characteristics Normalized to Biasing Conditions: Source Cross-Coupled Differential Amplifier Unsaturated Differential Amplifier WLOG consider the case where: ID2 = 0 WLOG consider the case where: ID2 = ISS This occurs at a differential input voltage of: Corresponding to this input is an ID1 value of: This occurs at a differential input voltage of: Corresponding to this input is an ID1 value of:

29 ISS 2ISS 3ISS 4ISS 5ISS ID1ID2 ID1ID2 Source Cross-Coupled Differential Amplifier Unsaturated Differential Amplifier Transfer Characteristics Normalized to bias conditions

ISS - 4ISS - 3 ISS - 2 ISS - ISS 3 ISS 2 ISS ISS Source Cross-Coupled Differential Amplifier Unsaturated Differential Amplifier Source Coupled Diff-Pair Output Transfer Characteristics Normalized to bias conditions

31 1.Off-Center Common-Mode Range 2.2 Gate Input Capacitances 3.Uses 10 FETs 4.ID1 or ID2 equals zero for large step input 5.Small Signal Transconductance: Comparison of Source Cross-Coupled Diff-Pairs Source Cross-Coupled Differential Amplifier Nonsaturated Differential Amplifier 1.Centered Common-Mode Range 2.1 Gate Input Capacitance 3.Uses 8 FETs 4.ID1 & ID2 Never Equal Zero 5.Small Signal Transconductance: “Large Step” Transconductance becomes approximately equal for a large enough input step.

32 THE BIG QUESTION!

33 Which one has the most useful advantages???

34 Class AB Amplifier Combines high- gain common source amplifier with a unity gain source follower No output slew-rate limitations Output voltage swing limited to a threshold below VDD and above VSS

35 Current Limiting on AB Output I OUTMIN = V THP /R I OUTMAX = V THN /R Gate drive is removed from M1 or M2 if current leaves range

36 Mr. Hyde

37 Specific Design Challenges Power Limitation (P=IV) High Voltage required Slew Rate = I/C c Output Voltage Limitations

38 Physical Implementation Challenges Must bias devices within specifications Power limitation means biasing devices so minimal voltage drop across each Allow maximum current through devices

39 Devices Found TO92 Package: Zetex ZVN0545A Zetex ZVP0545A Surface Mount: Zetex ZVP0545G

40 TO92 Specifications N-ChannelP-Channel Drain-Source Voltage 450 V-450 V Continuous Drain Current 90mA-45 mA Pulsed Drain Current600 mA400 mA Power Dissipation700 mW Gate-Source Voltage+/- 20 V

41 Surface Mount Specifications N-ChannelP-Channel Drain-Source Voltage 450 V-450 V Continuous Drain Current 140 mA-75 mA Pulsed Drain Current600 mA-400 mA Power Dissipation2 W Gate-Source Voltage+/- 20 V

42 Device Models Have working PSPICE models for devices BSIM3v3 models Verified with I DS v. V DS plots

43 Cost of Devices NMOS (TO92) –10 Parts for $20.70 –100 Parts for $ –500 Parts for $ PMOS (TO92) –10 Parts for $23.22 –100 Parts for $ –500 Parts for $ NMOS (Surface Mount) –10 Parts for $11.25 –100 Parts for $67.50 –500 Parts for $ PMOS (Surface Mount) –10 Parts for $13.55 –100 Parts for $81.27 –500 Parts for $316.05

44 PCB Sierra Proto Express PCB Express Advanced Circuits

45 Project Schedule Finalize Amplifier Topology – 11/19/04 Preliminary Simulation Results – 1/17/05 Final Simulation Results – 1/28/05 Perfboard Testing Completed – 2/11/05 PCB Layout Finalized – 2/18/05 Preliminary Modeling – 3/4/05 Write Test Procedures – 3/11/05 PCB Test and Measurement – 3/19/05 Final Modeling – 3/25/05 Tie up Loose Ends by EXPO! – 4/29/05

46 Q & A

47 References [1] H. Lee, et al., “A Dual-Path Bandwidth Extension Amplifier Topology With Dual-Loop Parallel Compensation,” IEEE J. Solid-State Circuits, vol. 38, no. 10, Oct [2] H.T. Ng, et al., “A Multistage Amplifier Technique with Embedded Frequency Compensation,” IEEE J. Solid-State Circuits, vol. 34, no 3, March [3] H. Lee, et al., “Active-Feedback Frequency-Compensation Technique for Low-Power Multistage Amplifiers,” IEEE J. Solid-State Circuits, vol. 38, no 3, March [4] K. Leung, et al., “Three-Stage Large Capacitive Load Amplifier with Damping-Factor-Control Frequency Compensation,” IEEE Transactions on Solid-State Circuits, vol. 35, no 2, February [5] H. Lee, et al., “Advances in Active-Feedback Frequency Compensation with Power Optimization and Transient Improvement,” IEEE Transactions on Circuits and Systems, vol. 51, no 9, September [6] B. Lee, et al., “A High Slew-Rate CMOS Amplifier for Analog Signal Processing,” IEEE J. Solid-State Circuits, vol. 25, no. 3, June [7] E. Seevinck, et al., “A Versatile CMOS Linear Transconductor/Square-Law Function Circuit,” IEEE J. Solid-State Circuits, vol. SC-22, no. 3, June [8] J. Baker, et al., CMOS: Circuit Design, Layout, and Simulation. New York, NY: John Wiley & Sons, Inc., [9] B. Razavi, Design of Analog CMOS Integrated Circuits. Boston, MA: McGraw Hill, [10] Sedra, Smith, Microelectronic Circuits, 5th ed. New York, NY: Oxford University Press, [11] Schaumann, Van Valkenburg, Design of Analog Filters. New York, NY: Oxford University Press, [12] V. Kosmala, Real Analysis: Single and Multivariable. Upper Saddle River, NJ: Prentice Hall, 2004.