Integrated DC-DC Converter with Ultra-Low Quiescent Current by Christine Chen S.B. EE, M.I.T, 2012 Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2013 @2013 Massachusetts Institute of Technology. .... .............. Author..................................... Department of Electrical Engineering and Computer Science May 2013 Certified by.................... Mark Vitunic Design Section Leader, Linear Technology VI-A Thesis upervisor ' Certified by.............. Michael P. Whitaker Design Engineer, Linear Technology VI-A Thesis Supervisor .7..... Certified vy...................... .-- -- David J. Perreault Professor of Electrical Engineering r4 fTS, s Supervisor Accepted by............. ................. Prof. Dennis M. Freeman Chairman, Masters of Engineering Thesis Committee 2 Integrated DC-DC Converter with Ultra-Low Quiescent Current by Christine Chen Submitted to the Department of Electrical Engineering and Computer Science on May 21, 2013, in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering Abstract Based on the LTC3588, the design of a bandgap reference and a comparator for use in the control circuitry of DC-DC converter with an ultra-low quiescent current of 150nA is presented here. Not only will this thesis discuss the challenges encountered over the course of designing circuits to operate at such low current levels, but it will also provide proof of concept silicon evaluation data of modified LTC3588 chips demonstrating that such low current operation is viable. VI-A Thesis Supervisor: Mark Vitunic Title: Design Section Leader, Linear Technology VI-A Thesis Supervisor: Michael P. Whitaker Title: Design Engineer, Linear Technology Thesis Supervisor: David J. Perreault Title: Professor of Electrical Engineering 3 4 Acknowledgments I am grateful to Linear Technology Corporation for having the opportunity to work on this project for my thesis research. In particular, I would like to especially thank Sam Nork for his endless support and advice throughout my entire VI-A experience with the LTC at the Boston Design Center. I would also like to thank Mark Vitunic and Mike Whitaker for being such wonderful thesis supervisors. There was never a dull moment working with them, and I always came away with some new piece of information after every pow-wow. I would like to thank Professor David Perreault for his help and guidance over the course of this thesis research. I would also like to recognize Victor Fluere for all his infinite wisdom about bandgap circuits, Ron Swinnich for always being able to fix my evaluation boards even when I did not think it was possible, and Aspiyan Gazder for his brainstorming help and advice over the course of this project. Special thanks to my Linear family, including but not limited to Wendi Rieb, Eko Lisuwandi, and John Fiorenza, for making my experience working at the Boston Design Center such a wonderful one. I would especially like to thank Thilani Bogoda for being such an awesome roommate and source of advice and support when I needed it. My heart goes out to the amazing people I met here at MIT, who have seen me at my best and my worst and never judged me for any of it: Alicia Erwin, Hilary Monaco, Bridget Wall, Isabella Lubin, Vamsi Aribindi, Alejandro Arambula, and William Chow. Likewise, many thanks go out to Ted Shinta, Mauri Laitinen, and Bruce Kawanami for being such great teachers and sources of inspiration and encouragement on my way to MIT. Lastly, I would like to thank my family without whom I would not be where I am today. I am forever grateful for my parents for their support and encouragement on the path that I have taken and for always believing in me even when I did not. Their infinite patience with me is not something I have always appreciated, but recognize now with sincere gratitude. Thank you so much for letting me find my own way and make my own mistakes so that I could learn from them. 5 6 Contents 1 2 17 . . . . . 1.1 Prior Work 1.2 Proposed Work . . . . . . . . . . . . . . . . . . . . . . 2.2 2.3 System Operation and Analysis . . . . .... ....... 19 2.1.1 The Sleep State . . . . . . . . . . . . . . . . . . . . 20 2.1.2 The Active State . . . . . . . . . . . . . . . . . . . 20 Figures of Merit . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . 21 2.2.1 Line and Load Regulation 2.2.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.3 Output Voltage Ripple . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Quiescent Current Modifications . . . . . . . . . . . 23 2.3.2 Other Modifications . . . . . . . . . . . . . . . . . 24 2.3.3 Weak Bias Blocks . . . . . . . . . . . . . . . . . . . 26 2.3.4 Figure of Merit Evaluation . . . . . . . . . . . . . . 26 2.3.5 Summary . . . . . . . . . . . . . . . . . . 28 Proof of Concept 29 Bandgap Reference 3.1 18 19 System Overview 2.1 3 17 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.1 Widlar Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.2 Feedback and AC Stability . . . . . . . . . . . . . . . . . . . . 32 Theory of Operation 7 3.2 3.3 33 3.2.1 Bipolar 3 Variation . . . . . . . . . . . . . . . . . . . 33 3.2.2 Emitter Area Ratio . . . . . . . . . . . . . . . . . . . 38 3.2.3 Collector-Substrate Leakage at High Temperatures 39 3.2.4 Layout and Matching Techniques . . . . . . . . . . . 41 Start-up Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3.1 Supply Voltage Dependence . . . . . . . . . . . . . . 43 3.3.2 Final Design . . . . . . . . . . . . . . . . . . . . . . . 45 3.4 Trim Range and the ZTC Voltage . . . . . . . . . . . . . . . 46 3.5 Bandgap Ready and Undervoltage Lockout Signals . . . . . 47 3.6 3.7 4 . . . . . . . . . . . . . Design Variations and Non-Idealities 3.5.1 Bandgap Ready Circuitry . . . . . . . . . . . . . . . 47 3.5.2 UVLO Signal Circuitry . . . . . . . . . . . . . . . . . 50 3.5.3 Combining the Bandgap Ready and UVLO Signals . 51 3.5.4 Final Design Integration . . . . . . . . . . . . . . . . 56 . . . . . . . . . . . . . . . . . . . . . . . . 59 3.6.1 Measurement Setup . . . . . . . . . . . . . . . . . . . 59 3.6.2 Measurement Data and Analysis . . . . . . . . . . . . 60 Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.7.1 Schematics . . . . . . . . . . . . . . . . . . . . . . . . 63 3.7.2 Simulation Results . . . . . . . . . . . . . . . . . . . 64 Proof of Concept 67 Sleep Comparator 4.1 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 BJT and MOS Device Characteristics . . . . . . . . . . . . . . . . . . 68 4.2.1 MOS in Subthreshold . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.2 Differential Pairs . . . . . . . . . . . . . . . . . . . . . . . . . 69 Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.1 DC Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.2 AC Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Adaptive Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3 4.4 8 Gain per Stage 4.6 Topology Comparison..... 4.7 4.8 5 75 . . . . . . . . 4.5 76 4.6.1 Topology I . . . . . . . 76 4.6.2 Topology II . . . . . . 77 4.6.3 Topology III . . . . . . 78 4.6.4 Topology IV ...... 79 4.6.5 Topology V . . . . . . 79 4.6.6 Simulation Results . . 81 . . . . . . . 81 4.7.1 Measurement Setup . . 81 4.7.2 Measurement Data and Analysis 83 Proof of Concept Final Design . . . . . . . . . . 87 4.8.1 Schematic . . . . . . . 87 4.8.2 Current Bias Leg . . . 87 4.8.3 Simulated Results . . . 88 89 Conclusion . . . . . . . . . . . . . . . . . . . . . . 89 . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1 Combined Simulated Results 5.2 Recap and Future Work 9 10 List of Figures 2-1 LTC3588 Block Diagram [5] . . . . . . . . . . . . . . . . . . . . . . . 19 2-2 Buck Converter Topology . . . . . . . . . . . . . . . . . . . . . . . . 20 2-3 Disabled Blocks in LTC3588 Modifications [5] . . . . . . . . . . . . . 24 2-4 Pin Re-purposing in LTC3588 Modifications . . . . . . . . . . . . . . 25 2-5 Line Regulation with Ct=100pF . . . . . . . . . . . . . . . . . . . . 26 2-6 Load Regulation Ct=100pF . . . . . . . . . . . . . . . . . . . . . . 27 2-7 Efficiency Curve for V,.=1.8V . . . . . . . . . . . . . . . . . . . . . . 28 3-1 Summation of CTAT and PTAT Voltages [8] . . . . . . . . . . . . . . 29 3-2 Producing with two Bipolar Transistors . . . . . . . . . . . . . 30 3-3 Graphical Analysis of the Intersection of Eq. 3-2 and Eq. 3-3 . . . . . 31 3-4 Widlar Bandgap Cell where m>0 . . . . . . . . . . . . . . . . . . . . 32 3-5 Modified Feedback Circuit . . . . . . . . . . . . . . . . . . . . . . . . 33 3-6 8 as a function of the Collector Current [9] . . . . . . . . . . . . . . . 34 3-7 Gummel Plot for the Base and Collector Currents [10] . . . . . . . . 35 3-8 Addition of R, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3-9 Splitting of RE such that RE=RE1+RE2 . . . . . AVBE . . . - -. . . . 37 3-10 Gain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3-11 3-D Representation of Base-Emitter Junction [9] . . . . . . . . . . . . 39 3-12 Temperature Dependence of Collector-Substrate Leakage . . . . . . . 40 . . . . . . . . . . . . 41 . . . . . . . . . . . . . . . . . . . . . . . . . 42 3-15 PMOS Cross Sections [13] . . . . . . . . . . . . . . . . . . . . . . . . 43 3-13 Equalizing Collector-Substrate Current Leakage 3-14 Sample Start-up Circuit 11 3-16 I-V Characteristics of Depletion Mode PMOS . . . . . . . . . . . . . 44 3-17 Start-up Leg with Self-Regulating Depletion Mode PMOS Current Source 44 3-18 Start-up Leg Current as a function of Supply Voltage for RST = 320MQ 45 3-19 Trim Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 . . . . . . . . . . . . . . . 48 3-21 Supply Voltage DC Sweep Simulation Results for Topology #1 . . . . 48 . . . . . . . . . . . . . . . 49 3-23 Supply Voltage DC Sweep Simulation Results for Topology #2 . . . . 49 3-24 Bandgap Circuit Dependent UVLO Signal Circuit . . . . . . . . . . . 50 3-25 Bandgap Inspired UVLO Signal Circuit where 'VSUPPLYMIN 51 3-20 Bandgap Ready Comparator Topology #1 3-22 Bandgap Ready Comparator Topology #2 = VREF 3-26 Bandgap Ready Circuit Supply Voltage DC Sweep Simulation for Var- ious RBGR -.. . .... ................................... 3-27 Bandgap Ready Topology Variation #1 . . . . . . . . . . . . . . . . . 52 53 3-28 Bandgap Ready Topology Variation #1 Supply Voltage DC Sweep Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3-29 Bandgap Ready Topology Variation #2 . . . . . . . . . . . . . . . . . 54 3-30 Bandgap Ready Topology Variation #2 Supply Voltage DC Sweep Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3-31 UVLO Signal Circuit with Modified Bandgap Start-up Leg . . . . . . 55 3-32 VGS and VBE Temperature Coefficients for 5nA of Drain and Collector Bias Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3-33 UVLO Signal Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3-34 Evaluation Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 . . . . 60 . . . . . . 61 3-37 Simulated Reference Voltage . . . . . . . . . . . . . . . . . . . . . . . 62 3-38 Untrimmed Reference Voltage with Varying Supply Voltage . . . . . . 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3-40 Bandgap Trim Network . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3-41 UVLO Signal Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3-35 Measured Untrimmed Reference Voltage with VSUPPLY=3.5V 3-36 Measured Trimmed Reference Voltage with 3-39 Bandgap Circuit 12 VSUPPLY=3.5V 3-42 Simulated Bandgap Reference Voltage over Temperature at 5V ....... VSUPPLY = 65 ..................................... 3-43 Simulated UVLO Signal over Supply Voltage . . . . . . . . . . . . . . 65 4-1 Base Current Cancellation Technique . . . . . . . . . . . . . . . . . . 70 4-2 Bipolar Device Cross Section [14] . . . . . . . . . . . . . . . . . . . . 71 4-3 MOS Device Cross Section[14] . . . . . . . . . . . . . . . . . . . . . . 72 4-4 Two Stage Comparator with AC and DC Hysteresis Circuitry . . . . 73 4-5 Two Stage Comparator with Adaptive Biasing . . . . . . . . . . . . . 75 4-6 Topology I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4-7 Topology II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4-8 Topology III where I, = 9I . . . . . . . . . . . . . . . . . . . . . . . 78 4-9 Topology IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4-10 Topology V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4-11 Measurement Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 81 4-12 QFN Evaluation Board for Single Part . . . . . . . . . . . . . . . . . 82 4-13 Large QFN Evaluation Board . . . . . . . . . . . . . . . . . . . . . . 82 . . . . . . . . . . . . . 83 4-15 Comparison of Output Ripple for Various Capacitors for EXP13 . . . 84 = 22pF . . . . . . . . . . . . 85 4-14 Output Ripple as a Function of Load Current 4-16 Comparison of Output Ripple with C, 4-17 Comparison of Output Ripple for Various Quiescent Current Levels and Output Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4-18 Sleep Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 13 14 List of Tables 1.1 Specifications for several current Linear Technology Switching Converters and the Proposed Converter [2][3][4][5][6] . . . . . . . . . . . . 18 2.1 LTC3588 Experiment Variations . . . . . . . . . . . . . . . . . . . . . 23 3.1 Key Bandgap and UVLO Simulation Data . . . . . . . . . . . . . . . 65 4.1 npn and pnp Junction Capacitances at Zero Bias . . . . . . . . . . . 71 4.2 NMOS and PMOS Parasitic Capacitances at Zero Bias . . . . . . . . 72 4.3 Comparison of Propagation Delay and Output Ripple for Various Sleep Comparator Topologies with VSUPPLY=3.5V, Cot=100pF, ILOAD=5OmA 81 4.4 Labeled vs. Actual Capacitance Values . . . . . . . . . . . . . . . . . 4.5 Sleep Comparator Simulation Data with VSUPPLY=5V, Cot=100pF, ILOAD=5OmA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 85 88 Sleep Comparator Measurements with Bandgap Circuit with VSUPPLY=3.5V, Cot=100ptF, and ILOAD=5OmA . . . . . . . . . . . . . . . . . . . . . 15 89 16 Chapter 1 Introduction In a world increasingly concerned with maximization of device lifetimes, demand for highly efficient DC-DC converters with ultra-low nominal operating current exists across a variety of industries. In particular, such converters find specific applicability in both remote battery-based systems where changing the battery can be especially troublesome and in portable battery-based systems where constantly changing the battery can become costly and inconvenient. Applications for such converters predominately include sensors and biomedical devices. For example, with the advent of new low power communication protocols, wireless sensors simply do not need to consume very much power at all. If such sensors were monitoring a factory production line, replacing the batteries powering such sensors necessitates a costly partial or complete shutdown in production. In biomedical applications, implanted medical devices such as pacemakers and cochlear implants already operate at very low energy levels [1]. With a highly efficient switching converter with low operating current, these devices can extend their battery lives or increase the on-board computational power for the same battery life. 1.1 Prior Work The demand for and benefits of highly efficient DC-DC converters that have a low quiescent current are reflected in the rise in popularity of micropower converters. 17 Related research has also been conducted in previous theses on lowering quiescent current in switching converters (Gardner, MIT, 2008) as well as conference papers on designing converters and regulators for portable applications (Xiao, UC Berkeley, 2003). Commercially, many switching converters operate with a quiescent current in the single digit pA range and are available for a range of input and output voltages and load currents. VIN Range (V) 42 3.2 - 16 2.5 ISUPPLY (yA) 2.7 LT3971 4.3-38 1.19-30 1.2 2.1 LTC3103 LTC3588 LTC3388 Proposed 2.5 - 15 2.7 - 20 2.7 - 20 1.8 - 5 0.6 - 13.8 1.8 - 3.6 1.2 - 5 1.8 - 3.6 0.3 0.1 0.05 0.1 1.8 0.95 0.82 < 0.150 4 - VOUT Range (V) IOUT,MAx Part LT3975 (A) Table 1.1: Specifications for several current Linear Technology Switching Converters and the Proposed Converter [2] [3] [4] [5] [6] 1.2 Proposed Work The focus of the work presented here is to push the quiescent current even lower and design a low voltage, high efficiency switching converter with an ultra-low quiescent current of less than 150nA, as seen in Table 1-1. Based on the LTC3588, a piezoelectric energy harvesting buck converter with a no-load quiescent current of 950nA, the proposed converter will operate with a similar hysteretic control scheme to maintain high efficiency. Reaching the substantially lower quiescent current levels proposed here requires the re-design of two of the main operating blocks in the LTC3588 system, the bandgap and sleep comparator circuits. To do this effectively, the effects of low current operation were first evaluated in modified versions of the LTC3588 fabricated with lower operating currents. The evaluation results then informed the strategies used in the low current design of the bandgap and sleep comparator blocks. 18 Chapter 2 System Overview Although the stated low quiescent current objective is achieved through the re-design of various blocks, the primary functionality of the blocks and the connections between the blocks remain largely unchanged. As a result, the converter system presented here will still possess the same overall control scheme as that in the LTC3588. 2.1 System Operation and Analysis V5 FM 20VW COM G REF~t VowT 01,00 COWPR Figure 2-1: LTC3588 Block Diagram [5] 19 1MPO The relevant control blocks that determine the system operational state are marked in the block diagram of Figure 2-1. First, the undervoltage (UVLO) block determines the on-off state of the entire system based on a minimum input supply voltage. If this minimum is met, then the result of a comparison between the bandgap voltage and a preselected fraction of the output voltage decides whether or not the buck converter is active. Internal to the converter itself is a boundary mode control scheme (not shown in detail) that generates the switching function and thus sets the frequency of operation based on the output inductance. When the converter is on, called the active state, the sleep comparator checks to see if the output voltage has reached regulation yet, whereas in the sleep state when the converter is off, the sleep comparator checks to see if the output voltage has fallen out of regulation. Regardless of the converter state, the UVLO continues to track the supply voltage to ensure that the minimum voltage for proper operation has been met. 2.1.1 The Sleep State In the sleep state, the main current consuming blocks are the UVLO, bandgap, sleep comparator blocks, although a number of blocks still remain weakly biased for fast wake up from sleep. When the output is in regulation, the overall quiescent current is equal to the proposed no-load quiescent current listed in Table 1-1. The target supply current total of 150 nA is then allocated evenly among the sleep comparator block, the combined bandgap-UVLO block, and the weakly biased blocks. 2.1.2 The Active State L +s _ (t) + cev, td Figure 2-2: Buck Converter Topology 20 In the active state, the converter dominates the total current consumption. For a generic buck converter, such as that pictured in Figure 2-2, the input-output voltage relationship is determined by the duty cycle D of the switching function q(t), and the average supply current is a function of D and the average inductor current. In this case, the switching function q(t) is controlled by a peak current comparator block, which limits the maximum inductor current to the same value each cycle. However, with the converter running at the boundary of continuous and discontinuous modes of operation, the output inductance and output voltage set the time it takes for the inductor current to ramp up to and down from its peak value. 2.2 Figures of Merit Though the functionality of the re-designed blocks for low quiescent current operation does not affect the control flow, the system should still be evaluated for the following system level figures of merit to assess its effects, if any, on the overall performance: line regulation, load regulation, efficiency, and output voltage ripple. 2.2.1 Line and Load Regulation Line and load regulation measure the accuracy of the DC output voltage versus changes in the input supply voltage and load current, respectively. For a robust system, the output voltage should vary as little as possible across the entire range for both parameters. Line Regulation AVOUT = VOUTIVSUPPLY=V1 - VOUTI VSUPPLY=V2 [mV/V] (2.1) V 1 - V2 Load Regulation AVOUT = VOUTIILOAD=Il - VOUTIILOAD=I2 I - 12 21 [mV/mA] (2.2) 2.2.2 Efficiency The efficiency of the system is a measure of how well the system is able to transfer power from the input to the output. Efficiency r = PO The input power PIN (2.3) - V VINIIN PIN can further be re-written as the sum of the output power and the power dissipation resulting from the control blocks and various resistive, capacitive and inductive losses [1]. Pin = Paut + Pconduction + Pswitching + Parasitics+ Pcontroi + Pleakage From this breakdown of the components contributing to PIN, (2.4) as long as the output power is the dominating term, the efficiency will remain high as the load current decreases. However, once the load current is small enough, the efficiency will begin to drop as the unwanted power dissipation terms begin to dominate in the input power expression. If the dominant power dissipation term is due to the control blocks, then the lower the sleep state quiescent current, the lower the load current at which the efficiency will begin to decrease significantly. 2.2.3 Output Voltage Ripple Due to the propagation delay and built-in DC hysteresis of the comparator comprising the converter control loop, the output capacitor will see some voltage variation, determined as a function of the output capacitor size and load current. 2 where Vhysteresis + 1 1o[tPHLILOAD + tPLH(ICHARGE - ILOAD) (2.5) aut = tPHL = sleep comparator propagation delay to turn the converter on, tPLH = sleep comparator propagation delay to turn the converter off, CHARGE SIL,PEAK - 2 22 As such, to keep the output voltage ripple as close as possible to just the built-in DC hysteresis, either the comparator needs to be very fast or the output capacitor must be very large. In any case, the lower the output ripple, the better the system's ability to maintain the output voltage as close as possible to the desired value. Proof of Concept 2.3 2.3.1 Quiescent Current Modifications To test the performance and functionality at low current operation, modified versions of the LTC3588 possessing lower current consumption in the bandgap, sleep comparator, and weak bias current generation blocks were fabricated and evaluated. The various versions of the fabricated parts listed in Table 2.1 can be broken down into three distinct groups: one set where only the bandgap current is varied, one set where only the sleep comparator current is varied, and one set where the quiescent currents in the two blocks are varied together. To identify the chip variation since all variations were fabricated on the same wafer, an identification resistor RID was added as well. Experiment % of IBANDGAP % of ISLEEPCOMP % of IWEAKBIAS RID 10kQ, GND 20kQ, GND 40kQ, GND 80kQ, GND 160kQ, GND 320kQ, GND 640kQ, GND 10kQ, VDD 20kQ, VDD 40kQ, VDD 80Q, VDD 160Q, VDD 320Q, VDD * the EXP09 bandgap has a non-essential core resistor short ed out as a side EXP01 EXP02 EXP03 EXPO4 EXP05 EXP06 EXP07 EXP08 EXPO9 EXP10 EXP11 EXP12 EXP13 100 50 33 25 16.7 50 33 25 16.7* 16.7 16.7 16.7 16.7 100 100 100 100 100 50 33 25 16.7 50 33 25 16.7 100 100 100 100 100 25 25 25 25 25 25 25 25 experiment Table 2.1: LTC3588 Experiment Variations 23 Because the fabrication of the modified parts was limited to changes in the mask for the resistive and metal layers, the values of resistors in the bandgap, the sleep comparator and the weak bias current generation blocks were increased by scaling down their widths in order to change the quiescent current. While pushing the quiescent current even lower would have been desirable, the minimum resistor width design rule limited the lower bound of possible quiescent current reduction to 16.7% without making major layout changes. The maximum number of versions that could be fabricated on a single wafer also influenced the chosen quiescent current percentages. 2.3.2 Other Modifications N1ERML RAL "3 CAP S SW 7VW P22 2 CWMAR PUM0 Figure 2-3: Disabled Blocks in LTC3588 Modifications [5] Aside from the quiescent current modifications, other circuitry changes were made both to isolate the low current effects and to allow for the evaluation of such effects. In the LTC3588 block diagram reproduced again in Figure 2-3, the marked nonrelevant blocks, such as the piezoelectric energy harvesting diode bridge and high voltage shunt, were disabled. While the internal rail generation block was originally necessary for the gate drives of the converter switches, the change in the specified 24 input supply voltage range from up to 20V to between 1.8V and 5V rendered the block unnecessary. By doing so, the supply current measured in the sleep state will solely represent the sum of the quiescent currents of the bandgap, sleep comparator and weak biased blocks. At the output, the resistors and capacitors forming the output divider for the feedback node input of the sleep comparator were connected differently to produce the correct feedback voltage. To evaluate the performance of the bandgap block, three pins were re-purposed to bring out the reference voltage, the bandgap ready signal, and the bandgap supply voltage, as shown in Figure 2-4. To identify the different variations since all of them were fabricated on the same wafer, a resistor of varying value was connected to ground or the supply voltage at one end and a bond pad for a new identification pin at the other. While the disabling of the diode bridge freed two pins, the multiple output voltage option had to be eliminated as well to release the remaining two pins needed, resulting in the permanent selection of the 1.8V output voltage. RDN N BG5UPPLY BGREADY VREF COFgeOR icto PM Figure 2-4: Pin Re-purposing in LTC3588 Modifications 25 2.3.3 Weak Bias Blocks Not active during the sleep state,the weak bias blocks are those that benefit from a small "keep alive" bias for faster power up when the system returns to the active state. While lowering the amount of weak bias to the bare minimum necessary falls under the quiescent current minimization objective, the solution and process by which to do so will not be addressed here. The effect of the lowered weak bias current in the fabricated variations was not fully characterized during the evaluation process although the change did not appear to significantly affect the expected system operation. 2.3.4 Figure of Merit Evaluation Line and Load Regulation 1.78 1.767 1.76 1.72 1 1.71 1 2.5 3.0 3.5 4.0 4 5.0 Supply Voltage (V -+-EXP05_25mA -e-EXP0S_7SmA -)- -*- EXP13_7smA -- EXP13_25mA -a-EXP05_125mA EXP13_125mA Figure 2-5: Line Regulation with Cat=100pF To determine the line regulation, the DC output voltage was measured at fixed load currents across the supply voltage range of 2.5V to 5.OV in 0.5V increments. Conversely, for the load regulation, the DC output voltage was measured at fixed supply voltages across the load current range of 25mA to 125mA in 25mA increments. Based on the evaluation data graphed above, the output voltage varied by less than one percent in the worst case scenario of VSUPPLY = 5V and ILOAD = 125mA, respectively, between EXPO5 and EXP13. 26 1.78 1.77 1.76 1.7S 1.74 1.73 1.72 1.71 21 0 75 100 125 Load Current (mA) -+-EXPO5_2.5V--EXPOS_3.V--EXP5_5.OV -U- EXP13_2.SV-u- EXP13_3.5V-.- EXP13_5.OV Figure 2-6: Load Regulation Ce=100pF Efficiency To calculate the efficiency, four different measurements must be taken: the DC supply voltage, the average supply current, the DC output voltage and the DC output current. While the DC supply voltage, DC output voltage, and DC output current can be easily measured with multimeters, the measurement of the average supply current is taken by placing a large multipole low pass filter in series with the ammeter and allowing the measurement to settle over a very long time to the proper DC value. Since the supply current varies depending on whether the system is active or sleeping, the series filter performs an averaging function to determine the average overall quiescent current. Once the measurements are taken, the efficiency r7 can simply be calculated as presented in Section 2.2.2. From the efficiency data presented in Figure 2-7 for the LTC3588 and EXP13, the load current at which the efficiency begins to drop off significantly is higher for the LTC3588 due to its higher sleep quiescent current. In addition, the efficiency over the load current range is slightly higher for EXP13 at a supply voltage of 2.5V compared to 5V, which can be attributed to the slight decrease in the components contributing to power loss that scale with the supply voltage. 27 100 90 'e 70 60 P 2 30 10 10 0.00001 0.001 0.01 0.01 0.1 1 10 100 Load Current (mA) -4- EXP13_5V -- EXP13_2.5V -a-3588_5V Figure 2-7: Efficiency Curve for Vo,,=1.8V 2.3.5 Summary Based on the silicon evaluation data for the system level figures of merit presented here, the reduction of the quiescent current in the sleep comparator and bandgap reference circuit by up to 16.7% had no apparent adverse effects on chip operation. Moreover, lowering the quiescent current of the chip in the sleep state extended the load current range over which the efficiency stayed at its maximum value. 28 Chapter 3 Bandgap Reference A bandgap circuit is often employed when a stable reference voltage is needed across a wide range of temperatures for comparison purposes. Often, the reference voltage produced by this circuit is the extrapolated bandgap voltage of the transistor material at OK (EGE). For instance, the bandgap voltage associated with silicon transistors is 1.206V while that associated with Gallium Arsenide (GaAs) transistors is 1.52V [10]. In addition, bandgap circuits can be stacked or otherwise configured to generate integer or fractional multiples of the bandgap voltage. 3.1 Theory of Operation VarVp? VB1'V/ . vi P A*sLops - - F r VTVOf IO. 2B -- V..V. +V", WJSTc INCREASE with l - Figure 3-1: Summation of CTAT and PTAT Voltages [8] 29 The fundamental premise of a bandgap circuit is that a temperature independent voltage can be produced through the summation of voltages with negative and positive temperature coefficients. To employ this idea, the circuit utilizes the natural negative temperature dependence of the base-emitter junction voltage, VBE, Of the bipolar transistor as the complementary to absolute temperature (CTAT) component. Conversely, the difference in the VBE of two bipolar transistors Qi and Q2 operating with different collector current densities acts as the proportional to absolute temperature (PTAT) component. IC '1C2 1 n AVb, R Figure 3-2: Producing AVBE with two Bipolar Transistors AVBE = kT -In-q Jc1 kT = -Jc2 q kT = ln nm q In AE2IC1 AE1IC2 where n=- AE1 and m=- IC2 (3.1) The dependence of the collector current density on the emitter area and collector current indicates that multiple combinations of the two variables produce the same AVBE value. As a result, the ratios of the two emitter areas and collector currents can be chosen as needed to fit design objectives. The amount of PTAT needed to balance out the CTAT component is generally achieved through a resistor ratio coefficient on the AVBE term. The application of Kirchoff's Voltage Law to derive the expression for AVBE COmbined with the selected current ratio m produces the following system of equations relating Ic, and IC2 that must hold true in order for Eq. 3-1 to be valid. 30 Ic = IM = 'C2 JCR Icec2 (3.2) mIc2 (3.3) Graphical analysis of the equation pair for m = 1 in Figure 3-3 reveals both degenerate and particular solution sets. To avoid the degenerate case, a start-up circuit is employed to force the bias currents into the non-zero state in combination with a feedback loop to maintain the desired operating point indicated by the particular solution set. 9 8 Ici 7 e "$ = 7 n 6particular solution 5 Ci = IC2 S4 3 2 degenerate 1 solution 0 o 0 1 2 3 4 5 6 c2 (nA) Figure 3-3: Graphical Analysis of the Intersection of Eq. 3-2 and Eq. 3-3 3.1.1 Widlar Cell While many different bandgap circuit topologies exist, the bandgap core circuit implemented here is based on the Widlar cell, seen in Figure 3-4. Based on the previous discussion, the CTAT component is the result of the diode connected transistor Q, or Q3, and the PTAT voltage is the result of the configuration of Q, and Q2. The addition of Q3 biases the collector voltage of Q2 to match that of Q, as closely as possible to equalize the voltage drops across R1 and mR 1. Since the currents through the resistors are approximately equal to the transistor collector currents, the feedback action of Q3 works to maintain the desired DC bias collector currents 31 o VREF R, mR, Q, Q Q2 n 1 RE Figure 3-4: Widlar Bandgap Cell where m>O through VBE Q, and Q2. For instance, if the output node, VREF, increases slightly, the of Qi (and thus Q2) will increase, thereby increasing the collector currents as well. This, in turn, will decrease the VBE Of Q3, pulling VREF back down. Although the AVBE expression exhibits two degrees of freedom, the current minimization objective constrains that down to just one by setting the two collector currents to be equal. For such a case, m equals 1 in Figure 3-4, and the reference voltage can be found by inspection by summing the voltage drops in the left leg. IC1 = IC2 = 1 kT Inn RE q -- 2 VREF VBE1 + (3.4) RTR + R1 kT - nn + R RE 3.1.2 (3.5) q Feedback and AC Stability In the modified cell variation in Figure 3-5, an additional device Q4 is placed at the collector of Q, such that the current mirror comparison of the collector current of and Q4 Q3 drives the collector voltages of Q, and Q2 to be equal. The result of the Ic3 and Ic4 comparison, which is an indirect comparison of Ici and IC2, then regulates the feedback node at the gate of the voltage follower NMOS, thereby controlling the 32 sum of Ici and IC2- 0 ®RTR Q4 mR1 R, ,1 2 O n 1 RE Figure 3-5: Modified Feedback Circuit Here, any disturbance at the base of Q, experiences positive gain at the feedback node through Q4, whereas the loop through Q3 provides negative gain as marked in the figure. For AC stability, the net gain of the two feedback loops must be negative. In addition, the compensation capacitor at the feedback node helps to ensure good phase margin for AC stability by reinforcing a low frequency dominant pole. 3.2 Design Variations and Non-Idealities Although the derived reference voltage equations from previous sections demonstrate a first-order temperature independence, certain idealized approximations were made to reach the simplified form. This section will introduce non-idealities associated with various approximations as well as design techniques for mitigating the resulting errors. 3.2.1 Bipolar 3 Variation Since the AVBE expression is derived from 1E and not IC, an error arises in the PTAT component of the voltage reference equation, which assumes that the # of the bipolar device is very large such that the emitter and collector currents of Q, and Q2 are 33 equal. While this approximation results in an error of less than 1% in the assumed collector current when 8 is greater than 100, the # of a bipolar device can drop much lower when it is running at very low or very high collector currents (Figure 3-6). The reduction in / at both ends can be explained by studying the components that make up the base current of an npn operating in the forward active region. In the forward active operating regime, the base current of a npn transistor is the sum of the base-to-emitter hole injection current and the space charge region recombination current at the base-emitter junction. IB = Ipbe + Iscrbe = -- (e is qqflF __ kT - 1) + IBo,scR(e nkT - 1) where n>1 (3.6) The flat portion of the graph of 8 v. Ic in Figure 3-6 indicates the collector current range where the space-charge region recombination current is small enough to have a negligible effect on #. However, as seen in Figure 3-7, as VBE decreases, the collector 100 1.0 0.01 100 1C, mA Figure 3-6: / as a function of the Collector Current [9] current Ic still decreases linearly towards Is on a log scale as predicted with a slope of , but the base current does not follow suit in a parallel manner towards -I. Rather, once the base to emitter hole injection portion of the base current becomes small enough, the space charge region recombination current is no longer negligible. As a result, the base current decreases with a slope less than A towards IBO,SCR 34 log IC, IB IC 1B n=1 is / 'BoSCR A IS VBC<O _F 0 VBE Figure 3-7: Gummel Plot for the Base and Collector Currents [10] as VBE decreases. The - factor difference in the exponential terms of the base and collector currents when recombination current dominates is demonstrated in the nonzero slope of 3 of A (1 - ) on a logarithmic scale at low currents in Figure 3-6. On the other end, for high collector currents, the Kirk effect dominates as a result of high level injection, increasing the effective base width due to the formation of a current-induced base in the space-charge region of the collector. Although bipolar transistors are usually operated in the flat region of the 3 plot to maximize forward gain, the target quiescent current level here sets the current through each transistor to be 5nA. At this particular operating point, the forward gain 3 can be as low as 75 at typical conditions depending on the process, which produces a 1.3% error. Across process corners and temperature variation, 8 can drop even lower, resulting in even greater error. The exact substitution of the relationship between IE and Ic and the inclusion of base currents as non-negligible reveals the 8 dependence of the PTAT component of the reference component. VPTAT,Widlar = /3+ 1RE [R1(1+ 35 -) 0 + 2RTR(1 + )] q In n (3.7) Technique #1: Adding R,3 One technique to reduce variation in AVBE across 3 is to introduce another resistor R6 between the bases of Qi and Q2 as shown in Figure 3-8. Now of the voltage drop across RE AVBE is the sum and R6, both of which are dependent upon /. AVBE IB2R6 + IE2RE = 1 8+ 1 = IC2( R + 3 RE) (3-8) "I RTR R , Q, 1 m R, CR R 0 3 n RE Figure 3-8: Addition of R,3 Due to the inverse 3 relationship, the additional factor j is generally negligible for high 3. On the other hand, for low 3, the base current required by Q, and Q2 to sustain the same amount of collector current increases, leading to a decrease in the collector current of Q1. To compensate for the increased base current loss at the collector of Qi, the j term is used to decrease the effective VBE Of Q2 to better match the collector currents of Q, and Q2. To determine the optimal value of R4, the bandgap circuit can be simulated using a parameter sweep on R8 for a specified range of /. Then, an appropriate value for R,6 can be selected based on the smallest amount of reference voltage variation across 8. 36 Nonetheless, one drawback to the implementation of Ra in the bandgap circuit is its location from a noise perspective. The magnitude of the thermal noise is not only directly proportional to the size of R3, but also multiplied by a gain factor to the output. Therefore, the resulting improvement in reference voltage variation must be balanced with the increase in noise. Simulations of the bandgap core with and without the addition of RO show only very slight differences in the reference voltage curves, and as such, the R technique was not implemented due to its undesirable noise effect. Technique #2: Splitting RE RTR R, mR, REI Q12 _, 1 n RE2 Figure 3-9: Splitting of RE such that RE=RE1+RE2 Another way to compensate for 3 variation involves the addition of a second resistor above the collector of Q1. The newly added resistor and the Q2 emitter degeneration resistor still sum to the original parts. In this case, the two resistance values RE and split the RE1 and RE2 AVBE voltage into two vary with # in opposing manners. VBE=IC( aly t RE1 t+1 + RE2) isb where Ic = Ici = C2 (3.9) = Mathematically then, the change in AVBE due to 3 is reduced by a factor of 37 # if RE1=RE2 from .±1 t3(,+1). However, as with Rp, the noise effect must be considered as well as part of a holistic evaluation of the addition of RE1. Through Vin R R Vout Vin + + I vn (a) Test Circuit r. } gM OVout ro (b) Small Signal Model Figure 3-10: Gain Analysis analysis of the small signal model of Figure 3-10(b), the gain vi"(5) '"'(") is found to be Vot Vin r. R (I - gmR) (3.10) + r. From the equation above, zero gain can be achieved if gmR = 1 which occurs when the voltage drop across the resistor R equals the thermal voltage k. q Selecting the value of RE1 then based on the bias collector current through Q, could allow for some # compensation while minimizing the resulting undesirable noise effect. One important aspect to note is that the desired AVBE generated must be at least as large as the thermal voltage in order to use this technique. Nevertheless, algebraic analysis reveals that for unequal values of worse than the original 3.2.2 . RE1 and RE2, the variation due to 6 is actually difference, limiting the utility of the technique. Emitter Area Ratio One important degree of freedom embedded in the design of the bandgap core is the emitter area ratio between Qi and Q2 that determines the magnitude of the generated AVBE. While the chosen area ratio will impact the necessary layout area of the bandgap core, its effect on the current density of Q2 is even more critical as the larger the ratio, the smaller the current density. 38 From the low P discussion in the previous section, the magnitude of the space charge region recombination current becomes increasingly important as the operational collector current decreases. Although both the hole injection and recombination current densities are generally scaled by just the emitter area AE to produce the corresponding currents, the recombination current at the sidewall regions of the base-emitter junctions cannot be ignored at low bias currents [9]. The inclusion of sidewall recombination results in an increase in the effective recombination scaling area, further decreasing the low current 3. Aeff = BL + rXjeb(B + L) /3 scaling factor 1 = 1 +7rje X B+L (3.11) (3.12) L A'f' Figure 3-11: 3-D Representation of Base-Emitter Junction [9] This analysis indicates then that the larger the area ratio, the greater the effect of the recombination current on /. For the final bandgap design here, an area ratio of four was chosen. 3.2.3 Collector-Substrate Leakage at High Temperatures With the substrate connected to the lowest voltage and the bipolar device operating in the forward active region, the only current flowing through the substrate should be the leakage current from the reverse biased collector-substrate junction diode. At room 39 temperature, this current is normally negligible; however, as temperature increases, the leakage current likewise increases rapidly with the following proportionality [11]. oc T 3e ileakage oc (3.13) 120 100 U 80 60 40 20 0 -50 50 0 100 150 Temperature (*C Figure 3-12: Temperature Dependence of Collector-Substrate Leakage Not only does the leakage current exhibit a strong temperature dependence, but it is also proportional to the collector n-well size of the bipolar device. Although the collector n-well size does not always scale with the emitter area of the bipolar device depending on the fabrication process, devices with larger emitter area AE generally have larger collector n-well sizes. As a result, the leakage current of the two devices generating AVBE will be unequal at high temperatures. To compensate for this difference, the extra leakage current can be taken away at the collector of Q, via a dummy device that mimics the area size of Q2. Another method returns the extra leakage current to the collector of Q2 through a current mirror in conjunction with a dummy device. In both methods seen in Figure 3-13, the dummy device works to maintain equal collector currents across temperature to keep the reference voltage as stable as possible. When simulating the circuit that includes the equalizing dummy device, the emitter area of the device is labeled as n-1 in order to simulate the collector n-well size correctly. 40 I ,f I Q, n-1 I L TR3 fRTR R1 I mR1 Q3 R mR1 3 Q2 n n-1 1 Q R2R RE (b) Dummy Circuit #2 (a) Dummy Circuit #1 Figure 3-13: Equalizing Collector-Substrate Current Leakage 3.2.4 Layout and Matching Techniques While some of the design options presented here can be used to compensate for process variations, all of the previous mathematical analysis of the bandgap reference circuit assumes that all devices of the same type are identical, when in fact this can never be true. The mismatch between devices can be mitigated by employing good layout techniques. For instance, when placing bipolar devices for the core, the common centroid technique is generally used, in which the devices comprising the transistor with the larger emitter area are centered around the smaller device. Similarly, MOSFET devices utilize common centroid layout while also employing interdigitization arrays for best matching [12]. Well-matched resistors also play a large role in the accuracy of the simplified reference voltage equations in Section 3.1.1. When matching different resistor values, resistors of the same width are laid out, often in arrays of unit cells to ensure that any value inaccuracies are consistent across all resistors being matched. In addition, resistors with larger widths tend to match better than those with smaller widths to a point. 41 3.3 Start-up Circuit As mentioned in Section 3.1, a start-up circuit is necessary to avoid the zero-current state of a self-biased bandgap circuit, such as that in Figure 3-5. This start-up circuit often works by injecting a small amount of current somewhere into the bandgap core such that the collector current of Qi and Q2 cannot be zero. From the graphical solution analysis in Figure 3-3, this amounts to making the y-intercept of the linear collector current curve non-zero, thus eliminating the possibility of the degenerate solution. To ensure the non-zero current state, start-up circuitry often consists of some combination of resistors and diodes that creates a direct path from the supply voltage to ground at all times. The DC current produced is then "injected" into the bandgap core through current mirrors or diodes. While it is difficult to design start-up circuitry that turns off once the circuit biases up properly, the mechanism by which the current injection occurs can be made to be self-activated. 1 B RE Figure 3-14: Sample Start-up Circuit For instance, Figure 3-14 shows a simple start-up circuit consisting of a resistor and a string of diodes, where the injection mechanism is a diode leading from the string of diodes into a specific node A in the circuit. Here, the injection diode will conduct, forcing current through Q1, which in turn requires a non-zero voltage at 42 node B. Once the voltage at Node A rises high enough such that the voltage drop across the diode is too small for appreciable current to flow, the injection diode turns off. With a goal of minimizing the total quiescent current, the bias current of the start-up circuit would ideally be very small since it will burn DC current at all times. However, even though the bandgap circuit may only require a small amount of current to ensure a non-degenerate state, caution must be exercised when lowering the bias current of the start-up circuit so as not to render the start-up circuit ineffective. 3.3.1 Supply Voltage Dependence Another consideration to be made is the variability of the bias current in the startup leg across supply voltage: for example, the bias current for the start-up circuit in Figure 3-14 above scales directly with the supply voltage based on the value of RST. In this case, although the current levels in the rest of the bandgap hardly vary with supply voltage, the total quiescent current of the bandgap circuit can increase significantly simply due to the start-up leg. Depletion Mode PMOS 1 VSG -S G 11 S0 D PD (a) Enhancement Mode PMOS Cross Section (b) Depletion Mode PMOS Cross Section Figure 3-15: PMOS Cross Sections [13] To mitigate the direct proportionality of the current to the supply voltage, a depletion mode PMOS is added in series with the start-up resistor RsT as shown in Figure 3-17. Unlike enhancement mode PMOS devices used in the rest of the circuitry 43 here, the depletion mode PMOS device is fabricated with additional p-type dopant implants in the channel of the device, requiring a positive threshold voltage to turn off the device, as seen in the I-V characteristics graphed in Figure 3-16. 3.0 2.5 Z 2.0 - 91.5- 01.00.5 0.0 -2 -1 0 1 2 3 Gate to Source Voltage (V) 4 5 Figure 3-16: I-V Characteristics of Depletion Mode PMOS By employing the voltage drop across RST as its gate to source voltage, the PMOS device acts as a self-controlled current source once the supply voltage reaches a certain value. Below that value, as the supply voltage rises, the current through the resistor increases, likewise increasing the VGS of the PMOS. The increasingly positive VGS reduces the current carrying capability of the PMOS by depleting away the majority carriers in the channel. Finally, the current in the start-up leg stops increasing when the resistor current and resulting VGS drop satisfy the following set of equations. Rs- Mx to BG Figure 3-17: Source Start-up Leg with Self-Regulating Depletion Mode PMOS Current 44 VGS = -IDRST -ID = -2G (3.14) (3.15) _T2 Solving the equation set or running a test simulation reveals the value of VGS to which the PMOS self-regulates. The value of RST can then be calculated based on the maximum allowable current in the start-up leg. 4.5 4.0 3.5 3.0 2.5 .52.0 1.0 0.5 0.0 0.0 1.0 3.0 2.0 4.0 5.0 Supply Voltage (V) Figure 3-18: Start-up Leg Current as a function of Supply Voltage for RST 3.3.2 = 320MQ Final Design For the final start-up circuit leg using the topology of Figure 3-17, keeping with the maximum current of 5nA per leg results in a RST value of 320MO. As the supply voltage increases past a diode drop, the current flow will generate a non-zero voltage at the gate of the current mirror injection device Mx. Once this NMOS has been turned on, a direct path from the supply to ground will be created in the bandgap core, initiating the flow of current and thus avoiding the degenerate operational state of the bandgap circuit. As soon as the injection point in the circuit rises above a VBE, Mx will begin to turn off, with full shut off once the injection node reaches the gate voltage of Mx, that is VBE ± VGS45 3.4 Trim Range and the ZTC Voltage As discussed in Section 3.1, the PTAT voltage is generated by scaling AVBE with a resistor ratio. While hand calculations reveal the exact resistor values necessary for a ZTC reference voltage for a given bias current, they can vary due to process variation and device mismatch for any given fabricated part. To compensate for this variation, the resistor RTR in Figure 3-4 is broken up into a string of resistors that make up the trim range of the bandgap circuit. The purpose of this trim range is to fine-tune the reference voltage, and thus the temperature coefficient once the part has been fabricated by leaving in or shorting out various resistors that make up Vb, Od Vbl RTR1 Vb2 *-1 R2 Vb 3*- R3 V Ru4- I RT 4 RTR. R1R RTs Figure 3-19: Trim Resistors Good design practice dictates that the trim range designed into the circuit should be made larger than the minimum range determined through simulation across process combinations to account for any device inaccuracies and unknown sources of error. Once the desired trim range is known, the remaining degree of freedom is the number of bits the trim range should contain, thereby setting the number of trim resistors and the size of the least significant bit (LSB). The size of the LSB determines how well the trim range compensates for process variation in order to produce a reference voltage with a temperature coefficient as close to zero as possible. Put another way, a smaller LSB size allows for greater granularity when dialing in the desired PTAT voltage component. 46 For the final bandgap core, the minimum trim range necessary simulated out to be just over 40mV. Conservatively doubling this variation brings the total voltage drop in the trim range to about 100mV with 5 selectable bits chosen for an LSB step size of 3.23mV. This doubling is done to account for device mismatch in process variation and model inaccuracies as the bias currents are lowered away from the well-defined SPICE model operating points. Bandgap Ready and Undervoltage Lockout Sig- 3.5 nals The speed with which the bandgap reference voltage reaches its final value is dependent on a number of variables such as temperature and the input supply ramp rate. Depending on how the circuitry downstream relies on the reference voltage, a bandgap ready circuit can be useful to shut down downstream circuitry to avoid incorrect operation while the bandgap is still powering up. Similarly, an undervoltage lockout (UVLO) circuit can be employed to shut down circuitry if the supply voltage is too low for proper operation. 3.5.1 Bandgap Ready Circuitry The bandgap ready signal is generally created by comparing two different voltage nodes: one that reaches its final value very quickly and one that reaches a similar value more slowly. Two examples of bandgap ready circuit topologies are discussed below. Topology #1: Comparing Collector Voltages One way to generate the bandgap ready signal is to compare the voltages at the collectors of VBE Q3 and Q4 in the bandgap core. Due to the diode connection of Q1, the of Qi and Q4 will quickly approach its final value at start-up. On the other hand, while VBE1 also immediately fixes the voltage at the base of Q2, the degeneration of 47 21 RTRi BGREADY R, Q4 Q3 1 1 H10 RE Figure 3-20: Bandgap Ready Comparator Topology #1 Q2 as well as the difference in emitter area results in the collector current of Q2 reaching its final value at a slower pace. In addition, any compensation capacitance placed at the collector of Q3 to ensure AC stability will slow the rise of the collector voltage due to the increased capacitance charging time. Thus, the bandgap ready signal trips once the collector voltage of Q3 is close to that of Q4, indicating that the bandgap circuit is close to its final DC operating point, as seen in the results of a DC sweep simulation on the supply voltage in Figure 3-21. 2.00 1.75 1.50 1.25 1.00 -0.750.50 0.25 0.00 1.00 1.25 1.75 1.50 supply V~eCw i 2.00 t Figure 3-21: Supply Voltage DC Sweep Simulation Results for Topology #1 48 RTR BGREADY Q4 1Q5 Q Q3 R, R, RBGR 2 RE Figure 3-22: Bandgap Ready Comparator Topology #2 Topology #2: Comparing Currents Rather than using a differential pair, another method is to use a current mirror as a form of current-difference comparison to generate the desired signal. Part of the simplicity and variability of this topology is that the trip point is the point at which the current in the two legs of the mirror balance perfectly. The diode connection of the left half of the current mirror sets up quickly as the collector voltage of Q2 reaches its final value; on the right half of the current mirror, the output node rises as current flows through the resistor as the current mirror works to reach its balance point. Once the balance point is reached, the bandgap ready signal trips. 2.00 1.75 1.50 1.25 11.00 0.750.50 0.25 1.00 15 1.50 Supply Voltage (V) 1.75 2.00 Figure 3-23: Supply Voltage DC Sweep Simulation Results for Topology #2 49 3.5.2 UVLO Signal Circuitry The utility of the UVLO signal comes in detecting whether or not the minimum supply voltage specification has been met, which can be critical for proper operation of certain blocks. Like the bandgap ready signal, the state of the UVLO signal is determined through a comparison of two values: the supply voltage and some kind of a reference term. Topology #1: Using the Bandgap Reference BGREADY -F>H R cR UVLO V VREF +- Figure 3-24: Bandgap Circuit Dependent UVLO Signal Circuit One topology for producing the UVLO signal follows directly from the bandgap circuit, whereby a pre-determined fraction of the supply voltage is compared to the reference voltage produced in the bandgap circuit. In this case, the bandgap ready signal would be used to keep the UVLO circuitry off until the desired comparison can be made. Topology #2: Bandgap-Inspired Circuitry A different UVLO topology presented in Figure 3-25 is independent of the bandgap circuit although still largely based in bandgap principles. Mimicking the core of a different type of basic bandgap cell, the Brokaw cell, the circuit implements a current difference comparison between the two legs based on the supply voltage dependent bias applied to the bases of Q, and Q2. Since the combination of Q1, Q2, R 1, and R 2 is designed using single cell bandgap equations, the trip point of the current difference 50 comparator occurs when the voltage applied to the bases of the bipolars is equal to the bandgap voltage. R cR 1 01 Q2 UVLO R2 R, Figure 3-25: Bandgap Inspired UVLO Signal Circuit where 7VSUPPLYMIN VREF When the supply voltage is too low, the collector current of Q2 wants to be greater than that of Q1, pulling down the current mirror output node. Conversely, when the supply voltage is greater than the minimum value, the opposite is true, pulling up the current mirror output node and switching the state of the UVLO signal. Similar to the start-up circuit, the resistor divider leg in the two above topologies suffers from the same current scaling effects with the supply voltage, which can also be alleviated through the implementation of the self-regulated current source with a depletion mode PMOS device. 3.5.3 Combining the Bandgap Ready and UVLO Signals As described in the last two sections, the bandgap ready and UVLO signals both serve to avoid incorrect operation but switch state with different triggers. Comparing the bandgap minimum supply voltage and the specified system minimum supply voltage reveals that the two values differ by only 300mV. Thus, the overall quiescent current in the system could be decreased if the two signals were combined into one as this would allow for the elimination of one entire circuit block. 51 Bandgap Ready Signal Base Knowing when the bandgap reference can be used reliably is critical to regulating the output voltage to the desired level since it is used in the sleep comparator. This section will explore the possibility of modifying the existing bandgap ready circuitry to fit UVLO specifications. Since the lower-bound supply voltage specification is higher than the minimum supply voltage required for the bandgap circuit, the limiting case is when the supply voltage comes up slowly. In this case, the bandgap ready signal could be triggered before the supply voltage has reached the minimum specified system supply voltage. Transient simulations with varying ramp rates for the supply voltage can be run to determine the difference in the thresholds. 2.0 1.8 1.6 1.4 21.2 t 1.0 0.8 0.6 0.4 0.2 0.0 , 0.0 0.5 m a 1.0 1.5 2.0 Supply Voltage M -12M - - 24M - - -48M Figure 3-26: Bandgap Ready Circuit Supply Voltage DC Sweep Simulation for Various RBGR Based on the data above, the minimum supply voltage at which the bandgap ready signal triggers is in the range of approximately 1.1V to 1.3V depending on the value used for the resistor RBGR in the current difference comparator. Since the supply voltage at the trip point is about one forward diode drop below the minimum supply voltage, the bandgap ready signal could also serve as the UVLO signal with the addition of a forward diode drop somewhere in the comparison, such as in the two topology variations introduced below. 52 Variation #1: Output Node BGREADY RBGR Va Figure 3-27: Bandgap Ready Topology Variation #1 In the first variation, the diode drop recovery is attempted just above the output node of the bandgap ready signal comparator. Here, the hope is that the rise of the output node will be slowed by the additional voltage drop incurred by the diode connected device. Nonetheless, based on the simulation results, the additional diode drop in the output leg does little to affect the supply voltage at which the bandgap ready signal trips. 2.00 1.75 1.50 1.25 1.00 0.50 0.25 1.00 1.25 1.50 1.75 2.00 Figure 3-28: Bandgap Ready Topology Variation #1 Supply Voltage DC Sweep Simulation 53 BGREADY VQ RBGR Figure 3-29: Bandgap Ready Topology Variation #2 Variation #2: Supply Voltage When the diode drop is instead placed in series with the supply voltage, it lowers the effective supply voltage seen by the comparator. In this case, the addition of the diode connected device does increase the supply voltage at which the bandgap ready signal trips by slowing the rise of all nodes in the bandgap circuit. However, the variability in the diode drop of the MOS device across process makes the technique rather inexact. 2.00 1.75 1.50 1.25 41.00 0.75 0.50 0.25 0.00 1.00 1.25 1.50 SupplyVoltage (V) 1.75 2.00 Figure 3-30: Bandgap Ready Topology Variation #2 Supply Voltage DC Sweep Simulation 54 UVLO Signal Base Rather than modifying the bandgap ready circuitry to meet UVLO specifications, the opposite approach is considered, i.e. modifying the UVLO signal circuitry to meet bandgap ready specifications instead. To integrate the two signals together properly, the modified UVLO signal circuitry must be able to track the transient nature of the bandgap circuit. In both of the UVLO circuit topologies presented in Section 3.5.2, a resistor divider is utilized to create the correct supply dependent voltage at the reference voltage trip point. In the bandgap circuit, the closest thing to a resistor divider is the start- up leg. Modifications can be made to the bandgap start-up leg and the topology of Figure 3-25 such that the two circuits share the start-up leg, effectively lowering the overall quiescent current by eliminating one leg of DC current. In this modified version, having the balance point equal to a non-integer multiple of the reference voltage showcases the versatility of the bandgap cell. ~T_ R3 -- 0UVLO to BG F, R2 Q2 1 Q3 n R1 Figure 3-31: UVLO Signal Circuit with Modified Bandgap Start-up Leg The UVLO signal circuitry is based on a current difference comparison, where the comparator trips when the collector currents of Q2 and Q3 are equal. Because the collector currents of Q, and Q2 are also equal, the balance condition can be written by inspection and rearranged to find the value of the supply voltage at the trip point 55 as follows. VSUPPLY - ______-_- VBE - VGS VBE -__=_- R2 R3 VSUPPLY 1 kI --R1 q (3.16) R3 )VBE R2 (1 + = in n VGS + R3 kT - R1 q In n (3.17) Both the VGS and VBE of MOS and bipolar devices respectively have negative temperature coefficients, so the same bandgap principles can be applied to the sizing of the resistors such that the supply voltage trip point is independent of temperature. However, when determining the amount of PTAT compensation necessary, the VGS of the MOS device must be weighted by 1.5 so as to take into account the difference in the negative temperature coefficients as shown in Figure 3-32. 0.8 0.7 0.6 0.5 slope = -2.4mV/*C 20.4 slope =-1.5mV/*C .-- 0.2 - 0.1 - 0.0 -50 0 50 100 150 Temperature (*C) - - VGS -VBE Figure 3-32: VGS and VBE Temperature Coefficients for 5nA of Drain and Collector Bias Currents 3.5.4 Final Design Integration Since the UVLO signal circuitry was found to be more amenable to modifications to meet bandgap ready conditions, the bandgap ready signal circuitry was eliminated from the final bandgap design. In implementing the UVLO signal circuitry, its minimum temperature stable supply voltage trip point can be calculated from the known 56 npn VBE and NMOS VGS at the current trip point. VSUPPLY =VBE + 1.5VGS VBE Unfortunately, at the desired current trip point of 5nA, the calculated minimum supply voltage is about 1.9V, which is slightly higher than the specified minimum system supply voltage. The necessary elimination of the diode connected NMOS from the start-up leg in order to achieve the desired supply voltage trip point thus requires separating the UVLO signal circuitry from the bandgap circuitry. Although this separation means that the additional leg of DC current must be added back into the circuit, the combined consumed current of the bandgap and UVLO blocks together still just meets the target current goal of 50nA. RST -> -UVLO Q1 Q2 Q3 R2 R, Figure 3-33: UVLO Signal Circuit As the core of the UVLO block is very similar to the bandgap circuit, a similar design procedure can be used to determine the parameter values for the UVLO circuitry. First, the balance condition of Eq 3-16 is re-written to reflect the elimination of the diode-connected NMOS in the start-up leg. VSUPPLY - RST VBE VBE R2 1 kT R1 q 57 VSUPPLY RST kT RST (1 + RS-)VBE + = R1 R2 q In n (3.20) In continued imitation of the bandgap circuit, the emitter area ratio in the UVLO circuit was selected to be four with the current trip point set at 5nA, making the value of the degeneration resistor R1 of Q2 equal to 7.2MQ as well. Calculating the necessary PTAT voltage using the specified minimum supply voltage then determines the values of the the remaining resistors. VPTAT RST R2 = VSUPPLY VSUPPLY - = R1 VTnn= q- = In n VREF VREF VBEI I=5nA 189.6MQ 433.2Mg RST (3.21) (3.22) (3.23) VREF Simulating the UVLO block across temperature and process corners with the resistor values calculated above revealed that the UVLO signal did not switch states for certain process corner and temperature combinations since the npn collector currents never reached the trip point of 5nA. To restore the intended UVLO block functionality, the start-up resistor RST was split into two separate resistances to ease the current limiting effects of the depletion mode PMOS. One of the two resistors continued to set the VGS of the depletion mode PMOS, and the other resistor was used to connect the drain of the depletion mode PMOS to the collector of Qi. To minimize the resulting increase in current consumption, simulations sweeping the value of the start-up resistor bounded by the depletion mode PMOS were run to determine the minimum split needed to restore proper operation. To be able to fully use the UVLO signal as a replacement for the bandgap ready signal, the UVLO comparator must trip after the reference voltage is close to its final pre-trim value. To ensure this condition, the UVLO and bandgap blocks were simulated together at a specified supply voltage, and the reference voltage and UVLO signal curves plotted together. From the simulations, the UVLO signal appeared to 58 switch states before the reference voltage had reached within 1OOmV of its final value for certain process corners. To slow down the UVLO signal block to match the transient nature of the bandgap block, a load capacitor was added to the output of the current difference comparator. To keep the additional layout area needed as low as possible, simulations sweeping the load capacitance value were run to determine the minimum load capacitance needed, which was 5pF. 3.6 Proof of Concept As presented in Section 2.3, thirteen different quiescent current level versions of the LTC3588 were fabricated to explore the effects of lower current levels on chip operation particularly in the bandgap and sleep comparator blocks. The bandgap circuit was evaluated over temperature for each of the five different bandgap current levels, ranging from the original 250nA down to 50nA. The operation of the bandgap circuit with the lowest current level is valid proof of concept for the bandgap design presented in the next section because the current per leg of the two circuits is very similar (6.67nA/leg fabricated to 5nA/leg designed), and the total quiescent current level is the same for both. 3.6.1 Measurement Setup To evaluate the chips, a part was placed on an evaluation boad with posts for each pin connection. Since the objective specifications laid out in Table 1-1 are based on operation during the sleep state, the output node was connected to the supply voltage externally to keep the converter off at all times. An adjustable power supply was connected to the input supply voltage pin, and Agilent multimeters and a Keithley picoammeter were used to monitor the supply and reference voltages and current levels. 59 Figure 3-34: Evaluation Board Across the supply voltage range of 1.8V to 5V, room temperature measurements of the total supply current, the bandgap block current, the reference voltage, and the supply and reference voltages at the bandgap ready signal trip point were taken. Reference voltage measurements were then taken for a supply voltage of 3.5V across the temperature range of -50 C to 130*C in 20 C increments. 3.6.2 Measurement Data and Analysis Temperature Variability 1.205 1.195 1 51.185 - .1.175 - - -- - 1.145 1.135 1.125 - -50 -30 -EXPOl -10 10 30 50 70 Temperature (*C) - - EXPO2 - --EXP03 - -EXPO4 90 - 110 130 150 -EXPOS Figure 3-35: Measured Untrimmed Reference Voltage with VSUPPLY=3.5V The untrimmed reference voltage data shown in Figure 3-35 displays a wide spread 60 of over 50mV at room temperature across the different current levels, while also exhibiting a greater negative temperature coefficient for lower current levels. However the increasingly negative temperature coefficient can be explained by revisiting the reference voltage equation. The original LTC3588 bandgap circuit was designed for operation at 40nA/leg, which fixes the VBE component of the reference voltage equa- tion at a particular value. Therefore, the amount of PTAT voltage designed into that particular bandgap circuit is the ideal reference voltage of 1.2V minus the VBE needed by the npn at 40nA of collector current at room temperature. Any npn bipolar then running at a collector current less than 40nA would exhibit a lower VBE, requiring a larger PTAT voltage to be added to it to sum to the ideal reference voltage. 1.205 1.195 - ~1.185 1.175 - ... . . S1. 165 1.155 1.145 1.135 1.125 -50 -30 -10 10 30 50 70 90 110 130 150 Temperature (*C) -EXPO1 - - EXP02 - --EXPQ3 - -EXPO4 - -EXP05 Figure 3-36: Measured Trimmed Reference Voltage with VSUPPLY=3.5V After parts of each type were trimmed, not only did the magnitude of the temperature coefficients of the reference voltage drop dramatically as expected, but the spread in reference voltage across the different current levels also decreased significantly as seen in Figure 3-36. However, the flattest reference voltage could not be reached for some of the lower current levels because the calculated number of bits to trim was between two different combinations or greater than the maximum number of possible trim bits. To construct the theoretical flattest reference voltage curve for each part graphed 61 in Figure 3-37, the actual LSB size at each temperature point was calculated based on the pre-trim and post-trim reference voltage data and then combined with the pre-trim reference voltage data to simulate trimming a non-integer number of bits. 1.205 1.195 - ---- - -- ----- 1.185 to 1.175 - C1.165 ! -- - 1.155 1.145 1.135 1.125 -50 -30 -EXPO1 10 -10 -- 70 50 30 Temperature (*C) EXP02 -.- EXP03 -- EXPO4 90 -- 110 130 150 EXP05 Figure 3-37: Simulated Reference Voltage LSB size VREFUT - # VREFT (3.24) of bits trimmed Although the reference voltage curves constructed with the ideal trimming are very similar to the measured post-trimmed part data, the constructed curves further demonstrate the potential of low current bandgap circuits to produce stable reference voltages across temperature if the PTAT component is adjusted properly. Supply Voltage Variation Aside from temperature, another variable that could affect the bandgap circuit operation is the supply voltage. To check for supply voltage dependence, measured reference voltage data was taken at room temperature (T=22 C) through the specified supply voltage range of 1.8V to 5V in 1OOmV increments. As seen in Figure 3-38, the reference voltage is does not vary across supply voltage. 62 1.21 1.20 51.19 bo 1.18 . ba 5 1.17 . .... -.. . . . .. . . . . . .. . ..-.. C ca 1.16 1.15 1.14 -EXP01 4.5 4.0 3.5 Supply Voltage (V) 3.0 2.5 - - EXPO2 - --EXP03 - -EXPO4 5.0 -EXPOS - Figure 3-38: Untrimmed Reference Voltage with Varying Supply Voltage Final Design 3.7 3.7.1 Schematics M5 RSTM4 5/320 5/320 320MO M,,l 4/40 M, M M6 5/8 5/8 M12 4/40 M13 4/2 4/40 M16 4/2 M,42 M3 1 100/0.8 10/1 10/8 1 Mis 2 2 M2 4/40 2 2 20/5 M14 4 VREF 3pF Q/ 4 1 Q3 C, 3pF RT VTR 9 10/0.8 1 M1, 1VTRs R, R2 8 120MO 120Mf Q4 Q2 Q, r 9 10/0.8 2 4 Q5 R3 7.2MO) Figure 3-39: Bandgap Circuit 63 M170. 2 VREF M, XM2 Vb4 1.4/0.6 5.16Mn M, X2 Vb3 4 X3 (from Fig 3-39) R6 M, 1.4/0.6 Vb2 - M4 1.4/0.6 2.58MO M5 R RT4 M" X M, X, a V645k VbO MIO 1.4/0.6 Rro 322.5kn Figure 3-40: Bandgap Trim Network Ms M3 4/256 4/256 2 RaS 160MO 2 M, 4/12.8 M8 1.4/6 4/12.8 M, 1/0.6 2 2 29.6MO7 -UVLO M, 0 1/0.6 R2 Q, 43.M1 Q2 Q3I 1 '4 1/0.6 43.2E 84MD 7.2MD 1./6 5p Ml-4M Figure 3-41: UVLO Signal Circuit 3.7.2 Simulation Results As can be seen in the bandgap simulation data over temperature in Figure 3-42, the bandgap reference voltage is nearly constant across temperature as expected at about 1.18V. For the UVLO circuit, M2 and R3 (in Figure 3-41) create a DC hysteresis of approximately 40mV in the supply votlage UVLO trip threshold. For the two blocks 64 IBG,SUPPLY (T=25 C) AVREF across T= [-50 0 C,130 'C] VREF IUVLO,SUPPLY VSUPPLY VSUPPLY (UVLO Rising Threshold) (UVLO Falling Threshold) 30nA 1.1769V 3.3mV 21.5nA 1.749V 1.712V Table 3.1: Key Bandgap and UVLO Simulation Data combined, the total supply current is 51.5nA, as listed in Table 3-1, which is just above the total allocated current of 50nA. 1.25 1.24 1.23 1.221.21 - 1.20 1 1.19 - 1.17 - 1.16 - 1.15 -50 -30 -10 10 30 Temperar 50 70 90 110 130 (C) Figure 3-42: Simulated Bandgap Reference Voltage over Temperature at VSUPPLY 5V 2.0 1.6 51.2- 0.8* 0.4 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Supply Vo1ta. (V) Figure 3-43: Simulated UVLO Signal over Supply Voltage 65 = 66 Chapter 4 Sleep Comparator In order to determine whether or not the buck converter should be on, the system employs a comparator that continuously checks a pre-determined fraction of the output voltage against the bandgap reference. If the output voltage drops below the desired value, the comparator outputs a digital low signal that turns on the buck converter. Conversely, if the comparator senses that the output voltage is back in regulation, its output is a digital high signal that turns off the converter. 4.1 Design Considerations Ideally, the comparator will trip near instantaneously such that the output voltage remains as close as possible to the desired value. However, finite propagation delay in the comparator creates higher voltage ripple at the output node than the DC trip points would suggest because the output will continue to slew during the delay. While the amount the output slews is dependent on the size of the output capacitor, a smaller delay time results in a lower minimum output capacitor needed to achieve a specified output voltage ripple. For a very small propagation delay, each stage of the comparator should have a large slew rate at its output while achieving high gain. Both characteristics can be reached with a high bias current and large device transconductance. However, the attainable bias current in the comparator is constrained by the target 50nA quiescent 67 current for the whole block as defined in Chapter 2. As such, the difficulty lies in how to best minimize the delay time given a total available quiescent current. For comparison purposes, the target maximum allowable propagation delay is the delay time achieved by the sleep comparator in the LTC3588 running at the same total quiescent current level. 4.2 4.2.1 BJT and MOS Device Characteristics MOS in Subthreshold MOS devices are generally operated in the triode or saturation regimes, in which excess carriers in the inversion layer move from the drain to source via drift. However, when the gate-to-source voltage VGS is less than VT, the device is not off entirely but rather still conducting a small amount of current. This is known as the weak inversion or subthreshold regime, wherein the free carriers in the space charge region move by diffusion similar to in a bipolar device. Like the bipolar, the current through a MOS device in subthreshold is exponentially proportional to the gate to source voltage [10]. ID = qVG15 oe nkT (1 + AVDS) W qVZ where I, = WpCthe-nkT and n>1 L (4.1) The expression for the transconductance of a MOS device in subthreshold is then found to be that of the bipolar expression multiplied by an additional - factor. The intrinsic gain expression gmr 0 for the two device types can then be written as follows. MOSFET: g.ro = BJT: gro = _ _ ___2 _ nkT IDA kT n( -ID V kT Ic = - VA kT With typical values for VA of at least 30V and A of at around 0.1V (4.3) 1 , the gain of bipolar devices will typically be higher than that of MOS devices operating at the 68 same bias current. 4.2.2 Differential Pairs Since MOS devices in subthreshold behave similarly to BJTs in addition to maximizing their transconductances per unit of bias current, MOS and bipolar devices can be considered analytically interchangeable for the input devices of each differential stage of the comparator. Thus, the other differing characteristics between the two influence the type of device selected in each stage. Input Current Minimization of input current into the first stage of the sleep comparator is critical in order to maintain an accurate reading of the output voltage because the input current is stolen from the feedback resistor divider at the output, creating an error in the output divider. Using MOS devices as the input pair of the sleep comparator offers the benefit of zero input current due to infinite gate resistance whereas bipolar devices require a small amount of input current into the base node for operation. To mitigate the effects of the non-zero base current, the values of the resistors in the output feedback divider can be reduced so that any input current taken away is a smaller fraction of the total current through the divider. However, this technique increases the total current consumption of the divider. Another technique for diminishing input current in the bipolar case is base current cancellation. The premise of this approach is to inject the necessary base current into the two base nodes of the input pair from elsewhere, thus eliminating the need for either the reference or feedback node to provide the base current. With this technique, even if the exact amount of base current is not fully injected, the amount of current taken from either input node is still greatly decreased, increasing the effective # of the input bipolars as seen by either input node. Therefore, the effect of any mismatch between the / of the input bipolars is likewise reduced due to the boosted effective 03. 69 8 1B R R REF 1 1B FB ~214 Figure 4-1: Base Current Cancellation Technique Input Offset For any differential pair, its input offset voltage influences the accuracy of its input voltage trip point. When the pairs are cascaded in multiple stages, only the minimization of the input offset of the first stage is key as the input offset of the subsequent stages referred back to the input will be divided down by their respective cumulative gains. For typically well-matched npn's, the input offset at 3o is of the order of 1-2mV. On the other hand, for MOS devices, the 3a input offset is approximately 3mV. VWL For a smaller offset, the input MOS devices must be large, generally with a very large W compared to L. However, the larger the MOS device, the slower it is due to increased parasitic capacitances, which increase the loading on the preceding stage and result in a slower slew rate as will be discussed below. For both device types, the variation of the input offset in the differential pair over temperature is not well characterized. Capacitive Loading An indication of the speed of the response of the stage to differential changes at the input, the slew rate at the output node of the stage is effectively the charge rate of 70 the parasitic capacitances by the bias currents. For the system here, the bias current of the stage is limited by the total block target quiescent current. For the bipolar device, the dominant parasitic capacitances are those from the base-to-emitter, base-to-collector, and collector-to-substrate. In the forward active regime, while all three junctions will possess a component corresponding to their respective pn junction depletion capacitances, the base-to-emitter junction will see an additional diffusion capacitance CB in parallel with its depletion capacitance Ce. The depletion capacitances of the three pn junctions decrease from their zero-bias values with a factor, where 1 VD is the applied bias and Ob is the built-in potential of the associated pn junction. A function of the bias current, the diffusion capacitance CB is the product of the transconductance g, and the forward transit delay F. Coer Epi n 1Wo P Base Emtter Ban Emitter IOP Epi Collector nIS BL n+BL+ Figure 4-2: Bipolar Device Cross Section [14] npn pnp Cie 15.3 fF 5.5 fF Cjc Cjs 16.7 fF 35.6 fF 6.5 fF 103 fF Table 4.1: npn and pnp Junction Capacitances at Zero Bias In the MOSFET device, the parasitic capacitances are those from the gate-tosource Cg, gate-to-drain Cgd, source-to-body Cb, and drain-to-body Cdb. Included in both the gate-to-source and gate-to-drain capacitances are components resulting from the channel charge and the gate overlap with the source and drain diffusion wells. The source-to-body and drain-to-body capacitances are made up of the vertical depletion junction capacitance and the sidewall capacitance of the source and drain diffusion wells created by the pn junction from the source or drain to the body. 71 G&We Body SoreDrain GJAe Body Source rain 2 . Nw&l nIS Epi n BL n+ oP PwllP bso P Bpi a BL n+ Figure 4-3: MOS Device Cross Section[14] Co Cj NMOS 2.4" 0.52m-' Ci,, 0.34 Cgdo 0.19 PMOS 2.4m 0. 72 "n 0.30 0.25 n Table 4.2: NMOS and PMOS Parasitic Capacitances at Zero Bias From the process data in Tables 4-1 and 4-2, the parasitic capacitances of a minimum-sized MOSFET are much smaller than those of the bipolar, which would favor using MOSFETs as the differential pair input devices. However, if the MOSFETs are sized such that their input offset is comparable to the bipolar input offset, the MOSFET parasitic capacitances become much larger than those of the bipolar. The larger load capacitances indicate that the speed of the stage will be slower as the larger capacitances take longer to charge and discharge while also decreasing the bandwidth of the stage by lowering the frequency of the pole at the output node. The main tradeoff between using MOSFETs or bipolars then is between having increased input offset or a non-zero input current. 4.3 Hysteresis To avoid false tripping or chatter at the comparator output due to noise or other disturbances, AC and/or DC hysteresis is often incorporated into the comparator itself. If the comparison being made is clocked rather than continuous, a latch can be used to ensure that the output changes only at the correct time. 72 DC Hysteresis 1 21 Schmitt Trigger 1 !AC Hysteresis vI F v ) sOUT Figure 4-4: Two Stage Comparator with AC and DC Hysteresis Circuitry 4.3.1 DC Hysteresis When implementing DC hysteresis, the rising and falling trip points of the comparator differ and are symmetric with respect to the desired trip point: the rising trip point is higher than the desired value, and the falling trip point is lower than the desired value. With this method, chattering due to noise can be mitigated since the differing trip points work like positive feedback thereby reinforcing the transition in both directions. To generate the DC hysteresis, resistors can be placed in series with the input devices, with the resistors on the two sides alternately shorted out based on the comparator output, as marked on the left side of Figure 4-4. Moreover, the series resistance slows down the comparator, and using MOS devices to short out the resistors can cause false tripping. However, since the current in the output inductor cannot change instantaneously, some inertial hysteresis exists as well, which can eliminate the need for explicit DC hysteresis. Rather than directly changing the comparator trip points, the time it takes for the current acting on the load to change directions can be considered "dead time" during which the comparator decision is reinforced. Unlike explicit DC hysteresis, the amount of inertial hysteresis in the comparator is not precisely defined, due to its dependence on the size of the inductor as well as the output voltage being generated and the load. These parameters define how long 73 it takes for the output voltage to stop changing. Furthermore, the deviation at the output from the desired value at the end of this time period is contingent upon either the average charging current or the load current in addition to the size of the output capacitor. Aside from generating hysteresis at the comparator inputs, a Schmitt trigger can be utilized at the output as well to further protect the system against noise, such as at the output in Figure 4-4. In this case, the Schmitt trigger operates as an inverter with varying rising and falling thresholds created using positive feedback with greater than unity gain. Similar to the input hysteresis, the Schmitt trigger works to ensure that the comparator transition is reinforced. 4.3.2 AC Hysteresis Chatter at the comparator output feeding into the Schmitt trigger can be avoided by employing AC hysteresis at the comparator output node using one shot circuitry. The one shot circuitry not only increases the slew rate of the output stage of the comparator right at the transition point of the inverter at the output, but also works to reinforce the comparator decision at the trip point by holding the output node of the last stage in the desired state during the transition. The AC hysteresis can be accomplished using logic gates and a RC delay to set how long the output node is held at the transition point as seen in the center marked subcircuit of Figure 4-4. 4.4 Adaptive Biasing With the objective of lowering the quiescent current consumed while the buck converter is sleeping without compromising speed, one solution is to simply lower the operating current of the comparator during the sleep state, while providing extra bias current during the active state. Increasing the bias current during the active state can create switching noise due to turning on and off the devices that provide the extra current as well as change the gain of the associated stage(s) of the comparator. 74 Caution must be exercised 21I 2I 1 I2 1 OUT Figure 4-5: Two Stage Comparator with Adaptive Biasing so that the bias current increase or decrease does not cause false tripping during the transition. Another option that fulfills the same goal is to have two different comparators, one optimized for the sleep state at the target current level and one optimized for the active state at a higher current level. 4.5 Gain per Stage When designing the comparator, another consideration is the number of stages. In considering current consumption, fewer stages means fewer legs of current, allowing each stage to have a higher proportion of the total block quiescent current. Based on the device behavior described above, the increase in bias current should decrease the propagation delay of the stage due to to a larger slew rate at the output node. At the same time, for a given overall gain, the gain per stage must be higher for fewer stages. From this qualitative analysis, increasing the total number of stages initially can decrease the propagation delay. For a given total current level, the propagation delay will begin to increase once the benefits of lower single stage gain are over-shadowed by the delay from lower bias currents. In distributing the gain and bias current in a multistage comparator, the propagation delay of the first stage proves to be the dominant factor in the total propagation 75 delay. The disparity in the delay of the first stage to that of the other stages is the result of the size and rate of change of the differential input being detected. To minimize the disparity, the first stage carries more bias current than any other stage in the comparator. 4.6 Topology Comparison In designing the new sleep comparator, many different topologies were simulated to capture the benefits of both MOS and bipolar devices. Topologies that were under consideration but not listed below were eliminated due to headroom constraints at the minimum supply voltage. 4.6.1 Topology I 91 Re, 4.51 R, SLEEP VREF "VFB R2 R2 R2 Figure 4-6: Topology I In the LTC3588, a two stage topology couples an input MOS differential pair with explicit DC hysteresis to a common source output stage for a wide output swing and additional gain. In this topology, not only are MOS devices used as the input devices to eliminate input current, but they are also near minimum sized for the best speed performance. To alleviate inaccuracies due to mismatch in the MOS devices, source degeneration is implemented in the current mirror of the first stage even though 76 doing so decreases the gain of the stage. A one-shot circuit is also employed to reduce possible chatter at the output. Since this project is based on the LTC3588, the performance of the following different comparator topologies are compared against that of the original LTC3588 comparator with and without explicit DC hysteresis running at the same target quiescent current in the sleep state. 4.6.2 Topology II 21 21 SLEEP HVFB VREF Figure 4-7: Topology II For Topology II, the inputs feed into a PMOS-based source follower (SF) stage that is followed by an npn-based differential pair stage and a common source amplifier output stage. Although the SF stage increases the number of total stages and consumes current, its buffering action for the reference and feedback nodes are not the limiting factor in decreasing the total propagation delay due to its unity gain. An npn differential pair is used for the comparison computation rather than MOS devices to minimize both the input offset and self-capacitive loading while maximizing intrinsic gain. Since the single-ended output of the differential pair is taken such that the output stage is at zero bias in the sleep state, the bias current can be distributed between the SF and npn differential stages. Based on the delay time contribution of each 77 stage determined through simulation, most of the current is allocated towards the npn differential stage to maximize comparator speed. Due to the headroom constraints imposed by the 1.8V minimum input supply voltage, the reference input voltage selected for this topology is 0.6V rather than 1.2V. The decrease in the common mode voltage ensures that the PMOS input devices in the SF stages have enough overdrive in the balance state. 4.6.3 Topology III ~T~ 41, , 41, 1, SLEEP VREF VFB r ei2.51, 141, Figure 4-8: Topology III where I1 = I Similar to the previous topology, the inputs again are initially buffered by a PMOS-based SF stage that requires a 0.6V common mode input voltage and subsequently feeds into an npn differential pair. In this topology, the common source output stage is replaced by a folded cascode made of MOS devices attached to the outputs of the differential pair. The comparator output is then taken directly off of the output of the folded cascode. Again, most of the bias current is allocated towards the combined npn differential pair and folded cascode stage. In splitting the bias current between the two parts, the most important aspect is that the current through the NMOS cascode devices never falls to zero due to the increased delay time resulting from the reformation of the inversion layer and charging of the parasitic device capacitances. 78 4.6.4 Topology IV 1 VREF 3 3 4/r SLEEP VFB I8 41 Figure 4-9: Topology IV In another two stage topology variation, the MOS-based first stage of the LTC3588 sleep comparator is replaced with an npn differential pair with a current mirror active load. The use of npn input devices requires the input common mode voltage to be 1.2V to ensure that the input devices are operating in the forward active regime at the balance point and to allow the tail current source sufficient headroom. Compared to Topology II, although the base current cancellation component requires an additional leg of current, slightly more of the total bias current can be allocated towards the npn differential pair due to the loss of the SF stage. Again, the single-ended output of the differential pair can be chosen such that the common source output stage is at zero bias in the sleep state. 4.6.5 Topology V In a fifth topology variation, two resistively loaded npn differential pair stages are cascaded and followed by a MOS differential pair with a current mirror active load and a common source output stage. Base current cancellation has been added to the bipolar input stage to minimize the effect of non-zero input current on the reference and feedback nodes. An additional series resistor has been placed at the reference 79 2 2 R, R, R2 R2 >VFB VREF 1 SLEEP 1 212 41 I Figure 4-10: Topology V input node as well to match the small signal input resistance seen at the feedback node due to the output resistor divider. For the first two npn stages, the gain of each stage is equal to the voltage drop across the resistor load at balance divided by the thermal voltage. The maximum gain possible in each stage is limited by the maximum resistor voltage drop such that the bipolar devices remain in the forward active region. Once the gain has been chosen, the value of the load resistances can be determined based on the bias current through the stage. To maximize the comparator speed, the MOS devices in the third stage are chosen to be minimum sized. Although this sizing results in a large input offset for this stage, its contribution to the overall input offset is actually quite small as it is divided down by the product of the gains of the first two stages. To reduce the dominance of the propagation delay of the first stage with respect to the others, the bias current running through each of the npn devices in the first stage is twice that of the other legs in the circuit. Even with the doubling of the bias current, the simulated propagation delay of the first stage is still at least twice that of any other stage in the comparator. 80 VFB VREF t AOUT H (b) Output Ripple Definition (a) Propagation Delay Definition Figure 4-11: Measurement Definitions Topology tPHL (Ps) Topology I 23.64 15.47 25.4 Topology I w/o DC hysteresis Topology II Topology IV 8.03 14.11 23.4 5.8 9.97 23.08 9.13 17.0 31.4 Topology V 5.63 13.93 14.6 tPLH (As) AVt (mV) Table 4.3: Comparison of Propagation Delay and Output Ripple for Various Sleep Comparator Topologies with VSUPPLY=3.5V, Cot=100MF, ILOAD=5OmA 4.6.6 Simulation Results 4.7 Proof of Concept Of the variations listed in Table 2-1, those evaluated for the performance of the sleep comparator at low currents were EXP05, EXP10, EXP11, and EXP13. For these four types, the sleep comparator quiescent current ranges from the original 160nA down to 27nA, where the current level of EXP11 most closely matches the target 50nA current level. 4.7.1 Measurement Setup Unlike the bandgap block, the sleep comparator block was evaluated with the part in plastic QFN packaging rather than in ceramic sizebraze prototype packaging. The VIN, VIN2, and VBGSUPPLY pins were all tied together and connected to an adjustable power supply. Agilent multimeters were used to measure the DC output 81 Figure 4-12: QFN Evaluation Board for Single Part voltage and bandgap reference as the load was varied. An adjustable current source load box was connected in series with an ammeter to measure the load current to the VOUT pin. Connecting the SW and VOUT pins was a 1OpH inductor, manufactured by Sumida. Figure 4-13: Large QFN Evaluation Board Using an oscilloscope, the output voltage ripple and the sleep and awake time periods were measured at room temperature for a nominal supply voltage of 3.5V, load currents varying from zero to 125mA, and surface mount output capacitors ranging from 10pF to 100pF. 82 80 70 60 30 20 10 0 0 10 20 30 -10uF 40 - 50 60 70 80 Load Current (mA) 90 100 110 120 -22uF - - -47uF --- 100uF Figure 4-14: Output Ripple as a Function of Load Current 4.7.2 Measurement Data and Analysis Load Current Variability As seen in Figure 4-14 above, the measured output ripple is displayed for EXP05 as a function of the load current for varying output capacitances. A characteristic of the measured data seen in all the evaluated parts is the variation in the output ripple with load current. While the load current can affect the propagation delay of the first stage via the slope of the input voltage on the feedback node side, the overall propagation delay of the sleep comparator still remains mostly uniform across load current. A more likely explanation for the output ripple variation deals with the states of the switches when the comparator output signals to turn off the converter. In the LTC3588, when the sleep signal goes high, the NMOS in the switching pair turns on to allow the inductor current to ramp back down to zero if it is not on already. The "excess" ripple generated then is is dependent on the magnitude of the inductor current when the signal switches: in the best case scenario, the signal switch matches perfectly with the point at which the inductor current is at zero whereas the worst case scenario corresponds to when the inductor current is at its peak value. 83 This dependence is due to the asynchronous nature of the sleep transition and the inductor current waveform. A 1 A~ince, L (4.4) CVoutexcess out () -(IL ~ILOAD)IL VDC,OUT 0 Output Capacitor Variability 225 200 175 150 - 5125 100 75 - -------------------- - ------ - - - --------------- 50 25 - 0 0 10 20 30 40 -10uF - 50 60 70 80 Load Current (mA) 90 100 110 120 -22uF - --47uF --- 100uF Figure 4-15: Comparison of Output Ripple for Various Capacitors for EXP13 When analyzed as a function of the size of the output capacitor, the overall output ripple demonstrates a decreasing trend as the capacitor increases due to the inverse relationship between the change in voltage across the capacitor and the capacitance value. 1 (ICHARGE AVt= - ILOAD)tawake (4.5) __1 ILOADtsleep = (4.6) C.t To more accurately represent the relationship between the output ripple and the size of the output capacitor, the "actual" capacitances, listed in Table 4.4, were calculated based on measurements taken for EXP05. 84 Cactuat = ILOADtsleep Cactual (pF) (pF) Clabeled (4.7) AV., 10 22 9 15 47 25 100 37 Table 4.4: Labeled vs. Actual Capacitance Values That being said, the change in output ripple for each upward step in capacitance is still nonuniform using the actual capacitance values as seen in Figure 4-15. This nonuniformity thus predicts some lower bound on the output ripple, suggesting that increasing the output capacitor without bound will not continually reduce the output ripple. Although the nonuniformity is seen across all the evaluated parts, the lower bound trend is best seen in the data for EXP05 from Figure 4-14. Quiescent Current Variability 160 I 140 -* - 120 100 E 8 80 a -. .-.-. - 60 .- . . 40 20 0 5 25 -EXP05 45 - 65 Load Current (mA) -EXP10 - -- EXP1i 85 105 125 --- EXP13 Figure 4-16: Comparison of Output Ripple with C., = 22pF At the heart of the evaluation analysis is the dependence of the output ripple on the comparator quiescent current. As expected, as the quiescent current decreased, 85 the output ripple increases, as seen in Figure 4-16. Since the built-in explicit DC hysteresis is the same for all four parts, the increase in output ripple is predominately the result of the increase in the sleep comparator propagation delay. Based on the data, the increase in the propagation delay does not appear to scale at the same rate as the decrease in the quiescent current. 80 - 60 - 00 550 40 030 20 10 0 0 10 20 -10uF_EXP05 30 40 80 50 60 70 Load Current (mA) - - -1O0uF_EXP13 90 - -22uF_EXP10 -- 100 110 120 22uFEXPlI Figure 4-17: Comparison of Output Ripple for Various Quiescent Current Levels and Output Capacitors Nevertheless, as seen in Figure 4-17, the effect of the increase in propagation delay on output ripple can be mitigated by increasing the size of the output capacitor. From the graph, the same average output ripple of EXP05 with an actual output capacitance of 9pF can be achieved by EXP13, which operates at one-sixth of the original by quadrupling the actual capacitance. For EXP11, which is operating at a quiescent current level closest to the target value at one-third of the original value, the same average output ripple can be achieved by doubling the actual output capacitance. Based on the evaluation data, the output ripple generated by the propagation delay appears to dominate over any built-in explicit DC hysteresis at the lower current levels. Because of this, the final design does not contain any explicit DC hysteresis and relies only on the intrinsic inertial hysteresis. This implementation thus decreases the amount of switching noise in the first stage as well. 86 4.8 Final Design In comparing the simulation results of the various topologies in Section 4.6.6, Topology V possesses the lowest simulated propagation delay coming out of the sleep state for a given quiescent current budget and is used as the final sleep comparator design. 4.8.1 Schematic M, 4/4 M7, 414 1 I X - X F1NtLTr4M UVLO 2 RZ 25N n '.M49.6 T R, 1.4/Q6 22Mn P. 22AAn A MIS 1.4/&6 T MI. 1.4/&6 1.4/0.66 A062 M" 10/0.6 10/0,6-- IA*6 4 Q3 C, I VFS OfF o X 10U.Mn 4 1 M1 1 M4 - MIS 4/0.6 2 MIS M C;W 410A 2 M71 M17 M20 2 2 1 MIS QUA ? M9 A/I& 4 X5 5LEEP Mn Q. as we 4/0A c, M, 1 GA)/6 1.4/&6 1.416 'R X)l 762kn 762 1 4110 C2 law Figure 4-18: Sleep Comparator 4.8.2 Current Bias Leg The topologies in Section 4.6 were simulated with the bias legs powered by an ideal 5nA current source. To avoid adding extra legs of current to the circuit, the best way to construct the bias leg would be to mirror the needed 5nA from another bias leg elsewhere. Unfortunately, the current mirrors in the bandgap circuit, where a 5nA biased leg is most likely to be found, are all PMOS-based, while the sleep comparator uses NMOS-based current mirrors. The solution to the bias leg problem ends up still being found in the bandgap circuit, with the sleep comparator using the reference voltage in yet another manner. With the reference voltage always producing a node of known voltage, a second node of known voltage is the drain voltage of the diode-connected NMOS cascode current 87 source running at 5nA. Now, a resistor sized for a bias current of 5nA can be placed between the to two to create the bias leg of the sleep comparator. 4.8.3 Simulated Results tPHL tPLH AVou ISLEEP,SUPPLY 5.63ps 13-93ps 14.6mV 50nA Table 4.5: Sleep Comparator Simulation Data with ILOAD=5OmA VSUPPLY=5V, Cot=100pF, Compared to the original LTC3588 biased at a total of 160nA, the new sleep comparator possesses a wake-up propagation delay that is not quite three times as large while running at slightly less than one-third the original current level. In addition, it meets the target total supply current allocation of 50nA from Chapter 2. 88 Chapter 5 Conclusion 5.1 Combined Simulated Results In the two previous chapters, the new bandgap and sleep comparator blocks were simulated as stand-alone blocks for the simulation results listed. Here, the bandgap and sleep comparator blocks are simulated together to ensure that the connections between the sleep comparator and the bandgap block do not significantly disrupt the reference voltage node. The bandgap reference voltage settles to 1.1814V as its final value. VREF 1.1814V tPHL 5.84ps 9.09ps tPLH AV, 10.3mV Sleep Comparator Measurements VSUPPLY=3.5V, Cou=100pF, and ILOAD=5OmA Table 5.2 5.1: with Bandgap Circuit with Recap and Future Work In Chapters 3 and 4, new designs for the bandgap and sleep comparator blocks were presented to fit the proposed work laid out in Chapter 1 of a converter system with a no-load quiescent current level of 150nA. Because of the large difference between 89 the target current level and the lowest quiescent current level currently commercially available, modified versions of the LTC3588 were fabricated with varying quiescent current levels to evaluate the effect of low current operation, driven largely by the lack of precise device modeling at the desired current levels. Nonetheless, even the current device models show that the 5nA/leg implementation presented here is approaching the limit of adequate device operation in the current technology, as evidenced by the discussion on the impact of low 8 on the accuracy of the bandgap reference voltage. Due to this lower limit, the quiescent current level certainly cannot continue to decrease ad infinitum to zero. Furthermore, over the course of the silicon evaluation of the modified LTC3588 chips, both benefits and disadvantages of low current operation were discovered. For instance, although the efficiency at the lower current levels stayed at its maximum value for a wider range of load currents (Figure 2-7), the output capacitor had to be increased proportional to the first order with the quiescent current level reduction in order to maintain the same output voltage ripple (Figure 4-17). Such performance tradeoffs ultimately determine the breadth and types of applications for a converter with ultra-low quiescent current. In the future, until the lower limit has been reached, certain aspects of the system presented here merit further study to push the quiescent current level even lower. Currently, the weak bias blocks consume small amounts of "keep alive" current during the sleep state in order to wake-up faster during the transition from the sleep to the active state. These blocks can be examined to determine both the effectiveness of such currents as well as the optimal combination, if any, of the weak bias current and the response time. Similarly, while the intrinsic load current is not directly counted towards the supply current, the output divider can be explored to find ways of reducing this current without significantly sacrificing the response time of the feedback node to perhaps increase the load current range with maximum converter efficiency. Even with simply the quiescent current reduction presented here, the converter system discussed here already has the potential to further maximize the lifetime of 90 batteries in portable and remote battery-based applications beyond what is commercially available today. Moreover, these applications range across a wide spread of industries from manufacturing to biomedical devices to sensors. 91 92 Bibliography [1] Chandrakasan, Anantha, Naveen Verma, and Denis C. Daly. "Ultralow-Power Electronics for Biomedical Applications." Annual Review of Biomedical Engineer- ing. 10. (2008): 247-275. Print. [2] Linear Technology Corporation, Milpitas, CA. 42V, 2.5A, 2MHz Step-Down Switching Regulator with 2.7pttA Quiescent Current, 2012. LT3975 Datasheet. [3] Linear Technology Corporation, Milpitas, CA. 38V, 1.2A, 2MHz Step-Down Regulator with 2.8pA Quiescent Current, 2009. LT3971 Datasheet. [4] Linear Technology Corporation, Milpitas, CA. 1.8pA Quiescent Current, 15V, 300mA Synchronous Step-Down DC/DC Converter, 2011. LTC3103 Datasheet. [5] Linear Technology Corporation, Milpitas, CA. Piezoelectric Energy Harvesting Power Supply, 2010. LTC3588-1 Datasheet. [6] Linear Technology Corporation, Milpitas, CA. 20V High Efficiency Nanopower Step Down Regulator, 2010. LTC3388-1 Datasheet. [7] Kassakian, John G; Schelcht, Martin F; Verghese, George C. Principles of Power Electronics. Addison Wesley, 1992. [8] Gilbert, Barrie. Accurate Design of Low- Voltage, Low-Power Monolithic References. 1996. Print. [9] Roulston, David J. Bipolar Semiconductor Devices. McGraw-Hill Companies, 1989. Print. 93 [10] del Alamo, Jesus A. Integrated Microelectronic Devices: Physics and Modeling, Prentice Hall. 2011. Print. [11] Liang, Yung C, and Samudra, Ganesh S. Power Microelectronics: Device and Process Technologies. World Scientific Publishing Co, 2009. [12] Hastings, Alan. Art of Analog Layout. Prentice Hall, 2nd edition, 2005. [13] Neaman, Donald. Semiconductor Physics and Devices. Mc-Graw Hill Publishing, 2002. Print. [14] Gardner, John U. Designing an Ultra Low Quiescent Current Buck Switching Regulator, MIT, 2008. 94