Advanced RC Phase Delay Capacitive Sensor Interface Circuits for MEMS by Yuan Meng A thesis submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Master of Science Auburn, Alabama May 9, 2015 Keywords: capacitive sensor, interface circuit, RC network, phase delay, MEMS Copyright 2015 by Yuan Meng Approved by Robert Dean, Chair, Associate Professor of Electrical and Computer Engineering Thomas Baginski, Professor of Electrical and Computer Engineering Thaddeus Roppel, Associate Professor of Electrical and Computer Engineering Abstract Many types of sensors in MEMS technology convert a measurand to a proportional change in capacitance. One of the techniques of measuring capacitance is utilizing the phase delay of an RC network with a resistor and the sensor capacitor. Specifically, the state of an input square wave signal is delayed by the RC network and gives a pulse width modulated signal according to the phase delay at the output, which is proportional to the capacitance, if the resistance is fixed. However, the response of this method becomes severely nonlinear if the phase delay is bigger than approximately 45°. Two improved implementations are presented to avoid the nonlinearity caused by the capacitor being not fully charged and discharged each cycle. The first one uses a PMOSFET switch to charge the unknown capacitor and an NMOSFET to discharge it during each measurement cycle. The second one uses an analog switch to switch the resistance to be significantly lower when the capacitor needs to be fully charged or discharged in each cycle. Both methods were simulated and proved effective. Prototype circuits were also implemented and tested with an 8 − 128pF variable capacitor, and linear responses were measured. These techniques produced a linear response over different and large capacitance ranges, and can possess fast response times. ii Acknowledgments I would like to take this opportunity to give thanks to Dr. Robert Dean for his kindly help and wise guidance during my pursuing my Master’s Degree. He is not only a responsible loving advisor, but also an honorable life mentor for me. I also would like to thank William Abell for his help in mounting components on adaptors, Aubrey Beal for his help in LTSpice, and Luke Jenkins for his help in finding proper parts to use in this thesis. Special thanks to Linyuan Zhang, my girlfriend, for her constant encouragement, enduring love and unwavering support, and to my parents Yanjun Meng and Zhihua Chen for their constant support and sacrifice both financially and emotionally. Also thanks to all my brothers and sisters in Christ for their love, support and prayers. Thank God for all. iii Table of Contents Abstract ............................................................................................................................... ii Acknowledgments .............................................................................................................. iii List of Tables ..................................................................................................................... vii List of Figures .................................................................................................................... ix 1. INTRODUCTION ....................................................................................................... 1 2. LITERATURE REVIEW FOR CAPACITIVE SENSORS AND THEIR INTERFACE CIRCUITS .......................................................................................................................... 3 2.1 Capacitive sensors ............................................................................................. 3 2.1.1 Overview ................................................................................................. 3 2.1.2 A Capacitor ............................................................................................. 4 2.1.3 Spacing Variation .................................................................................... 6 2.1.4 Area Variation ......................................................................................... 8 2.1.5 Dielectric Material Variation .................................................................. 11 2.1.6 Capacitive Fringing Field Sensors ........................................................ 12 2.2 Interface circuits for capacitive sensors .......................................................... 14 2.2.1 Direct DC Circuits ................................................................................ 15 2.2.2 Bridge Circuits ...................................................................................... 16 iv 2.2.3 Oscillator Circuits ................................................................................. 18 2.2.4 Other Interface Circuit Techniques ....................................................... 20 3. THEORY BASIS AND DISCUSSION ..................................................................... 21 3.1 Analysis of RC circuit phase delay ................................................................. 21 3.2 Converting PWM to DC Voltage ..................................................................... 27 3.3 Resistance and gate capacitance of MOSFETs ............................................... 28 3.3.1 Basis of MOSFETs ............................................................................... 28 3.3.2 Output Resistance of MOSFET Used as a Switch ................................ 30 3.3.3 Output Capacitance of MOSFET Used as a Switch ............................. 32 4. MOSFET CIRCUIT ................................................................................................... 35 4.1 Circuit design .................................................................................................. 35 4.2 Circuit simulation ............................................................................................ 42 4.3 Circuit implementation .................................................................................... 44 4.4 Circuit testing .................................................................................................. 46 4.5 Results ............................................................................................................. 54 5. RESISTANCE SWITCHING CIRCUIT ................................................................... 68 5.1 Circuit design .................................................................................................. 68 5.2 Circuit simulation ............................................................................................ 71 5.3 Circuit implementation .................................................................................... 72 5.4 Circuit testing .................................................................................................. 73 5.5 Results ............................................................................................................. 77 v 5.6 Comparison with the MOSFET Circuit ........................................................... 91 6. SUMMARY AND CONCLUSION ........................................................................... 94 7. FUTURE WORK ....................................................................................................... 95 REFERENCE .................................................................................................................... 96 vi List of Tables Table 3.1 Truth table of an EXOR gate ........................................................................... 26 Table 4.1 Truth table of a NOR gate ................................................................................ 41 Table 4.2 Truth table of a NAND gate............................................................................. 42 Table 4.3 Results for the MOSFET circuit at input frequency of 5kHz. ......................... 56 Table 4.4 Results for the MOSFET circuit at input frequency of 10kHz. ....................... 58 Table 4.5 Results for the MOSFET circuit at input frequency of 16.67kHz. .................. 60 Table 4.6 Results for the traditional RC circuit with R=150kΩ at input frequency of 5kHz. .................................................................................................................................. 62 Table 4.7 Results for the traditional RC circuit with R=150kΩ at input frequency of 10kHz. .................................................................................................................................. 64 Table 4.8 Results for the traditional RC circuit with R=150kΩ at input frequency of 16.67kHz. ................................................................................................................. 66 Table 5.1 Results for the resistance switching circuit at input frequency of 5kHz. ........ 79 Table 5.2 Results for the resistance switching circuit at input frequency of 10kHz. ...... 81 Table 5.3 Results for the resistance switching circuit at input frequency of 16.67kHz. 83 Table 5.4 Results for the traditional RC circuit with R=271kΩ at input frequency of 5kHz. vii .................................................................................................................................. 85 Table 5.5 Results for the traditional RC circuit with R=271kΩ at input frequency of 10kHz. .................................................................................................................................. 87 Table 5.6 Results