P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 Bioinstrumentation i P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 Copyright ©2006 by Morgan & Claypool All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other except for brief quotations in printed reviews, without the prior permission of the publisher. Bioinstrumentation John D. Enderle www.morganclaypool.com ISBN-10: 1598291327 paperback ISBN-13: 9781598291322 paperback ISBN-10: 1598291335 ebook ISBN-13: 9781598291339 ebook DOI 10.2200/S00043ED1V01Y200608BME006 Library of Congress Cataloging-in-Publication Data SYNTHESIS LECTURES ON BIOMEDICAL ENGINEERING Lecture #6 Series Editor and Affiliation: John D. Enderle, University of Connecticut 1930-0328 Print 1930-0336 Electronic First Edition 10 9 8 7 6 5 4 3 2 1 Portions of this manuscript were reprinted from the following book with the Permission of Elsevier, INTRODUC- TION TO BIOMEDICAL ENGINEERING, ISBN 0122386626 2005, Chapter 8, pp403-504, Enderle et al 2nd edition. This permission is granted for non-exclusive world English rights only in both print and on the world wide web. Additional Information regarding the bestselling book, Introduction to Biomedical Engineering, 2nd edition 2005, by Enderle, Blanchard and Bronzino, from Elsevier can be found on the Elsevier Homepage http://www/elsevier.com. ii P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 Bioinstrumentation John D. Enderle Program Director & Professor for Biomedical Engineering University of Connecticut SYNTHESIS LECTURES ON BIOMEDICAL ENGINEERING #6 M &C Morgan & Claypool Publishers iii P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 ABSTRACT This short book provides basic information about bioinstrumentation and electric circuit theory. Many biomedical instruments use a transducer or sensor to convert a signal created by the body into an electric signal. Our goal here is to develop expertise in electric circuit theory applied to bioinstrumentation. We begin with a description of variables used in circuit theory, charge, current, voltage, power and energy. Next, Kirchhoff’s current and voltage laws are introduced, followed by resistance, simplifications of resistive circuits and voltage and current calculations. Circuit analysis techniques are then presented, followed by inductance and capacitance, and solutions of circuits using the differential equation method. Finally, the operational amplifier and time varying signals are introduced. This lecture is written for a student or researcher or engineer who has completed the first two years of an engineering program (i.e., 3 semesters of calculus and differential equations). A considerable effort has been made to develop the theory in a logical manner—developing special mathematical skills as needed. At the end of the short book is a wide selection of problems, ranging from simple to complex. KEYWORDS Bioinstrumentation, Circuit Theory, Introductory Biomedical Engineering, Sensors, Transducers, Circuits, Voltage, Current iv P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 v Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Basic Bioinstrumentation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Charge, Current, Voltage, Power and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1 Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.1 Kirchhoff’s Current Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 3.3.1 Kirchhoff’s Voltage Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 3.4 Power and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 3.5 Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 4. Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.3 Equivalent Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 4.4 Series and Parallel Combinations of Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 4.4.1 Resistors in Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 4.4.2 Resistors in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5 Voltage and Current Divider Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 4.5.1 Voltage Divider Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.5.2 Current Divider Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5. Linear Network Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 5.1 Node-Voltage Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.2 Mesh-Current Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.3 Linearity, Superposition and Source Transformations . . . . . . . . . . . . . . . . . . . . . . . 44 5.3.1 Linearity and Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.3.2 Equivalent Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 6. Th´evenin’s and Norton’s Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.1 Th´evenin’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Norton’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 vi CONTENTS 6.3 Dependent Sources and Th´evenin and Norton Equivalent Circuits . . . . . . . . . . . 59 7. Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.1 Power and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 8. Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.1 Power and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 9. Inductance and Capacitance Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 10. General Approach to Solving Circuits Involving Resistors, Capacitors and Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 10.1 Discontinuities and Initial Conditions in a Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 96 10.2 Circuits with Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 11. Operational Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 11.1 Voltage Characteristics of the Op Amp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130 12. Time-Varying Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 12.1 Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 12.2 Passive Circuit Elements in the Phasor Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 12.3 Kirchhoff ’s Laws and Other Techniques in the Phasor Domain. . . . . . . . . . . . .137 13. Active Analog Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 14. Bioinstrumentation Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 14.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 14.2 Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 13. Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 vii Preface This short book on bioinstrumentation is written for a reader who has completed the first two years of an engineering program (i.e., three semesters of calculus and differential equations). A considerable effort has been made to develop the theory in a logical manner—developing special mathematical skills as needed. I have found it best to introduce this material using simple examples followed by more difficult ones. At the end of the short book is a wide selection of problems, ranging from simple to difficult, presented in the same general order as covered in the textbook. I acknowledge and thank William Pruehsner for the technical illustrations. Portions of this short book are from Chapter 8 of Enderle, J. D., Blanchard, S. M., and Bronzino, J. D., Introduction to Biomedical Engineering (Second Edition), Elsevier, Amsterdam, 2005, 1118 pages, with Sections 1, 2 and 13 contributed by Susan Blanchard, Amanda Marley, and H. Troy Nagle. P1: IML/FFX P2: IML/FFX QC: IML/FFX T1: IML Morgan-FM MOBK036-Enderle.cls November 1, 2006 15:55 viii P1: KDD MOBK036-01 MOBK036-Enderle.cls November 1, 2006 16:0 1 C H A P T E R 1 Introduction This short book provides basic information about bioinstrumentation and electric circuit theory. Many biomedical instruments use a transducer or sensor to convert a signal created by the body into an electric signal. Our goal here is to develop expertise in electric circuit theory applied to bioinstrumentation. We begin with a description of variables used in circuit theory, charge, current, voltage, power, and energy. Next, Kirchhoff’s current and voltage laws are introduced, followed by resistance, simplifications of resistive circuits and voltage and current calculations. Circuit analysis techniques are then presented, followed by inductance and capacitance, and solutions of circuits using the differential equation method. Finally, the operational amplifier and time-varying signals are introduced. Before 1900, medicine had little to offer the typical citizen because its resources were mainly the education and little black bag of the physician. The origins of the changes that occurred within medical science are found in several developments that took place in the applied sciences. During the early 19th century, diagnosis was based on physical examination, and treatment was designed to heal the structural abnormality. By the late 19th century, diagnosis was based on laboratory tests, and treatment was designed to remove the cause of the disorder. The trend towards the use of technology accelerated throughout the 20th century. During this period, hospitals became institutions of research and technology. Professionals in the areas of chemistry, physics, mechanical engineering, and electrical engineering began to work in conjunction with the medical field, and biomedical engineering became a recognized profession. As a result, medical technology advanced more in the 20th century than it had in the rest of history combined (Fig. 1.1). During this period, the area of electronics had a significant impact on the development of new medical technology. Men such as Richard Caton and Augustus Desire proved that the human brain and heart depended upon bioelectric events. In 1903, William Einthoven expanded on these ideas after he created the first string galvanometer. Einthoven placed two skin sensors on a man and attached them to the ends of a silvered wire that was suspended through holes drilled in both ends of a large permanent magnet. The suspended silvered wire moved rhythmically as the subject’s heart beat. By projecting a tiny light beam across the silvered P1: KDD MOBK036-01 MOBK036-Enderle.cls November 1, 2006 16:0 2 BIOINSTRUMENTATION 1750 1800 1850 1900 1950 2000 1752 – Ben Franklin flew his kite in the storm. 1774 – John Walsh proved electricity passes through humans. 1791 – Galvani published his findings on “animal electricity.“ 1800 – Volta built the first battery. 1820 – Oersted discovered electromagnetism. Ampere measured the magnetic effect of an electric current. 1860 – Maxwell worked out the mathematical equations for the laws of Electricity and magnetism. 1886 – Hertz discovered the electromagnetic wave. 1897 – Thomson discovered electrons. 1903 – Einthoven discovered the galvanometer. 1909 – Millikan measured the charge of the electron. 1920s – Television was invented. 1935 – Amplifiers were used to record EEGs. 1948 – Transistors become readily available. 1959 – First transistor-based computer was made. 1972 – First CAT machine was made. First microprocessor was used. 1785 – Coulomb worked out the laws of attraction and repulsion between electrically charged bodies. 1826 – Ohm formulated law of electrical resistance. 1831– Faraday and Henry found that a moving magnet would induce an electric current in a coil of wire. 1895 – Roentgen discovered X-rays. 1904 – Fleming invented the vacuum tube. 1929 – Hans Berger recorded the first EEG. 1948 – The first large scale computer was built. 1960 – Chardock and Greatbatch created the first implantable pacemaker 1981 – IBM introduced the first personal computer FIGURE 1.1: Timeline for major inventions and discoveries that led to modern medical instrumenta- tion.