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Electronic Circuits with Applications to Bioengineering BME 123B Winter 2011 March 17, 2011 Derek Chang [email protected] Jessica Borja [email protected] TABLE OF CONTENTS OVERVIEW ......................................................................................................................................................... 3 ORIGINAL CIRCUIT LABS............................................................................................................................... 4 LAB 1 BASIC DC CIRCUITS ................................................................................................................................. 4 LAB 2 EQUIVALENT CIRCUITS ............................................................................................................................. 4 LAB 3 TRANSIENT RESPONSE OF RC/RL CIRCUITS .............................................................................................. 4 LAB 4 OPERATIONAL AMPLIFIERS ....................................................................................................................... 4 LAB 5 RC CIRCUITS AND AUDIO FILTERS ............................................................................................................ 4 OVERALL IMPRESSION OF CURRENT LABS .......................................................................................................... 5 OBJECTIVES AND TASKS ................................................................................................................................ 6 APPROACH ......................................................................................................................................................... 7 INTEGRATING THE LAB CONTEXT ....................................................................................................................... 7 BIOLOGICAL APPLICATIONS ................................................................................................................................ 8 Electrophoresis Gel........................................................................................................................................ 8 Lipid Bilayer .................................................................................................................................................. 9 Electrocardiogram (EKG) ............................................................................................................................ 10 DESIGNING LABS .............................................................................................................................................. 11 IMPROVED CIRCUIT LABS ........................................................................................................................... 13 EXPERIMENTS 1A & 1B: RESISTIVE CIRCUITS/GEL ELECTROPHORESIS ............................................................. 13 EXPERIMENT 3: TRANSIENT RESPONSE OF RC/RL CIRCUITS-LIPID BILAYER AS A CAPACITOR ........................... 17 EXPERIMENT 4: ELECTROCARDIOGRAM (EKG) ................................................................................................. 21 BUDGET ............................................................................................................................................................ 24 PERSONNEL ..................................................................................................................................................... 24 TABLE OF FIGURES ....................................................................................................................................... 25 BIBLIOGRAPHY .............................................................................................................................................. 26 Electronic Circuits with Application to Bioengineering Overview In the current bioengineering curriculum, students are required to take an introductory circuit course also known as EE-101. Many bioengineering students at University of California Santa Cruz claimed that the introductory electrical circuit course is irrelevant to their education. Students complained that the course is poorly taught, and some faculty members agree with this statement. Bioengineering students passed this course without understanding of how the content could be applied to the material taught in the biology courses. In order to motivate bioengineering students to learn the concepts taught in EE-101, we integrated the content to familiar biology apparatuses in labs that is concurrently taught with the lecture for students to design. The introductory course covers topics such as basic fundamentals of electrical engineering, circuit laws, equivalent circuits, operational amplifiers, RC/RL circuits, first and second order transient, phasors, and low and high pass filters. These topics appear to be irrelevant to bioengineering students, but some students don’t realize that these concepts are applied to apparatuses that have been taught by the biomolecular engineering department. Concepts such as filters are important because in order for researchers to get a reading they have to reduce noise. The problem about the EE-101 course is not that its irrelevant, instead the course doesn’t do an adequate job demonstrating the relevance to bioengineering students. Faculty members in the biomolecular engineering department heard the complaints from the students, and decided that a new course would be beneficial for future students. This course would be an introductory electrical course with biology applications. In order to apply the material taught in the course, appropriate labs need to be developed. The labs will allow students to design circuits based on the concepts they covered in lecture and apply them to biological applications. The course is still an electrical circuit course, so in order to preserve the credibility of the lab, goals in the current EE-101 labs will be integrated into the new labs. This newly developed course and lab will be offered to bioengineering students to resolve the current EE101 problems. For our project, we have developed labs that integrate concepts of electrical circuits to biological applications. We studied the concepts covered in lab 1, lab 3, and lab 4, and found applications that would be intriguing to bioengineers. In lab 1 we used an electrophoresis gel, a familiar set-up to bioengineering students. A lipid bilayer is another biology related topic that we applied for lab 3, and this biological molecule is introduced in an upper biomolecular engineering course. The electrocardiogram (EKG) is the design used in lab 4 to study how operational amplifiers are used in a biological setting. The rest of the labs will be rewritten by our client, Professor Peterson. Our end product will be a copy of the lab manuals that we wrote after doing some test with the biological apparatuses. Original Circuit Labs Lab 1 Basic DC Circuits The goal in lab 1 is to familiarize students with the lab equipment. Students have to build and analyze simple resistive circuits, measure circuit properties (voltage, current, power) of various elements in the circuit, and build a voltage divider. The design component of the lab asks students to build a resistance meter that allows them to determine unknown resistances. This lab covers voltage and current, Ohm’s law, resistive circuits, Kirchoff’s labs, node/mesh analysis, and power. Students should be familiar with these concepts, if they were covered in class. Each student must be able to design circuits and apply these concepts to the designs, assuming that they have an adequate understanding of the concepts. Lab 2 Equivalent Circuits The goals in lab 2 is to understand real voltage source, use an unknown circuit, match a resistive load to an unknown circuit for maximum power transfer, and understand the graphical method of a load line. Students have to build an equivalent circuit for a resistive network so that they may use their results to understand the load line. This lab covers Thevenin’s and Norton’s theorems, load line technique, and power transfer to load resistor. As mentioned in the previous lab, students must be able to apply these topics to the circuits they build. Lab 3 Transient Response of RC/RL Circuits The goals in lab 3 is to understand RC and RL circuits, measure the time-dependent response of an RC circuit, measure time-dependent signals on the oscilloscope, and design an RC transient circuit with desired properties. The topics covered are capacitors and inductors as energy storing circuit elements, transients in RC/RL circuits, RC time constant, and simple exponential functions, steady-state values. Lab 4 Operational Amplifiers The goals in lab 4 is to understand DC and AC op-amp operation, determine input and output resistance/impedance, measure the frequency response of an amplifier, build and characterize a preamplifier, and design an op-amp circuit that carries out a desired mathematical operation.This lab covers the op-amp circuit model, ideal op-amp technique, input and output impedance, basis op-amp circuits, and differentiators and integrators. Lab 5 RC Circuits and Audio Filters The goals in lab 5 is to understand sinusoidal signals and phasors, measure amplitude gain and phase shift of an RC filter, measure the frequency response of a first order filter, and design a filter with desired characteristics. This lab covers sinusoidal signals, phasors/phasor diagrams, impedance, frequency dependence, first order RC and RL filters, amplitude and phase response of a filter, and bode plots. These topics are a continuation to topics covered in lab 3, which teaches capacitance and RC circuits. Overall Impression of Current Labs The current labs have too high an expectation for the student. These labs are poorly written, and this makes it difficult for students to understand the goals. Students are only given two hours a week to work with a teacher’s assistants to finish the labs, and most of the time TA’s don’t have enough time to get to every student’s question. Students who work on the labs on their own get frustrated because the labs aren’t clear and concise. From personal experience and student feedback, the labs are too difficult to finish within two weeks. Since the current EE-101 labs are poorly written and are challenging, students don’t get the opportunity to fully grasp how the concepts are applied to actual situations. Most of the goals in the labs aren’t achieved because the students’ goal is to finish in time. They are unable to fully understand the concepts, and for bioengineering students there is no motivation to value the concepts because it seems irrelevant to them. Bioengineering faculty and students both saw the need to change these labs to make them feasible within two weeks and relevant to students. Objectives and Tasks Our objective for this project is to implement concepts from EE-101 labs into the new labs that will be taught concurrently with the newly developed circuit course. We have studied the concepts covered in the lab and our client, Professor Peterson, explained them in greater detail so that we would be able to design lab. After analyzing the goals of each labs and studying the concepts, we were able to create lab procedures that implement biological applications to electrical engineering concepts. One important aspect of the labs that we put into consideration is to make sure that the labs correspond to the lecture. A problem that students ran into is that labs covered topics that weren’t covered in lectures, and this made it difficult for students to understand concepts. We had weekly meetings with our client Professor Peterson to make sure that the topics covered in lab would have been taught to the students in lecture. After we made sure that the labs and lectures harmonize together, we decided that we would keep the labs a two week time span. The time given for a student to complete the labs would remain the same, except the labs will be feasible and not too challenging. We want students to finish the labs in a respectable amount of time. The labs should be challenging for students, but not too difficult that it seems impossible to accomplish in two weeks. We want to motivate students and not to discourage them. Although we had to plan the labs properly, our main focus was to create labs that would be hands on for bioengineering students. After we studied the concepts, we researched biological applications that could be applied into the new labs that we will design. There were multiple apparatuses that we considered, but only a few seemed to be suitable for the new labs. We eliminated the labs that weren’t appropriate for the topics we used in the new labs. To motivate bioengineering students to understand the materials we applied those biological applications and integrated them into the new labs. Approach Study and Understand Electrical Engineering Concepts Find Biological Applications Electrophoresis Gel Application Lipid Bilayer Electrocardiogram (EKG) Used to model a resistor Demonstrates how a lipid bilayer can act as a capacitor Used to understand the characteristics of an operational amplifier Figure 1: This is our block diagram of our approach. The steps we took were to understand the concepts, find biological applications, and design labs. Integrating the Lab Context We have adapted the concepts covered in the original labs into the new labs. In the beginning of the quarter we have analyzed the goals of each lab, and took some goals and concepts to incorporate them into the redesigned labs. We wanted to assure that these new labs will be credible to the course, which is the reason why we are adapting the concepts and goals into the newly developed labs. Some sections were taken from the present EE-101 labs and integrated into the new labs with the biology applications. After analyzing the goals and concepts in the current labs, we found a few biological applications that can be incorporated into the new labs. These biological set-ups can take on some goals that we considered to preserve in the new labs. For example, one lab will include an electrophoresis gel apparatus to study the circuit properties. Students will get familiar with their equipment in this lab, and study how the electrophoresis gel is relevant to electrical circuits. There are other biological applications that we have incorporated into the new labs which will be introduced later on. In the new labs, we reassured that the labs were feasible within in two weeks and that they were clear for students to comprehend. Bioengineering students felt that the labs covered too many topics to do within two weeks. When we reviewed the current labs, some of the concepts were not included in the labs that we designed. Biological Applications Electrophoresis Gel The gel electrophoresis apparatus is an application that will be used in the revision of lab 1. It will teach the basic concepts of resistive circuits and fundamental concepts such as Ohm’s and Kirchoff’s Laws. Gel electrophoresis is a technique that is used for separating DNA, RNA, or protein molecules by using an electric field that is applied to a gel matrix. There are analytical uses of gel electrophoresis such as after amplification of DNA from PCR (Polymerase Chain Reaction) or used as a preparative technique prior to use in DNA sequencing and Southern Blotting. [6] It is simply used to sort molecules based on size and charge. Using an electric field, molecules such as DNA can be made to move through a gel made of agar. The gel refers to the matrix used to contain and separate the molecules. Agarose gels are an ideal gel matrix for diffusion and electrokinetic movement of biopolymers because the gel is biologically inert and has controlled ionic properties. [10] Electrophoresis refers to the electromotive force that is used to move the molecules through the gel. The molecules are placed in wells within the gel and then an applied electric field will move the molecules through it at different rates based on their mass. The molecules move toward the anode if negatively charged or toward the cathode if positively charged. Figure 2: Gel Electrophoresis Apparatus & Circuit. Figure copied from National Diagnostics. “The Mechanical and Electrical Dynamics of Gel Electrophoresis”. The apparatus of gel electrophoresis represents an electrical/thermodynamic system. It receives energy from the power source and releases its energy as heat. The gel would sit in a well where the buffer solution fills up an upper and lower chamber. The general setup of the circuit is basically a resistor connected to a voltage source. In more detail, the circuit of a gel electrophoresis apparatus is simple DC circuit composed of a power source with three resistors in series. The resistors would be the upper chamber with buffer solution in it, the gel, and the lower chamber with buffer solution in it. The mass majority of the resistance in the circuit derives from the gel because the cross section of each electrode chamber is much greater than the cross section of the gel and the upper and lower chambers are also shorter in length to the gel. It is sufficient to say that the gel is the only resistor in the circuit, where most of the power is expended unless the buffer salts were absent from one or both chambers. [7] Ohm’s law and expenditure of power have direct relationships with the apparatus. As voltage is applied to the circuit, the majority of the current is represented by the migration of the buffer ions. Cations in solution migrate toward the negative electrode in the upper chamber, and the negatively charged molecules migrate toward the positive electrode in the upper chamber. Good electrophoresis results come about from management of heat generated by current flow as excessive current flow will result in excessive heat generation evaporate the solution or melt the matrix itself. [3] Since temperature regulation is an important consideration in this circuit, one of the conceptual viewpoints that will be introduced in this lab is the idea of heat dissipation and the effect it has on circuits and electronics. This concept will help students employ the concepts of using Ohm’s law in consideration with this circuit using constant values of voltage, current, or power. Lipid Bilayer The lipid bilayer application will be used to demonstrate the concepts introduced in the current lab 3 which is an introduction to the time constant in RC circuits, capacitance, and transient response. The electrical equivalent is modeled in figure 3, the lipid bilayer acts as a capacitor. The lipid bilayer is a thin membrane made up of two layers of lipid molecules. The membrane separates the external and internal conducting solutions thin insulator layer [1].The electrical equivalent of the power source would be ATP (Adenosine-5'-triphosphate), which is a nucleotide in cells that transports chemical energy within cells for metabolism. [4] Using a lipid bilayer, we can model the charging capacity of a capacitor as well as analyze transient response in the circuit. Figure 3: This is a basic RC circuit that is represented in a lipid bilayer. Figure copied from AMRITA. “Passive Properties of a Simple Neuron” (http://sakshat.amrita.ac.in/VirtualLab/index.php) We can model this apparatus to analyze transient response of RC circuits using the oscilloscope and function generator. Students can demonstrate the concept of the time constant with charging and discharging cycles or modeling the bilayer as a circuit that performs a specific function. The physical structure of the lipid bilayer would not be practical to use in the new labs due to the limitation of the equipment, but it can be demonstrated as a scaled up equivalent circuit on a breadboard. The current source applied to the actual lipid bilayer is too small to be controlled by the lab equipment which is the motive behind the larger scale. This means that an actual lipid bilayer setup would require a Faraday cage to cancel out any noise that will result in this particular circuit setup. We are going to explain that the actual physical setup for this apparatus will be performed in BME 150, molecular mechanics, where students will have handson interaction with making a lipid bilayer and will be able to see real signals on the oscilloscope. Electrocardiogram (EKG) Figure 4: This is the circuit schematic of the EKG that we used to model. Figure adapted from Scott Harden (http://www.swharden.com). An electrocardiogram (EKG) is used to measure heart rate over a period of time. The EKG measures the electrical potential taken from the surface of tissue, which comes from muscle contractions in the body [9]. The heart is a muscle that pumps blood throughout the body, but it also emits voltage. An EKG is used for biomedical practices on patients to monitor their heart rate. It is important that an EKG signal is accurate and comprehendible for records. In order to get an accurate reading, an op-amp is used to amplify a person’s heartbeat. The op-amp takes the small voltage potential emitted from the surface of the skin, and amplifies it so that a heartbeat can be analyzed clearly. To get the best results, op-amps are important building blocks in an EKG circuit with filters to avoid noise, but the op-amp will be the main focus for lab 4, operational amplifier. The schematic for an EKG circuit includes an op-amp, resistors, and capacitors. In figure 2, the schematic of a simple EKG circuit is illustrated, and this is the same circuit we used for lab 4. The differential voltage across a person’s chest is typically 1.8mV in amplitude [9]. The diagram in figure 4a illustrates how the placement of electrodes on a person can be used to measure a heartbeat. The voltage difference between the electrodes is known as the differential voltage which is amplified by an op-amp. Given the differential voltage and circuit diagram, students can analyze the characteristics of op-amps. a. b. Figure 5: a. This is a simplified circuit of how an op-amp and body is used in the EKG circuit. Figure copied from Chia-Hung Chen, Shi-Gun Pan, Peter Kinget “ECG Measurement System” (http://www.cisl.columbia.edu). b. In this figure the electrodes are applied to the arms. Figure copied from Analog Dialogue “ECG Front-End Design is Simplified with MicroConvertor”. In the operational amplifier lab, we integrated the EKG circuit shown in figure 4 for the newly designed labs. Students will design a simple EKG circuits and analyze the characteristics of an op-amp. They will study the placement of electrodes and apply it to their own bodies and as a result, they will be able to display a heart rate on the oscilloscope. There are some diagrams that indicate that electrodes can be placed on each arm as shown in figure 4b, and to keep the EKG circuit simple, students will place an electrode on each arm. Students can use the oscilloscope to read Vin and compare it to Vout. They will be able to observe the difference between the input and output such as noise and amplitude. The EKG circuit can be helpful to study op-amps, but there are some issues that may add variance to results. One problem is the EKG signals can be distorted because of various reasons such as noise from other devices, noise from the electrode, or muscle contractions [3]. This demonstrates the importance of filters within the circuits. Actual use of an EKG device requires doctors or nurses to make preparation that will not be used in the labs. In order to get the clear signals, nurses have to rub the skin with a mild abrasive to generate a better ion flow between the tissue and electrode [3]. Instead of reducing the impedance of the skin, students can see the importance of filters. Designing Labs As our final product, we have lab procedures with all of the biological applications that we were able to integrate. Our lab will require bioengineering students to design a circuit that is based on a biology apparatus. These new labs will deviate from the step-by-step procedures that most bioengineering students are used to seeing. Before the students will design, they will understand concepts by creating sections that will allow students to see how the topics are used in an electrical set-up. In order for students to design anything, they need understand the concepts that are covered in the labs. We were able to test each biological application for each lab, and we concluded that they were feasible for bioengineering students. We had to scale one of the biological apparatuses larger than the actual set-ups because the specifics were too small for the devices that are accessible to students. This allows bioengineering students to see how an electrical circuit could relate without working with the actual molecule. The other labs were actual set-ups for students to work with and get a visual of how the biological apparatuses are used. Our goal was to find biology applications for all of the current EE-101 labs and find students to test the new labs, but we were unable to find applications for certain concepts and ran out of time. Even though we haven’t covered all of the labs, our client, Professor Peterson, will rewrite the current EE-101 labs. Towards the end of the quarter we were still revising the new labs, and we were unable to let students test out the labs to make sure they are clear and feasible. Improved Circuit Labs Experiments 1a & 1b: Resistive Circuits/Gel Electrophoresis University of California at Santa Cruz Baskin School of Engineering Bioengineering Circuits Laboratory Experiments 1a & 1b: Resistive Circuits/Gel Electrophoresis I. DESCRIPTION AND OBJECTIVE Ohm’s law and Kirchoff’s Laws are fundamental rules that can be applied to simple resistive circuits as well as more complex systems of circuits. This laboratory will first acquaint students with concepts using hands-on exercises to demonstrate Ohm’s law, Kirchoff’s laws, and power from a traditional standpoint using resistors and a breadboard. The experiment will then transition to a biological apparatus setup where we will take a real life application to where these concepts can be demonstrated. This biological apparatus will be a gel electrophoresis setup that will demonstrate a real life model of a resistive circuit. Our objective is to develop the skill in analyzing these simple resistive circuits while understanding how we can visualize voltage, current, and wattage. II. GENERAL DISCUSSION Ohm’s law connects the relationship between current, voltage, and resistance where the amount of electric current that goes through a metal conductor in a circuit is directly proportional to the voltage that is impressed upon it, for any given temperature. This relationship between current, voltage, and resistance allows you to solve for any one of those three values when given the other two. Kirchoff’s voltage and current laws deal with the conservation of charge and energy in electrical circuits. Kirchoff’s voltage law implies that the directed sum of electrical potential voltage differences around any closed loop in a circuit will be zero. It is conservation of energy. After careful understanding of these laws you can model the relationships of resistors in a circuit and apply these laws to create a voltage divider, which is where a simple linear circuit can produce and output voltage that is a fraction of the input voltage. You will be able to visualize and confirm your results with the DMM. III. OBSERVATION AND INVESTIGATION OF RESISTIVE CIRCUITS You are to investigate the observed relationships in resistive circuits by building some simple circuits and analyzing how changing resistor values will affect the voltage drops and currents. You will analyze the performance of these circuits and draw upon Kirchoff’s and Ohm’s laws to analyze their underlying theory and function. 1. Resistive circuits We want to build a closed loop circuit with three different value resistors in series so we can observe their properties and see how it relates to Kirchoff’s Voltage Law. Make these three resistors to be R1, R2, and R3. Place R1, R2, and R3 in series and design a circuit where the voltage drops of R1, R2, and R3 are becoming larger (eg. Voltage drop of R1<voltage drop of R2<Voltage drop of R3. The sum of your voltage drops should add up to the value of your power source. Build this circuit and measure voltage drops across these three resistors. Discuss what values you should be getting. Verify that your results confirm Kirchoff’s Voltage Law. 2. Currents through a node Use the same resistors that you built your last circuit with. We will build a circuit (below) where we can measure currents entering and leaving a node to visualize Kirchoff’s Current Law. Use nodal analysis to find the currents flowing in each of the resistors and then use KCL to show that the sum of currents at each of the nodes A, B, C, and D is zero. From measuring the current flows in and out of the branches at nodes B, C, and D show that the sum of the currents at those nodes are zero. Note the direction of the currents and confirm your results. How does the current flow in node B? 3. Resistive circuits: parallel and series A circuit connected in a single path has the same current flowing through all the components (resistors) in that circuit. This is called a series circuit which means the sum of the voltage drops across each component in the circuit will equal the value of your power source. You confirmed this with Kirchoff’s Voltage Law. When components are connected in parallel the same voltage is applied to each component which means that the total current is the sum of the currents through each component. You will use light bulbs from your lab kit and build a circuit that shows the difference between a parallel and series circuit. Let the light bulbs be R 1 and R2. Set your power source to 5V and build a circuit where R1 will be brighter than R2 then build a circuit where R1 will have the same brightness as R2. Draw your circuit diagram and discuss how the light bulbs respond when in series and in parallel. Discuss your results. 4. Voltage divider A linear circuit that produces an output voltage as a fraction of the input voltage is known as a voltage divider. You are to create one that has an output voltage that is 1/3 of the input voltage. (V1/V2)=1/3. Draw a circuit diagram and create a voltage divider with a resistor and a potentiometer. The current from a voltage source is V in/(R1 + R2) and the current through the second resistor is V out/R2. If there is no load on the output the currents are the same: V in/(R1+R2) = Vout/R2 or Vout/Vin=R2/(R1+R2). (Hint: Draw upon this equation, Vout=R2/(R1+R2)*Vin.) IV. GEL ELECTROPHORESIS CIRCUIT We will now take a different approach to how we can view electrical circuits in a more applied setting. We can use agarose gel electrophoresis to separate and analyze DNA in a way where we can measure it. Information about DNA is visualized in a particular band in the gel with the addition of ethidium bromide. The ethidium bromide binds strongly to the DNA and becomes fluorescent by absorbing invisible UV light and emitting the energy as a visible orange light. We want to model how this apparatus is also a demonstration of Kirchoff’s Voltage Law and Ohm’s law. A gel electrophoresis apparatus works like a simple resistive circuit. There is a power source that produces a certain voltage that forces current through the gel and the buffer solution. The electromotive force of the current moves the DNA down the gel and then the fragments are shown as bands. These equations have practical consequences in gel electrophoresis: V=IR (Voltage = Current x Resistance) W=IV (Watts = Current x Voltage) The resistance of this circuit is determined by the thickness of the gels (eg. 0.7%-2%) being run and the type of buffer being used (eg. TAE, TBE). The resistance of the system will increase gradually as a result of highly conductive chloride ions in the gel being replaced by slower moving conductive ions from the running buffer1. 1. Resistive Circuit of Electrophoresis You should have a gel electrophoresis set up already with pre-cast gel and buffer solution and a power source. In your notebook, draw a diagram of what the gel electrophoresis circuit would look like and where you would plug in your DMM to record measurements. Confirm with your instructor or TA that you have a feasible diagram. We want to know if our electrophoresis circuit can be modeled as a linear system. Measure the resistance of the gel and take note of it. 2. Electrophoresis: Constant voltage, current, power When running your gels, you should be running at 5V/cm. For example this means if the electrodes on the tank were 10 cm apart, then the gel will run at 50V. Confirm the distance of your electrodes to determine the voltage that needs to be applied. R1 can be a 1 MΩ resistor on your breadboard and R2 is the gel. We will first run the gels with your calculated constant voltage. We will get the current through the gel by measuring the voltage drop of the gel. Be approximate with your measurement recording as biological apparatus will not behave linearly like components in your lab kit. From your measurements, discuss what happens when constant voltage, constant current, and constant wattage are applied to this system. Why is it recommended to use constant voltage rather than current and wattage? Draw upon Ohm’s law and any other physical considerations. Submit a report discussing the work that you have done in this laboratory that explains your reasoning. 1. Formulations and Protocols for Electrophoresis and Western Blotting Experiment 3: Transient Response of RC/RL Circuits-Lipid Bilayer as a Capacitor University of California at Santa Cruz Baskin School of Engineering Bioengineering Circuits Laboratory Experiment 3: Transient Response of RC/RL Circuits-Lipid Bilayer as a Capacitor I. DESCRIPTION AND OBJECTIVE Voltages and currents are signals that change over time. Such signals can be generated and analyzed using two pieces of equipment, which are the oscilloscope and the function generator. The oscilloscope is a piece of electrical test equipment that is used to show and measure timevarying signals or waveforms on a display. The connection of the oscilloscope to your circuit will be the same as if you connected a voltmeter to a DC voltage in your previous experiments. The function generator produces time-varying voltages the same way that the power source produces DC voltages, so a sinusoidal voltage can be produced. There are controls to set the amplitude of the voltage variations of the waveforms just as there are controls on the power source to set magnitude of its DC voltage. This laboratory will ask you to study the transient response of a series RC circuit and understand the RC time constant by analyzing measurements that you will see on the oscilloscope. II. GENERAL DISCUSSION The RC time constant is the measure of time required for charges in voltages and currents in RC and RL circuits. It is the product of the circuit resistance and circuit capacitance in ohms and farads and is directly related to transient response. Transient response can be visualized with a simple example. Given the output of a 5 volt DC power source when it is turned on, the transient response is from the time the switch is turned on to the time until it reaches 5 volts. In the case of an RC circuit, the transient response is the response to a change in a resistor or capacitor. When the resistor and capacitor are connected in series, the discharged capacitor will initially act as a short circuit and draw maximum current from it when it is attached to a voltage source. Once the capacitor reaches full voltage from the source, it will stop drawing current and behave as an open circuit. Voltages and currents that have reached their final value are in the steady-state response. The RC constant is the rate of charging for the RC circuit. Image taken from Langaliya, Rushi, “Capacior Transient Response”. Creativity, January 03, 2011, February 2, 2011. http://rushi-langaliya.blogspot.com/2011/01/capacior-transientresponse.html III. OBSERVATION OF A BASIC RC CIRCUIT We will build a basic RC circuit (below) where we can calculate the RC time constant. We will build this circuit and consider that our test equipment acts as a real voltmeter. This means that the voltmeter has a finite internal resistance so that your DMM draws current and affects the circuit. This is different from an ideal voltmeter which has infinite internal resistance and does not draw any current from your circuit. Measure V c, the voltage across the capacitor, at different time intervals to analyze the activity of a charging and discharging cycle. Figure 1. R=10MΩ C=10µF V=10V 1. RC time constant We want to calculate the time constant in the circuit above. Calculate that value for and record it for later use. Build this circuit and be sure to connect your capacitor correctly as it has different polarities. Throw the switch into position 1 record the capacitor’s voltage as a function of time by using the DMM. Record your values in a table and plot V C in volts versus time in seconds for the charging and discharging cycles. From Kirchoff’s laws, it can be shown that the charging voltage VC (t) across the capacitor is given by: VC (t) =V( 1- e-t/RC) t≥0 where, V is the applied source voltage to the circuit for t≥0. RC = is the time constant. The discharge voltage for the capacitor is given by: VC (t) = Voe-t/RC t≥0 Vo is the initial voltage stored in the capacitor at t = 0 and RC = . Determine the RC time constant of the circuit which is equal to the time after which the voltage has dropped to 37% of its original value (discharging cycle) or risen to 63% of its final value (charging cycle). Compare your calculate values with your actual measured values. There is a discrepancy between your calculated and measured values because of the finite internal resistance of the DMM which is modeled as RD. What can we change in the circuit above to minimize the effect of RD? Discuss this in your lab write up. 2. Transient response on the oscilloscope Figure 2. We want to vary frequency of an RC circuit with a function generator and observe signal voltage. We will now rebuild the circuit and use the both the oscilloscope and function generator to calculate the time constant. Replace your current circuit elements with a 22kresistor and a 1µF capacitor. The oscilloscope replaces the DMM in your circuit. We will attach channel 1 on the oscilloscope across points A and B and channel 2 for VC. Next we will replace the circuit on the left of A and B with the function generator. Set the generator to a square wave with a period of 5. Set the scope’s trigger to channel 1 and trigger the slope to be positive. Determine the time constant from what you see on the scope image by observing the signal voltage from the function generator on channel 1 and V C on channel 2. After finding the time constant we will vary the frequency of the square wave signal by adjusting the time scale on the scope so that we can see 2-3 periods of the applied signal on the screen. What happens as frequency is changed and why? Compare what you see for each frequency and compare V C to V. Discuss your results in your write up. I. Designing a Lipid Bilayer In this section, you will study the electrical properties of a lipid bilayer. You will design an equivalent circuit of a paramecium membrane, and study the properties of capacitance and conductance. The membrane acts as a capacitor and the channel a conductor. The membrane separates the internal and external conducting solutions by a thin insulating layer. The ion channels allow ions to flow across the lipid bilayer. Build a circuit with a resistor parallel to a capacitance shown in the figure above. The capacitor of a paramecium membrane is usually 1F/cm2 and the resistor is 106cm2. Calculate of the paramecium membrane. If you apply a voltage to this circuit then the capacitor begins storing the electricity. Apply 10V to the circuit and add a switch to measure the voltage across the capacitor. Use the oscilloscope to view the behavior of the lipid bilayer. Open and close the switch and draw the image that is displayed on the oscilloscope. Then apply 2mA to the same circuit and draw the image that is displayed on the oscilloscope. When does the capacitor reach maximum storage capacity? If a power supply was added in series to the capacitance, it would model the electrical properties of a gradient. How does the power supply and resistor relate to each other? Experiment 4: Electrocardiogram (EKG) University of California at Santa Cruz Baskin School of Engineering Bioengineering Circuits Laboratory Experiment 4: Electrocardiogram (EKG) I. Description and Objective Operational amplifiers, also known as op-amps, are important components of electronic circuits. Students will design and analyze an op-amp used in the circuit of a simplified electrocardiogram (EKG). An EKG circuit is used to interpret an electrical activity, such as voltage, over time. The EKG has a small electrical change caused from the heart muscle that can be amplified with the op-amp circuit. The op-amp can behave as inverting or non-inverting, and the EKG circuit shows that it is an noninverting op-amp. In this lab, students must be able to apply the mathematical equations to confirm the characteristics of an ideal op-amp. An oscilloscope is used to observe the result of the circuit designed by the students. This lab will demonstrate the characteristics of an ideal op-amp using an inverting op amp circuit and an EKG circuit. The objective of the lab is to understand the behavior of the op-amp, design an op-amp, and understand DC and AC op-amp operation. II. General Discussion Op-amps take the difference of two electrical signals, and it amplifies the differential input voltage. The op-amp has both inverting and non-inverting inputs. An ideal opamp can be characterized by having infinite input impedance, infinite gain for the differential input signal, and zero gain for the common-mode input signal. Most opamps are almost always used with negative feedback. Negative feedback is when the output signal is returned to the input in opposition to the source signal. In an ideal opamp, the open-loop differential gain is assumed to reach infinite, and negative feedback takes a fraction of the output and returns it back into the inverting input terminal. This forces the differential input voltage to zero. Since the input voltage is forced to zero, then the input current is also zero. This is known as the summing point constraint, which should have been introduced in the course. In an inverting amplifier, the voltage gain can be determined by applying the summing-point constraint which was mentioned earlier and KCL. An inverting amplifier vo will be the invert of vin. Once the summing-point constraint was employed, the voltage gain (Av) can be calculated by the following equation: For a non-inverting amplifier, the voltage gain is also calculated by applying the summing-point constraint and KCL. The equation for a non-inverting amplifier is the following: Electrocardiogram is a device that is used to measure the electrical activity of the heart over time. The heart generates an electrochemical impulse that spreads throughout the heart which is the heartbeat. The EKG works by detecting the electrical changes on the skin that are caused when the heart muscle depolarizes during each heartbeat. The body is conductive with its fluid content and the electrochemical action can be measured at the surface of the body. An approximate voltage potential is 1mV between two various points on the body. The EKG circuit is modeled as a non-inverting amplifier, and Vin is represented by the voltage potential 1mV. The amplifier that is used in the EKG circuit has a gain of about 1000, so the expected Vout ranges from 1V to 2V. Pre-lab questions: 1. 2. 3. 4. 5. III. Under what assumptions is the ideal op amp technique valid? Why input and output impedance of an op amp circuit are important for DC? How do you measure input and output of impedance? Where do you place EKG electrodes on your arm? Calculate Vout of a non-inverting amplifier. Given that R1 = 1k, R2 = 100k, Vin = 1mV. Fundamental Op Amp Properties In this section, you will investigate the behavior of an ideal inverting op amp by applying a DC voltage. You will build an inverting op amp and use the characteristics of an ideal op amp. After building a circuit, you will analyze and confirm the concepts of an ideal op amp. 1. Inverting Amplifier Build an inverting amplifier using a 741 op amp. The op amp circuit must have two resistors with R1 in series with the voltage source and R2 parallel to the op amp. Let the values of R1 be 10k and R2 be 22k. Let the power supply of the op amp be ±15. Then apply a DC voltage V1 and vary between -5V and +5V in 1V steps. Calculate V2 of each step, given R1 and R2 you can calculate the gain then record the actual output of V2. Does your value match your calculations? Graph the values of V1 versus V2. Verify that this is an inverting amplifier by your observation of your graph. 2. Behavior of the Op Amp Vary V1 from between the ±15V in 1V steps and measure V2. Plot V1 versus V2 and observe the behavior of the circuit. Explain the results of your graph. 3. Input and Output Resistance Using the same circuit, set V1 as 3V and measure I1 and determine the input resistance of the circuit. Then determine the output impedance Zout by measuring the open circuit voltage and the voltage and current with a load resistor R L. Let the value of RL be 10k. Do not short circuit the output. Can you justify your result for Z out with the ideal op amp laws? IV. Electrocardiogram EKG In this section, you will use the voltage potential from your skin and apply it as V in. The EKG circuit will model a non-inverting op-amp. In the beginning you will first model a larger scale of the voltage potential of a heartbeat to understand and analyze AC amplification. 1. AC Amplification Use the function generator as the input by applying a sinusoidal signal with amplitude of 100 mV and frequency 75 kHz. Build a non-inverting using a 741 op amp using two resistors in series. R2 is set to ground and R1 is parallel to the op amp. Let the values of R1 be 1k and R2 be 100k. After the op amp is built measure V1 and V2 with an oscilloscope. If built correctly, the oscilloscope will show two clean sine waves. Is the output signal what you expected? Given the two sine waves of V1 and V2 calculate the phase difference. 2. EKG Circuit Using the same resistors and op amp, build an EKG circuit. Set the power supply at ±9V. The EKG circuit is a non-inverting amplifier. The schematic will be similar to the circuit you built in the previous section. To reduce noise, place a 0.1F in series with V1. Let R1 be 1k and R2 be 100k. Once the EKG circuit is built, place the electrodes on your arms (Refer back to pre-lab question 4.). Connect your electrodes to the EKG circuit you built. Use the oscilloscope to measure V1 and V2. If done correctly the oscilloscope should display sharp peaks that are measure as 1V pp. Is V2 what you expected? Budget Items EKG Electrodes EE-101 Lab Kit Electrophoresis Gel Kit PowerEase500 Power Supply Total Quantity 4 1 1 1 Cost $5 $43 $100 $400 $548 Personnel Jessica Borja She will be able to bring the bioengineering-related applications to this project. Her connection with Nader Pourmand’s lab will be helpful in access to electrical lab equipment that maybe useful with application to newly designed lab experiments. Knowledge of current lab research in Poumand’s lab utilizing electrical equipment can also bring concepts into the applications of our newly designed lab exercises. Derek Chang Having a direct experience with the current EE 101/L curriculum, he is able to bring in knowledge taken from this circuit course. He will be able to apply the background concepts of circuits into bioengineering applications because of his experience with the EE 101/L course. Experience with the class will be valuable as it can provide insight on what direction this lab and class should be taken and what can be improved. He will act as the group treasurer and manage any finances that may be needed for this project. Steven Petersen Professor Petersen will be the mentor/client for this project and be able to provide the sufficient background needed for knowledge in the circuit content. Working in conjunction with Professor Petersen will allow for clarification of any engineering problems that we may run into. His knowledge of electrical engineering will be valuable with our lab design process as he has had many experiences designing his own labs for students in the past. Table of Figures Figure 1: This is our block diagram of our approach. The steps we took were to understand the concepts, find biological applications, and design labs. ........................................................................................... 7 Figure 2: Gel Electrophoresis Apparatus & Circuit. Figure copied from National Diagnostics. “The Mechanical and Electrical Dynamics of Gel Electrophoresis”. ................................................................. 8 Figure 3: This is a basic RC circuit that is represented in a lipid bilayer. Figure copied from AMRITA. “Passive Properties of a Simple Neuron” (http://sakshat.amrita.ac.in/VirtualLab/index.php) .................... 9 Figure 4: This is the circuit schematic of the EKG that we used to model. Figure adapted from Scott Harden (http://www.swharden.com). ..................................................................................................... 10 Figure 5: a. This is a simplified circuit of how an op-amp and body is used in the EKG circuit. Figure copied from Chia-Hung Chen, Shi-Gun Pan, Peter Kinget “ECG Measurement System” (http://www.cisl.columbia.edu). b. In this figure the electrodes are applied to the arms. Figure copied from Analog Dialogue “ECG Front-End Design is Simplified with MicroConvertor”. .................................... 11 Bibliography [1] B. Hille, Ion Channels of Excitable Membranes, 3rd ed., Massachusetts: Sinauer, 2001. [2] C. Chen, S. Pan, and P. Kinget. (2011, March 1) ECG Measurement System. [Online]. Available: http://www.cisl.columbia.edu/kinget_group/student_projects/ECG%20Report/E6001%20ECG% 20final%20report.htm [3] E. Company-Bosch and E. Hartmann, "ECG Front-End Design Is Simplified with MicroConverter," Analog Dialogue, 2003. [4] E. Gouaux and R. MacKinnon, "Principles of Selective Ion Transport in Channels and Pumps," Science, vol. 310, iss. 1113666, 2005. [5] G. B. Ermentrout. (2011, March 5) Electrical Properties of a Membrane. [Online]. Available: http://www.math.pitt.edu/~bard/classes/passive2/node5.html [6] J. M. Berg, J. L. Tymoczko, and L. Stryer, Biochemistry, 5th ed., New York: W H Freeman, 2002. [7] National Diagnostics. “The Mechanical and Electrical Dynamics of Gel Electrophoresis” Electrophoresis System Dynamics http://www.nationaldiagnostics.com/article_info.php/tPath/1_2/articles_id/4 [8] S. Harden. (2011, February 2) DIY ECG Machine on the Cheap. [Online]. Available: http://www.swharden.com/blog/category/ [9] S. Lee and J. Kruse, "Bipotential Electrode Sensors in ECG/EEG/EMG Systems," Analog Devices, 2008. [10] (2011, February 25) Properties, Manufacture and Application of Seaweed Polysaccharides Agar, Carrageenan and Algin. [Online]. Available: http://www.fao.org/docrep/field/003/AB730E/AB730E03.htm [11] (2011, February 2) Formulations and Protocols for Electrophoresis and Western Blotting. [Online]. Available: http://tools.invitrogen.com/content/sfs/appendix/Elec_Blotting/Electrophoresis%20and%20 Western%20Blotting%20Protocol.pdf