electronic circuits with applications to bioengineering.pdf
TRANSCRIPT
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 EE-
101 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
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.
Study and Understand Electrical
Engineering Concepts
Find Biological Applications
Electrophoresis Gel Application
Used to model a resistor
Lipid Bilayer
Demonstrates how a lipid bilayer can act
as a capacitor
Electrocardiogram (EKG)
Used to understand the characteristics of
an operational amplifier
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 hands-
on 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 R1 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 Vin/(R1 + R2) and the current through the
second resistor is Vout/R2. If there is no load on the output the currents are the same: Vin/(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 time-
varying 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-transient-
response.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 Vc, 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 VC 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 VC 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 VC 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 10
6cm
2. 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 non-
inverting 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 op-
amp 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 op-
amps 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 op-
amp, 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. Under what assumptions is the ideal op amp technique valid?
2. Why input and output impedance of an op amp circuit are important for DC?
3. How do you measure input and output of impedance?
4. Where do you place EKG electrodes on your arm?
5. Calculate Vout of a non-inverting amplifier. Given that R1 = 1k, R2 = 100k, Vin
= 1mV.
III. 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 RL. Let the value
of RL be 10k. Do not short circuit the output. Can you justify your result for Zout
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 1Vpp. Is V2
what you expected?
Budget
Items Quantity Cost
EKG Electrodes 4 $5
EE-101 Lab Kit 1 $43
Electrophoresis Gel Kit 1 $100
PowerEase500 Power Supply 1 $400
Total $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
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http://www.cisl.columbia.edu/kinget_group/student_projects/ECG%20Report/E6001%20ECG%
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http://www.nationaldiagnostics.com/article_info.php/tPath/1_2/articles_id/4
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http://www.swharden.com/blog/category/
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