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+Throughout the semester, students will be explore classic physical systems as a tool to increase their overall laboratory skills (i.e., experimental design, data analysis, collaboration, and scientific communication). In this course, students will be guided and supported through their development of these practices by emphasizing\\
+  -How to carry out experiments effectively by collecting data while attempting to minimize uncertainty.\\
+  -How to connect the results obtained experimentally with theoretical models in lecture while recognizing the limitations of each.\\
+  -How to thoroughly document the experimental design, data collection and analysis, the results, and the discussion/conclusions.\\
+  -How to report and communicate findings obtained in the laboratory.
-Purpose
+[[E&M – Bio-Electrical Measurements]]
-The human body is like a machine, using electrical pulses to do everything from causing a heart to
-beat to flexing a muscle. These actions create an electrical signal that can be measured. However,
-these signals are quite small compared to the larger background noise, which makes measuring
-them difficult. Therefore, specialized equipment and signal-‐processing techniques are needed to
-observe the electrical signals within our body.
-In this lab, your group will work to observe and measure signals from your heart and muscle on a
-laboratory oscilloscope. In order to be successful your group will need to develop an understanding
-of how periodic waveforms add & subtract as well as amplify & attenuate – this understanding
-forms the foundation for measuring the tiny signal that is your heartbeat. You will also need to
-familiarize yourself with the necessary electronics – an oscilloscope and differential amplifier.
-Theory
-The heartbeat is a signal that is periodic in time – that is to say the electrical pulse that causes the
-heart to beat repeats itself after a time delay. The frequency ( f ) of a signal (how often the signal
-repeats in a given second) can be related to the period ( T ) of that same signal (how long in time
-between two signals) by
-푓=
-!
-!^
-where the period is measured in seconds ( s ) and the frequency is measured in Hertz ( Hz ), or
-!
-!. ^
-Electrical signals like those measured by an EKG, and indeed any such signal, are termed “waves”
-and interact in predictable ways. Two signals (or waves) can interact resulting in the two forming
-one combined signal. The underlying mathematics that describes this interaction is not the main
-point of this lab, but rather the conceptual understanding that two waves can be added or
-subtracted to form a final wave is what is important. As such it will be prudent of you to do a bit of
-research on how waves can be added and subtracted from this conceptual perspective.
-Warning: Whenever using electricity and living bodies in the same experiment, it is important to
-consider safety. The pain threshold is typically accepted to be 1 mA of current, or about what you
-would get from a 120 V outlet with dry skin. In other words, unless you are sticking your finger in the
-outlets, you are very unlikely to hurt yourself in this lab or any other lab in this course. (If you would
-like to see for yourself, you can calculate the limitations using Ohm’s Law.) However, it is important to
-keep these aspects in mind and always be safe around electrical equipment.
-Research Concepts
-In order observe meaningful electrical signals from a body it will be useful to remind yourself or
-develop an understanding of:
-AC signals and DC signals
-Signal-‐to-‐noise
-What an oscilloscope measures
-How waves add and subtract (“interfere” https://goo.gl/FK4aH5 -‐ Primarily the
-Mechanism section, before “Between two plane waves”) and the principle of superposition
-(http://goo.gl/sziJxj -‐ the math is a bit unnecessary. Instead focus on 1st, 2nd, and 4th
-animations)
-In addition, the two connectors in Figure 1 will be very useful to
-you through this experiment. On the left is a splitter, sometimes
-referred to here as a “T-‐splitter.” It will take one signal and split
-it down two lines, or take two signals and combine them,
-depending on how it’s connected. On the right is a BNC-‐to-‐
-Banana-‐Plug connector, or “Y-‐cable.” It makes the connection
-between two different types of cables, and is necessary to
-connect the function generator to the oscilloscope.
-Measuring Heartbeats and Muscles
-(Note: the following primarily discusses observing a heartbeat, but the steps to measure muscle
-signatures are mostly the same. If you desire to measure muscles, instead of the heartbeat or in
-addition to, let your instructors know.)
-Part 1 – Signals in a human body
-In its simplest form, attaching an electrode to each side of the heart and measuring the signal
-between them is enough to observe a heartbeat on the oscilloscope. To attempt this measurement,
-turn the oscilloscope on and into its channel A plug in the BNC-‐to-‐Banana-‐Plug connector. The two
-ends of the banana plug can act as your electrodes, with the signal being measured on the scope.
-Have one member in your group hold the black plug in one hand and red plug in the other. The
-display will show the signal picked up from the human body.
-Can you observe a heartbeat in this signal? Try different positions and hand grips.
-What happens if another group member touches you while holding these electrodes?
-What is the displayed signal measuring?
-In theory, this should have been enough to measure a heartbeat. However, the world is full of
-electrical signals and our bodies are wonderful antennae. What you are observing is called noise,
-but your heartbeat is, in fact, in that signal. To observe it, we will have to reduce the noise and
-amplify the signal. This will require an understanding of signal processing, oscilloscopes, and
-differential amplifiers. We will start with the ‘scope.
-Figure 1
-Part 2 – The Oscilloscope
-Oscilloscopes are widely used tools in not only physics but also in science more generally (and in a
-slightly modified form, in medicine, too). They are a great way to measure signals that change in
-time and are especially useful for periodic measurements. Input a signal from the signal generator
-into the oscilloscope, using the connector from Part 1 and a BNC cable to attach the generator to
-the scope. On the signal generator, you should connect the banana plugs to the “Low Ω ” and “GND”
-ports. Play with the scope and signal generator to familiarize yourself with various functions and
-capabilities of the scope. A 100 Hz signal is a good starting point, but you should play with several
-signals noting any differences or similarities you find.
-How do you read the grid on the display? Using the oscilloscope, can you make the wave
-stretch out/compress? Grow/shrink? Make sure you sketch the signal and record the
-dials/buttons you press and their functionality in your notebook. (Remember to do this
-throughout the lab, even though it won’t always be explicitly stated.)
-Using the function generator, can you make the wave stretch out/compress? Grow/shrink?
-What does the green “Auto-‐Set” button on the oscilloscope do?
-Using the cursors, measure the period and amplitude of a
-sine wave.
-How does this relate to the signal you are putting into
-the scope?
-How does this relate to the values you can measure
-on the display/grid?
-Part 3a – Signal Analysis – Attenuation
-Now that your group has familiarized itself with the function
-generator and oscilloscope, you will add a new element to
-the circuit – an attenuator. Certain circuit elements can
-change the amplitude of a waveform. Called “gain,” this
-change can be an increase (amplification) or a decrease
-(attenuation) in the size of the signal. To measure the size of
-this change, you will put the same signal in the oscilloscope’s
-Channel A as Channel B. However, one of these signals will
-undergo attenuation. To do this, connect the function
-generator to the oscilloscope according to Figure 2. In this
-arrangement, the signal out of the generator is split. One end
-is sent to Channel A while the other goes into an attenuator
-(the blue cylinder) that connects to Channel B. By plotting both signals on the scope, you can
-determine the effect of the attenuator.
-What do you notice on the oscilloscope screen now? (Make sure to sketch and note any
-setting changes on the scope.) If you don’t see two waves, make sure Channel B is being
-shown and check the amplitude of the wave/voltage scale on the oscilloscope.
-By what factor, or gain, did the signal change? (Note: when talking about gain, a positive
-value means the signal got larger while a negative value means the signal got smaller.)
-Figure 2
-The equipment used to measure biological signals is sensitive and is limited to 3 V input. To ensure
-our function generators don’t put out too much, we will use attenuators. All connections for the rest
-of the lab will go through attenuation, and you will be reminded about this with each description.
-Part 3b – Signal Analysis – Addition and Subtraction: Single Signal
-For this part, you will want to make sure the exact same signal goes
-into channels A and B. Remember, we are attenuating every signal for
-the rest of the lab, so we will attenuate then split the signal, sending it
-to Channel A and B. (See the image.) You may want to hit Auto-‐Set to
-make sure both signals appear, and change the time scale so you see
-just one or two periods of the signal.
-In order to add and subtract signals with the oscilloscope, will need to
-turn the display from digital to analog (press the “Digital Memory” to
-turn the digital display off). The Add/Invert button has 4 stages in
-analog mode.
-What does each mode do?
-Can you get the signals to add together? What does this look
-like? (Try to sketch this out in your notebook.)
-Can you get the signals to subtract? What does this look like?
-(Again, sketch this out.)
-How does what you observe fit with the research you did on
-adding/subtracting signals and superposition?
-Part 3c – Signal Analysis – Addition and Subtraction in the Line
-You just observed how signals can be combined in the oscilloscope, but they can be combined
-before entering the scope as well. In fact, the cables and connectors are usually where noise is
-picked up in instrumentation and measurement, something that would mask your heartbeat signal.
-For this part, you will use two function generators.
-To observe the combination in the cables, send a signal out of each function generator that is very
-different from the other (100 Hz and 1000 Hz work well). Don’t forget to attenuate each signal. Plug
-a splitter directly into Channel A and connect each generator to the oscilloscope. You can also go
-back to digital memory/hit Auto-‐Set for a clearer image.
-What does this combined signal look like?
-Can you measure the period/frequency of both periodic waves of the combined signal?
-(Turning the 1000 Hz amplitude down and 100 Hz up may make this clearer, but you are
-encouraged to play with various settings.) How do these periods/frequencies compare with
-your input frequencies?
-Thinking back to the signal you observed in Part 1 (when you held the ends of the banana
-plugs), what do you notice about this signal that is similar? What is different?
-Figure 3
-(Optional) This is a signal of two very distinctly different waveforms, but there is a very interesting
-phenomenon that occurs when two similar waves interfere. If you’re interested in this, mention it
-to your instructor. They will be able to help you manage this with your desire to observe bio-‐
-electrical signals. For the sake of time, you can feel free to skip this section and come back to it after
-you observe your heartbeat.
-In this same set up, change the 1000 Hz signal to 101 Hz. This may look a bit weird at first, but play
-with the time domain a little.
-What do you observe?
-What is the period/frequency of the weird signal?
-How does this relate to the frequencies you are putting into the system?
-Part 3d – Getting rid of unwanted signals
-It is hard to control every bit of noise you measure through
-controlling your instrumentation (wires, connectors, etc). But
-if you can remove or reduce it, it is possible to observe small
-measurements within it. In this part, you will add two signals
-within one line, and subtract the noise signal from it, leaving
-you with just the important signal.
-You can leave the 1000 Hz signal as is, but will need to split the
-Hz signal. The image to the right depicts a signal properly
-split and attenuated. One end of the split will be plugged into
-Channel B while the other will get added to the 1000 Hz noise
-in Channel A.
-One channel should look like a normal signal, while the other
-looks like it did in Part 3c . It would be helpful to change the
-signal scale so that the wave amplitudes align. (The reason
-they don’t has to do with input impedance . If may take too
-much time to discuss this here, but can be revisited after your
-group measures bio-‐electrical signals.) Decrease the 1000 Hz
-amplitude/increase the 100 Hz amplitude until you can barely see the 1000 Hz signal.
-Can you measure the amplitude of the small wobble buried in the larger signal? How did
-you do it?
-This small signal is a representation of a common measurement issue, one that was mentioned
-earlier: signal-‐to-‐noise. When the 1000 Hz signal is of use, but it is buried in the 100 Hz wave, we
-can’t effectively measure it. In this simulation, your heartbeat is the small wobble amongst the
-larger one. If you remember from Part 1 , the heartbeat is so much smaller than the background that
-you couldn’t make it out at all from the noise.
-Using techniques you learned earlier (Review Part 3b), can you remove the 100 Hz noise to
-obtain only the 1000 Hz signal?
-Figure 4
-Questions to Think About
-What is a typical frequency of a heartbeat? What does this mean in terms of its period?
-What is signal-‐to-‐noise mean? Why does it matter?
-o If you’re listening to a radio station, but have some static, can you get the signal
-better by turn the volume up? Why or why not?
-Part 4 – The Differential Amplifier
-In this experiment, a differential amplifier does the same type of signal cancellation as what you observed in
-Part 3d . A differential amplifier takes two signals and subtracts them from each other, outputting the
-differential between them. The resulting signal is often very small, so the output signal is also amplified. Using
-this device, you can cancel the noise and observe your heartbeat. You will revisit this later.
-The differential amplifier has internal
-rechargeable batteries that will need to
-be charged. This can be done in a couple
-minutes using the charger.
-In this part, you will measure the gain of
-the amplifier. Once again, you will need
-to attenuate a signal from a signal
-generator (~100 Hz) and split it – one
-end will go into Channel A of the
-oscilloscope, the other will go through
-the differential amplifier first before
-going into Channel B. You will need a Y-‐
-Splitter to make the necessary
-connections, which are pictured here.
-In the image, one banana plug is connected from the black port of the differential amplifier to the
-black port of the splitter; one of the red ports on the amplifier also connects to the black port on the
-splitter while the other connects to the red port. The output of the amplifier connects to Channel B
-of the ‘scope.
-Because this is an AC signal, make sure the amp is switched to AC. The “Low” and “High” refer to the
-gain, which you will measure on the oscilloscope between Channels A and B. If the signal from the
-amplifier ever looks weird (this is called clipping), you probably need to turn the amplitude down
-on the generator.
-What is the value of the low gain? What is the value of the high gain?
-Does it matter which red output on the amplifier goes to the red output of the splitter? Why
-or why not? Test your hypothesis and note any changes.
-Measure the gain, low and high, for a few frequencies. Any will do, but try to have one of them low
-(~10 Hz) and one of them high (~1000 Hz).
-Does the gain depend on frequency?
-Part 5 – Heartbeat
-You should now be able to measure your heartbeat. To do so, you will need to attach 3 electrodes to
-your body: one just above your ankle, and one on each arm (the signal will be clearest the closer
-Figure 5
-you attach the electrode to your shoulder). If you wish to, you can wipe the area with an alcohol
-swap first and ensure clean skin for a good contact.
-The electrode on your ankle will be attached to the black port on the amplifier. Each arm electrode
-will attach to one of the red ports. To cancel even more noise, twist the wires together between
-your arms and the amplifier. At this point, for the clearest signal, the amplifier should be pulled as
-far away from the oscilloscope as possible. In addition, the person being measured should sit still,
-away from the equipment, and avoid touching metal.
-The output of the amplifier, on low gain, should be plugged into Channel A. Can you observe a
-heartbeat? If you’re having trouble, consider the average time between heartbeats and adjust the
-time scale on the oscilloscope accordingly.
-Why does this configuration of electrodes cancel the noise your body picks up? It may help
-to sketch the electrical path from each shoulder electrode to the common ground on the
-ankle.
-What is the size of the heartbeat?
-What is the frequency?
-Each group member can see their own heartbeat, if they wish. Disconnect from the amplifier when
-you’re finished.