Experiment 5 – Online version Bridges, Potentiometers, and ......Note: For Experiment 5 and Project 2 will work in with your full team of ~6 students. Submit a single team report

ENGR-2300 ELECTRONIC INSTRUMENTATION Exp. 5 Online version

J. Braunstein, K.A. Connor, P. Schoch Rensselaer Polytechnic Institute, Troy, New York, USA

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Experiment 5 – Online version Bridges, Potentiometers, and Harmonic Oscillation

Purpose: In the following exercises, you will learn what a bridge is and how it can be used to measure small changes in resistance. You will also learn how to balance a bridge using a potentiometer. Then you will use the bridge to measure small resistances from a strain gauge mounted to an oscillating cantilever beam. You will use the oscillation frequency and your knowledge of cantilever beams to determine material constants for the beam (mass and Young’s modulus) and through tables, the material of which the beam is made. Finally, we will extend the theory of oscillation to an electrical system, an oscillating circuit. Background: Before doing this experiment, students should be able to • Analyze simple circuits consisting of combinations of resistors, inductors, capacitors and op-amps. • Do a transient (time dependent) simulation of circuits using Capture/PSpice • Do an AC sweep (frequency dependent) simulation of circuits using Capture/Pspice, determining both the

magnitude and the phase of input and output voltages. • Determine the general complex transfer function for circuits. • Build simple circuits consisting of combinations of resistors, inductors, capacitors, and op-amps on protoboards

and measure input and output voltages vs. time. • Perform basic mathematical operations on electrical circuits using op-amps. • Review the background for the previous experiments. Learning Outcomes: Students will be able to • Use a combination of strain gauges and resistors configured in a bridge circuit to determine the position of a

cantilever beam. • Use a difference op-amp configuration to amplify the difference signal from the fixed and variable nodes in a

strain gauge Wheatstone bridge. • Apply harmonic oscillator analysis to both a mechanical and an electrical system. Equipment Required: • Analog Discovery/M2k (with Waveforms/Scopy Software) • Oscilloscope (Analog Discovery/M2k) • Function Generator (Analog Discovery/M2k) • Parts Kit Helpful links for this experiment can be found on the links page for this course. Note: For Experiment 5 and Project 2 will work in with your full team of ~6 students. Submit a single team report for Exp 5 and a single team report for Project 2. Every team member must do certain parts as listed below but you need to report results from only one team member. You should be looking ahead to Project 2 and assign member responsibilities for both Exp 5 and Project 2. Pre-Lab Required Reading: Before beginning the lab, at least one team member must read over and be generally acquainted with this document and the other required reading materials listed under Experiment 5 on the EILinks page. Hand-Drawn Circuit Diagrams: Before beginning the lab, hand-drawn circuit diagrams must be prepared for all circuits that are physically built and characterized using your Analog Discovery/M2k board.

http://www.ecse.rpi.edu/courses/F16/ENGR-2300/EILinks.html#Exp5



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Part A – Bridge Circuits - All team members do parts A1, A2 and A4, but only report the results from one member. A3 and A5 can be done by one member but all members are responsible for the material. Background Bridges and Voltage Dividers: In Experiment 1, we looked at one of the simplest useful circuits – the voltage divider. In many simple applications of electronics, we have only a small number of standard voltages in whatever circuits we are building. When we use a 9V battery or V+ on the Analog Discovery/M2k as our source, we have only one voltage level available, unless we use a voltage divider to get smaller voltages. We can also use a divider, to measure resistance, if we have some device with an unknown resistance. For example, if we connect an unknown resistor in series with a known resistor, then the voltage across the unknown resistor can tell us the value of the resistance. An even better measurement can be done by combining two voltage dividers in a configuration like the one shown in figure A-1, which you should recognize as being made from two dividers. Note that if R1 = R2 = R3 = R4, the voltages at the two points marked Vleft and Vright will be equal to half of the source voltage. Thus, their difference should be zero. Whenever the voltage difference dV = Vleft – Vright across a bridge output is zero, we say that the bridge is balanced. If one of the resistors (e.g. R4) is slightly larger or slightly smaller than the other three resistors, the output voltage dV will not be zero and becomes, as we shall see, a very sensitive measure of the difference in resistance.

Figure A-1.

The following equations apply to the bridge circuit:

rightleftrightleft VVdVVRR

RVVRR

RV −=+

=+

= 143

4121

2

When all four resistors are equal to 350Ω, the bridge is balanced:

021

211

3503503501

350350350

=−=−=+

=+

=VVVVdVVVVV rightleftrightleft

Experiment Modeling a bridge in PSpice In this part, we will set up a bridge in PSpice and look at the effect of a small change in one of the resistors on the difference across the bridge. • A.1 Look at the behavior of a balanced bridge circuit.

o Set up the circuit shown in Figure A-1. o Use a 9V amplitude, 1kHz frequency and no DC offset. o Place voltage markers at Vleft and Vright, or use the “voltage difference markers.” Then run a transient

analysis. (You have done enough transients now to be able to find a reasonable “run to time” and “step size.”)

V1

FREQ = 1kVAMPL = 9VOFF = 0

R1350ohms

R2350ohms

R3350ohms

R4350ohms

0

Vlef t Vright V-

V+



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o Add a Trace of the difference between the two voltages, (Vleft - Vright). (It will already be there if you used the “voltage difference markers.”)

o Is the difference zero? • A.2 Look at the behavior of an unbalanced bridge circuit.

o Now, change R4 to be equal to 360Ω, about a 3% change in R. o Do the analysis again and add the trace of the difference between the two voltages. o What is the amplitude of the difference voltage as a percentage of the source voltage? o All team members run the simulation but choose one to label their plot, copy it and include it with your

report. • A.3 Analyze this circuit by hand

o Use the voltage divider formula to find the voltages at the two points and their difference. Make sure that your answer agrees with the PSpice simulation.

o Assume that R1 = R2 = R3 are known resistors equal to R, and that R4 is unknown. Derive a formula for R4 in terms of R , the source voltage V1, and the voltage difference between the two divider voltages (dV=Vleft-Vright). [Hint: Substitute voltage divider expressions in for Vleft and Vright and solve for R4. This can be an open discussion but each team member should confirm the result.]

• A.4 Parameter sweep – this is a very useful PSpice tool, all team members run this simulation.

o In PSpice, it is possible to run simulations for several values of a component. Above you ran two separate simulations, one with R4=350Ω and one with R4=360Ω. Now you will do one run with 11 values for R4. This is called a parameter sweep.

o Change the resistance value of R4 from 360Ω to a variable name set within the curly brackets Rvar as shown in the figure below. You can make the name anything you want, but use something that reminds us what you are doing. The resistance value is now a variable.

o Next we have to tell PSpice that we are using a parameter. To do this, we go to the parts list and select PARAM, which we will find in a library called Special. Place this item in an uncluttered spot on your schematic.

o The PARAMETERS: “part” is a list of variables. You can now create and assign a value to your variable Rvar using the following procedure: • Double click on the word PARAMETERS: to display the spreadsheet • Click on New Property. • In the Property name textbox, enter your chosen name ( Rvar without the curly brackets). • Enter 1k for the default value. This value is only used to set a dc operating point, so the actual value

doesn’t matter. • Select the new column and then click Display. • In the Display Format window select Name and Value and then click OK. • Click Apply to update all the changes to the PARAM part. • Close the Parts spreadsheet. • When you have finished, you will see the parameter and its default value listed under

PARAMETERS:. • Now your circuit should look like the figure below. When you have finished, you will see the

parameter and its default value listed under Parameters. (Refer to Figure A-2 below.)

V1

FREQ = 1kVAMPL = 9VOFF = 0

R1300ohms

R2300ohms

R3300ohms

R4Rv ar

0

Vlef t Vright

PARAMETERS:Rv ar = 1k

V-

V+

350 350

350



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Figure A-2.

o Next we will set up the analysis (See Figure A-3 on the following page). Create a simulation. • Select Time Domain (Transient). • Check Parametric Sweep. • Check the Global parameter box. • Enter the variable name in the Parameter name box. • Pick a linear sweep, start value of 340, steps of 2 and end value of 360.

Figure A-3.

o Perform the simulation. • You will have all 11 simulations listed in the Probe window. • Use the All option. • Plot Vleft - Vright. • Note: if you right click on a trace, click on information, you can tell which value of R4 is plotted. • One team member copies this page and includes it in your report.

o Delete all traces from the plot window. Plot just Vright, for all values of R4.

• One team member includes this plot in your report • Comment on if it is easier to see the effect of a change in R4 using the bridge (Vleft - Vright)

compared to just using one side (Vright.)

• A.5 Sensitivity calculation – This should be an open discussion but only needs to be completed by one member. o Use the results from the plot to determine the sensitivity of the bridge circuit to changes in R4. o What is the change in (Vleft-Vright) divided by the change in R4?

Summary A bridge allows you to compare two voltages and to detect relatively small changes in a component value. We will use it in part B to observe small voltage differences caused by very small changes in the resistance of a strain gauge.



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Part B – Thermistors Background

Thermistor: quoting from Wikipedia: A thermistor is a type of resistor whose resistance is dependent on temperature, more so than in standard resistors. The word is a combination of thermal and resistor. Thermistors are widely used as inrush current limiters, temperature sensors (negative temperature coefficient or NTC type typically), self-resetting overcurrent protectors, and self-regulating heating elements (positive temperature coefficient or PTC type typically).

Thermistors are of two opposite fundamental types: • With NTC thermistors, resistance decreases as temperature rises. An

NTC is commonly used as a temperature sensor, or in series with a circuit as an inrush current limiter.

• With PTC thermistors, resistance increases as temperature rises. PTC thermistors are commonly installed in series with a circuit, and used to protect against overcurrent conditions, as resettable fuses.

The kit of parts includes a thermistor, see figure B-1. This is a TDK B57164K103J (R/T number 2904 on page 9 of the data sheets.) It has a nominal resistance of 10kΩ at 25°C. The data sheet shows the relative change in R as the temperature is changed. We will configure a bridge circuit with gain to measure small changes in the resistance of the thermistor due to small changes in the temperature of the thermistor. Experiment: B1: All students build the circuit but only report one result. • Build this circuit. 1+, 1-, 2+ and 2- are the inputs to channel 1 and 2 of the

Analog Discovery/M2k. Be sure to set and enable the +5V and -5V supplies.

o Let it sit at room temperature and record the voltages on both channel 1 and 2. These are the dc voltages, or average values.

o Now press and hold your fingers on the thermistor, wait of the signal to reach a steady state and record the voltages.

o Now change the -5V supply to be -4V and repeat the voltage measurements from both channels both for the room temperature thermistor and the one warmed by your fingers.

o Save these measurements from one team member for the report. When the power supplies are well matched, +5 and -5, the signals on both channels should look much the same. But if there is a variation on one supply you should now see a difference between the signals. Question: Is it reasonable to state that the signal on channel 2 is sensitive to changes in the power supply voltages while the signal on channel 1 is not? Channel 2 is simply a voltage divider and can be used to determine the value of the resistance of the thermistor but as shown above it will show false changes if there is noise on the power supply signal. While Channel 1 is the difference between a fixed divider and the divider with the thermistor. Power supply voltage changes effect both sides at about the same level and taking the difference will reduce the circuit sensitivity to that noise source. This is one reason to use a bridge circuit when using a thermistor to measure temperature. • Use the results and from channel 1 to calculate the resistance of the thermistor at both room temperature and at

finger temperature. • Use the thermistor data sheet and calculate the temperature of the thermistor for room temperature and warmed.

TDK B57164K103J (R/T number 2904 on page 9 of the data sheets.) Remember that data sheet is the change in resistance normalize by the thermistor resistance, 10k in this case.

Figure B-1

Thermistor10k

0

1-

R210k

-5V

1+ and 2+

R310k

+5V

R110k

2-

Figure B-2

https://en.wikipedia.org/wiki/Thermistor

https://en.wikipedia.org/wiki/Resistor

https://en.wikipedia.org/wiki/Electrical_resistance

https://en.wikipedia.org/wiki/Temperature

https://en.wikipedia.org/wiki/Heat

https://en.wikipedia.org/wiki/Resistor

https://en.wikipedia.org/wiki/Sensors

https://en.wikipedia.org/wiki/Resettable_fuse

https://en.wikipedia.org/wiki/Heating_element

https://eu.mouser.com/datasheet/2/400/NTC_Leaded_disks_K164-1317145.pdf




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Experiment: B2: A single team member may complete this part, but all students are responsible for the material. A differential op amp circuit can be used to amplify the signal from the thermistor bridge to better measure small changes in temperature. The differential op amp circuit was discussed in section D of Experiment 4.

Figure B-3

• Build this circuit. It uses the circuit already built for part B1. Note that channel 1 is still connect directly to the

bridge. This circuit uses all 5 of the 10k resistors provided in the kit of parts, hopefully none are missing. o Measure the voltage on channel 1 and channel 2 after the thermistor has had time to be at room

temperature. o Hold the thermistor to raise it to finger temperature and again measure the voltages. o Save these for the report.

Questions: • What is the mathematical relationship of the voltage on channel 2 to the voltage on channel 1? You may refer

back to Experiment 4 or use Crip sheet for Quiz 2. • Using the relationship for the difference op amp calculate the finger warm resistance of the thermistor and from

that estimate the warm temperature of the thermistor. • In a few words discuss why this circuit might be preferred if the goal is to be able to measure small temperature

changes that are close to room temperature. • In a few words discuss when this circuit will fail to provide useful information, referring to just temperature

effects. The thermistor functions over a wide range of temperatures. If you try other ways to heat or cool the sensor, please add come comments. But remember the protoboard, op amp, and certainly the Analog Discovery or M2k don’t function over as broad a temperature range.

Summary Bridge circuits have multiple uses, here it is used to measure small changes in voltage that correspond to small changes in resistance values. A more sophisticated form of this bridge circuit, called an impedance meter or RLC meter, can also be used to measure capacitance and inductance.

U1

OP-27/AD

+3

-2

V+7

V-4

OUT6

N1

1

N2

8

Ra21kR2f ixed10k

-5V

R1f ixed10k

1+

02-

Rb110k

Thermistor10k

+5V

Ra1

1k

R3f ixed10k

Rb210k

Vout 2+1-



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Part C – Cantilevered beam Background: To prepare for Project 2 you will create a cantilevered beam set up. Below are pictures of the one used for in-person experiments and 2 beams set up in the Schoch household.

Figure C-1

The beam for in-person classes, Fig. C-1, has strain gauges on the beam which won’t be available for on-line teams. Figure C-2 shows 2 possible beam setups, these are just suggestions, creativity is encouraged. In both of these cases the beam can oscillate in the vertical direction, that isn’t a requirement for your beam. For both in-person and online teams, the ADXL327 3-axis accelerometer in the kit of parts will be mounted on the beam and connected to the instrumentation board. In project 2 you will use this to measure the natural frequency of the beam oscillation with different amount of added weight on the beam. Those measurements will allow you to estimate the effective mass and Young’s Modulus of your beam. Experiment C1 – all team members All team members find a beam that can be used for Project 2. Professor Braunstein ran this in the summer of 2020 and I recommend you view his video. The Cantilever Beam In your house, identify at item that makes an effective cantilever beam. The video above shows a metal kitchen spatula. The picture above shows a metal framing square and a wood board. Your household beam should oscillate with a damped sinusoid. Metal is the best choice, though, wood may have similar characteristics. Plastic is unlikely to have the same properties. Experiment C2 – all team members All team member find a way to mount her or his beam with a proto board and an instrumentation board. It must be set so that if the tip is displaced and released that it will oscillate for a few or more cycles. You need to test it several times to ensure it doesn’t easily become loose. This must include a proto board connected to your beam. You do not need to mount the accelerometer chip or connect the instrumentation board, that will be coming next. Take a still picture of your setup; we don’t need a lot of videos. Include a picture of each team member’s setup in the experiment report. You will choose 1 or maybe 2 beams from the entire team to complete both Experiment 5 and Project 2. Experiment C3 – one team member for the entire team Choose one of the setups for this part. Note: Project 2 will require a working setup. That can be the same as the one used here or your team can choose to use different setup for the project. The team member(s) instrumenting the beam will be doing a significant amount of work. Other team members should take on other tasks either for this experiment of for the write up for project 2.

Figure C-2

https://youtu.be/Klx5lHYsGPk



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The Circuit – this is one team member for the beam chosen to complete Experiment 5. The following circuit can be used to create a signal proportional to the acceleration of the beam using the ADXL327 accelerometer in the parts kit. Data sheet for ADXL327. Important note: The ADXL327 needs a 3V power supply, not 5V. 5V may destroy the chip and you only have one. To get 3V: Analog Discovery: set Wavegen 1 to DC waveform and offset of 3V. Use the W1 wire, yellow, to supply Vs. M2k board: Signal Generator, channel 1, set to constant with a 3V value. Use the W1 wire, yellow to supply Vs. Make sure this is set correctly before enabling the Wavegen 1 (Analog Discovery) or the Signal Generator (M2k).

Figure C-3

The accelerometer is surface mounted and, thus, cannot be plugged into a protoboard. Therefore, we have mounted the chip on what is called a surfboard. The pin numbering is given in Figure 3 and a picture of the chip is given in Figure C-4. In the picture (and on the chip), you can see pins 1 and 16 labelled, with the remaining pins labelled consistently with standard chip labelling. For this laboratory, you will are only required to use one of the acceleration directions (the z-direction is likely easiest), though, you can investigate the other directions as well. CDC , Cx , CY , and Cz are already mounted on the surfboard. You don’t need to add any capacitors.

Connect to Vs (Pin 15) to the yellow wire, W1

Connect to COM (Pin 3) to a black wire, GND

Zout is pin 8, vertical accel. See data sheet if you need to use X or Y.

Figure C-4 Figure C-5

https://www.analog.com/media/en/technical-documentation/data-sheets/ADXL327.pdf



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You only need 3 connections between the Analog Discovery/M2k and the accelerometer, +VS, Ground, and ZOUT. These are pins 15, 3 and 8 respectively. Again remember that +VS is connected to W1, the yellow wire of the waveform generator/signal generator. Wires from these pins should be as loose as possible so they don’t damp the oscillator. This will reduce the effects the wires have on beam motion. The output of the accelerometer is sufficient to be recorded directly with Analog Discovery/M2k. Be very careful with the accelerometer. It is mechanically robust, but the surfboard is not. Also it is electrically sensitive. If you apply the wrong voltages, you may damage it. (Circuit components cannot be repaired). Please double check your settings before applying power. To verify that your circuit is working correctly, you can manually move/shake the protoboard. Set your scope to a fairly large time scale. Think of how fast you can manually move the board up and down to estimate the frequency, invert that value to get a period and set your time scale accordingly.

Important Note: This experiment does not work unless all your measurements are taken when the ‘effective mass’ at the end of the beam is the same. You may have seen in other courses that adding additional mass to the end of a cantilever beam slows down the frequency. This means that you need to have the accelerometer mounted to the beam when you take all your measurements or else your frequencies (and data) will be off. The wires attached to the accelerometer circuit also contribute to the effective mass at the end of the beam. Make sure your wires can move freely to minimize their influence on the data. Build this circuit, pluck the beam, and record a voltage trace. Save a picture of the signal and include it in the report. Keep this together as it is used for Project 2. Part D – Oscillating Circuits Background Energy storage in inductors and capacitors: In passive electrical systems, there are three kinds of circuit elements: resistors, capacitors and inductors. Resistors turn electrical energy into heat. When a current I flows through a resistor, there will be a voltage drop V across the resistor. The power dissipated by the resistor is equal to the product of I times V. Since resistors produce heat, it should be no surprise that they play the same role as friction in a mechanical system. The ideal pendulum will oscillate forever … a real pendulum will oscillate until all its stored energy is converted to heat through friction. Thus, if we wish to create a circuit analogous to the ideal harmonic oscillator, it can have no resistors in it. Rather, we will combine only inductors and capacitors. A typical inductor consists of a coil of wire. If we pass a current through the coil, a magnetic field will be created. Many of us have made simple electromagnets at some time in our lives by wrapping wire around some magnetic material like a nail. When a battery is connected to the wire, it is possible to attract small pieces of iron to the nail. The field created by the coil, the magnetic field, can do work and thus contains energy. The energy stored in an inductor is given by the expression

WM = (1/2) L I2 where we have used the subscript M to indicate that the energy is stored in the magnetic field and L is the inductance in units of Henries. Joseph Henry was honored by using his name for this unit because of his early work in developing practical electromagnets. He began his work here in New York’s capital district when he was teaching at the Albany Academy. There is a statue of this great scientist outside the original location of the Academy across the street from the Albany City Hall. Henry was a contemporary of Amos Eaton, the intellectual force behind the founding of RPI. He eventually left Albany for Princeton and the Smithsonian. A typical capacitor consists of two metal plates of large area separated by some insulating material such as Teflon or some other plastic. When a voltage source is connected to the plates, charge flows from the source to the plates with positive charge deposited on the plate with the highest voltage and negative charge deposited on the plate with the lowest voltage. Since these charges are opposite in sign and since unlike charges attract one another, there is a force between the two plates. Again, the existence of this force tells us that we have to do work to charge up the plates and that there is energy stored. In this case, the energy is stored in the electric field created by the charges. The energy stored by a capacitor is given by the expression



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WE = (1/2) C V2

where we have used the subscript E to indicate that the energy is stored in the electric field and C is the capacitance in units of Farads. Michael Faraday also worked on electromagnets and, being British, gained much more fame for his work, since America was a scientific backwater at the time. Henry showed him how to make better magnets, but Faraday’s work was much more far reaching. Henry also showed Morse how to build a telegraph! Aside: It is somewhat interesting to note that neither Henries nor Farads turns out to be much of a common practical unit. One Henry is a huge inductor, rarely seen in practice. One Farad is also rare, now occasionally seen in highly filtered power supplies for computers. We will need to use the prefixes milli-, micro-, nano-, pico-, etc. a lot when dealing with these components. We also do not see one Ohm all that much, but require the other kind of prefixes (kilo-, mega-, etc.). Conservation of Energy in a Harmonic Circuit: There are many important lessons we can learn from the harmonic oscillator, but perhaps one of the most useful is the value of conservation laws. It is fair to say that the most powerful problem solving technique is to first decide which conservation laws hold. Once the conservation laws are identified, they can be used to determine a great deal of information about any system.

Figure C-1.

Consider the simplest possible configuration of a single capacitor and a single inductor connected as shown in Figure C-1. Note that, since there are only two components, one can describe this connection as either in parallel or in series. Also assume that the capacitor has been charged up to some voltage V at time t = 0, at which time it is connected to the inductor. The charge will begin to flow creating a current through the inductor. After a short time, all the charge that was originally on the capacitor plates will be gone and the current through the inductor will reach its maximum value. Thus, we began with all the energy stored in the capacitor and none in the inductor and end with the opposite condition. The current flowing through the inductor will then charge the capacitor back up and the process will begin again. The energy is traded back and forth between the two storage elements. The total energy of the system must remain constant because there is no dissipative element (no resistor). The total energy, W, is a constant equal to the energy stored in the capacitor added to the energy stored in the inductor. Thus,

22

21

21

LC LICVW += . Since this is a constant, we can take the time derivative of this expression and set it equal to

zero.

00)2(21)2(

21

=+→=+= CC

LLL

LC

C Vdt

dVCIdt

dILdt

dIILdt

dVVCdt

dW

We want to do with this equation what we did with the energy conservation equation of the beam. This time, though, instead of expressing the equation in terms of the displacement, x, we want to express it in terms of the voltage, V. We can use the general equations for the behavior of the capacitor and inductor to make these substitutions:



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dtdVCI

dtdILV C

CL

L ==

For the circuit shown above, V is the voltage at the top of the circuit and I is the current flowing around the circuit. Since this is a series circuit with only two elements: V = VC = VL and I = IC = IL. Making these

simplifications, our equations become: dtdVCI

dtdILV ==

We can further conclude from the capacitor equation that, by solving for dv/dt, CI

dtdV

= and, by taking the time

derivative of both sides, 2

2

dtVdC

dtdI

= . Substituting into the conservation of energy equation, we get

000 2

2

2

2

=+→=+→=+ Vdt

VdLCVCICI

dtVdLCV

dtdVCI

dtdIL

This leads us directly to the harmonic equation for oscillating circuits: 012

2

=+ VLCdt

Vd

If we compare this to the general expression for harmonic oscillation, 0202

2

=+ Vdt

Vd ω ,

we can determine the resonant frequency of the circuit: LC1

0 =ω .

Also recall that this is the equation for the resonant frequency of any simple RLC circuit. Damped Oscillation: The circuit we modeled above is unrealistic because it has no resistance at all. This is analogous to a mechanical system with no friction. To make a more realistic system, we must add some resistance, as shown in Figure C-2.

Figure C-2.

The circuit will still oscillate; however, the oscillation energy will gradually dissipate because of the resistance. The output signal will be similar to the oscillation behavior of the beam - a damped sinusoid. Note that this circuit has no voltage source. It needs to have an initial amount of energy placed into it. This is similar to the initial displacement you place on the beam to make it oscillate. The damped circuit has the following oscillation equation

02 202

2

=++ VdtdV

dtVd ωα

where α is the damping constant. It can be shown that in an ideal damped oscillation circuit, α is given by the following equation below:

LR

2=α



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Experiment Part D: Modeling a damped oscillator This part is a team project, only on member needs to any one component of Part D. But all are responsible to know the material. We will now consider an RLC circuit, with all three kinds of passive components and observe the damped oscillations. Note that we are also using a diode, a device that only allows current to flow in one direction (to the right in the figure). When a diode is on (forward biased), about 0.6 – 0.7V drops across it. We will learn more about diodes in Experiment 8, but, for now, you can consider it to be a switch that turns on when a positive voltage exceeding 0.6 or 0.7V is placed across it and is otherwise off. We are using it here so that the combination of an inductor L and a capacitor C are forced to oscillate over and over, kind of like ringing a bell. The resistance in the circuit is the DC resistance of the inductor and not a separate component.

Figure D-1.

• D1: Create the oscillating circuit in Figure D-1 above in PSpice. The diode should be the D1N914 o The voltage source used is a square wave with a negative offset so that the positive voltage is smaller than

the negative voltage. Since the period is 20ms, what is the frequency of the square wave? o Place voltage markers on the circuit at the points labeled Vin and Vout. o Use PSpice to simulate the transient response of this circuit. You are interested in measuring the frequency

of the oscillations induced in the circuit and the damping constant, so adjust the time window displayed so that you make these measurements.

o Copy your results and include them in your report. o Use the plot to find the oscillation frequency of your circuit. How does it compare it to the calculated value

of LC

fπ2

1= ?

o Use the plot to determine the damping constant of the circuit. In a simple RLC circuit, such as this one, the damping constant can also be found mathematically using the expression α=R/(2L). Calculate the damping constant using the above formula and compare it to the one you found using the plot data.

o Keep your simulation active because you will be returning to it after the next task.

• D2: Build the same circuit on your breadboard and measure the same input and output voltages. o Remember that the resistance and inductor in the circuit are actually only the inductor in a physical circuit.

If possible, confirm that the DC resistance of the inductor is about 4Ω by measuring it with a multi-meter. o Set up the function generator to produce a square wave and set the frequency, amplitude and offset to

obtain the same values used in the PSpice simulation. o Connect the wires for channels 1 and 2 (1+ and 2+) at the points labeled Vin and Vout, and ground the

other wires for each channel (1- and 2-). o Set up the time scale on your scope to be able to measure the oscillation frequency and the decay rate. o You will likely need to adjust the signal triggering to get a good trace signal. One suggestion is to trigger

on the falling edge of Channel 1. o Copy your simulation and experimental results and include them in your report. o Answer the same questions as you did for your PSpice results. o Describe the similarities and differences between your simulated and experimental results.

0

D1

D1N914

L11m

V

V1

TD = 0

TF = 1uPW = .01PER = .02

V1 = -4

TR = 1u

V2 = 1

Vin

C10.1u

Vout

V

R14



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You should have found reasonable agreement between your simulated and experimental results. Our experience is that the decay constant may differ between the simulation and the experiment but that the initial oscillation amplitude the frequency are similar. The similar experimental and simulated results validate the simulation and permit us to use features of the simulation that are not available in experiments. For example, there is no simple way to obtain the current through the inductor in the experiment. (You may want to think about why this is the case.) In the simulation, it is possible to easily find the current by just adding a current probe to one of the ends of the ideal inductor. In the final task of this experiment, you are to use the simulation to determine the energy stored in both the inductor and capacitor and see how they vary with time. • D3: Energy conservation and storage: Return to PSpice

o Delete the voltage probe on the input and add a current probe to one end of the inductor. Your results plot should change without having to run the simulation again because PSpice calculates all voltages, currents and power each time.

o Unlike the Analog Discovery/M2k scope, the results display for PSpice does not allow for different vertical scales for each measurement. Thus, the current signal will be very hard to read because it is so small. To make it easier to see, multiply it by the value of the resistance (4). You may also find that it is negative. Change it to a positive value to be able to better compare with the output voltage.

o Now you have all information necessary to determine the energy stored in the capacitor and in the inductor.

Modify the two traces in your plot so that they display the energy in the inductor 2

21 LI and the energy in

the capacitor 2

21 CV . Also, add a third trace that is the sum of the two energies (e.g. the total energy).

o Copy your results and include them in your report. There should be some very interesting features in these plots. Be sure that you annotate them fully so that an observer can easily identify all features.

o Describe the key features of your energy data vs time, including the maximum stored energy in either the inductor or the capacitor.

Summary In this part of the experiment, you have related your knowledge of oscillating mechanical systems to an oscillating electrical system and created an oscillating circuit. Note that you will continue your study of harmonic oscillators in Project 2, where you will use the strain gauge set up from this experiment and an accelerometer to determine both the position and acceleration vs time for the beam. The beam will be loaded a little differently because you will install the accelerometer near the end. You will be using the two measurements to determine the velocity of the beam. Once you have both the beam position and velocity, you will be able to produce a plot that will look a good deal like the energy vs time plot for the RLC circuit.



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Checklist and Conclusions The following should be included in your experimental checklist. Everything should be labeled and easy to find. Credit will be deducted for poor labeling or unclear presentation. ALL PLOTS SHOULD INDICATE WHICH TRACE CORRESPONDS TO THE SIGNAL AT WHICH POINT AND ALL KEY FEATURES SHOULD BE LABELED. Hand-Drawn Circuit Diagrams for all circuits that are to be analyzed using PSpice or physically built and characterized using your Analog Discovery or M2k board. Part A (16 points) Include the following:

1. A.1 Nothing to plot. (0 pt) 2. A.2

a. Plot of Vleft - Vright with R4 modified. (1 pt) b. Fraction of output signal compared to Vac source. (2 pt)

3. A.3 a. Analysis of circuit in part A.2. (2 pt) b. Derivation of formula for Vout = dV (= Vleft – Vright) as a function of R4, V1, ... (2 pt)

4. A.4 a. Plot of all 11 Vout traces. (2 pt) b. Plot of just Vright for all 11 cases. (1 pt) c. Comment on the advantage of using a bridge (Vleft - Vright) vs. using just a divider (Vright). (2 pt)

5. A.5 What is the sensitivity of this circuit (change in Vout/change in R)? (4 pt) Part B (18 points) Part B-1: Include the following:

1. What are the measured voltages for circuit B-2, both at room temperature and when warmed by holding with the power supplies balanced at +5 and -5V? (2pts)

2. What are the measured voltages for circuit B-2, both at room temperature and when warmed by holding with the power supplies unbalanced at +5 and -4V? (2pts)

3. State in a few words the advantage of using the full bridge signal, channel 1 compared to just using a voltage divider, channel 2. (2pts)

Answer the following questions: 1. What is the thermistor resistance at room temperature? At finger temperature? (4pts) 2. Using the voltage measurements from channel 1 in part 1. above calculate the resistance for the thermistor

at both room temperature and when warmed. Using the thermistor data sheet, estimate the thermistor temperature. TDK B57164K103J (R/T number 2904 on page 9 of the data sheets.) Remember that data sheet is the change in resistance normalize by the thermistor resistance, 10k in this case. (2pts)

Part B-2: Include the following:

1. Measured voltages for channel 1 and 2 at both room and finger temperatures. (2pts) Answer the following questions:

1. What is the mathematical relation between the voltage on channel 2 compare to channel 1? (1pts) 2. What is the warm resistance of the thermistor and the estimated temperature? (1pts) 3. What advantage does this circuit have compare to part B-1 for small temperature changes? (1pts) 4. Under what temperature conditions will this circuit fail to give reliable results? (1pts)

Part C (16 points) Include the following:

1. C-1 and C-2: Pictures of beams from every team member (4pts) 2. C-3: M2k/Analog Discovery trace of accelerometer signal from plucked beam (12pts)




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Part D (20 points) Include the following plots:

1. PSpice plot of input and output from the oscillating circuit. Be sure to label your plot with the resonant frequency and damping constant of the circuit you analyzed using the PSpice plot. Write an equation for

the output in the form v(t)=Ce-αtsin(ωt). (4 pt) 2. Analog Discovery/M2k plot of input and output from the oscillating circuit. Again, be sure to determine the

resonant frequency and damping constant and include this information on your plot. (4 pt) 3. PSpice plot of the energy in the inductor, the energy in the capacitor and the total energy as functions of

time. Be sure to label everything interesting in these plots. Describe the key features of the energy plots. (6pts)

Answer the following questions: 1. Compare and contrast both your PSpice and M2k/Analog Discovery plots with the plots for the cantilever

beam. (2 pt) 2. In D1: What value did you calculate for f using the equation for the resonant frequency? How close of an

estimate is this to the resonance you found in the plot? (2 pt) 3. In D1: What value did you calculate for α using the equation? How close of an estimate is this to the

damping constant you found in the plot? (2 pt) Organization, completeness, ordering. Is this easy to grade? (8 pt) List member responsibilities. (2 pt) Summary (0 to -10 points) Summary/Overview (0 to -10 pts) There are two parts to this section, both of which require revisiting everything done on this experiment and addressing broad issues. Grading for this section works a bit differently in that the overall report grade will be reduced if the responses are not satisfactory.

1. Application: Identify at least one application of the content addressed in this experiment. That is, find an engineered system, device, process that is based, at least in part, on what you have learned. You must identify the fundamental system and then describe at least one practical application.

2. Engineering Design Process: Describe the fundamental math and science (ideal) picture of the system, device, and process you address in part 1 and the key information you obtained from experiment and simulation. Compare and contrast the results from each of the task areas (math and science, experiment, simulation) and then generate one or two conclusions for the practical application. That is, how does the practical system model differ from the original ideal? Be specific and quantitative. For example, all systems work as specified in a limited operating range. Be sure to define this range.

Total: 80 points for experiment packet 0 to -10 points for Summary

20 points for attendance 100 points

Attendance (20 possible points) 2 classes (20 points), 1 class (10 points), 0 class (0 points) Minus 5 points for each late. No attendance at all = No grade for this experiment.



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Experiment 5 Online version

Section: ______ Team: _____ Report Grade: ______

#1 name: #2 name:

#3 name: #4 name:

#5 name: #6 name:

Checklist w/ Signatures for Main Concepts

For all plots that require a signature below, you must explain to the TA or instructor: • the purpose of the data (using your hand-drawn circuit diagram), • what information is contained in the plot and • why you believe that the plot is correct. Any member of your group can be asked for the explanation. Some checkoffs need to be for every student on the team, but in those cases only report data from one team member. PART A: Bridge Circuits A2: Behavior of unbalanced bridge circuit – all members of team do this.

1. Plot of Vleft – Vright with R4 modified _________________________ Enter “Y” for each student who was checked for the line above. Student 1 Student 2 Student 3 Student 4 Student 5 Student 6

2. Fraction of output signal compared to Vac source

A3: Analyze circuit by hand – team effort (not individual) 1. Analysis of circuit in part A.2 2. Derivation of formula for Vout=dV(=Vleft – Vright) 3. Enter Y for each student that was checked for the plot:

A4: Parameter sweep – all members of team do this but just provide one in report

1. Plot of all 11 Vout traces______________________________________ Enter “Y” for each student who was checked for the line above. Student 1 Student 2 Student 3 Student 4 Student 5 Student 6

2. Plot of just Vright for all 11 cases 3. Comment on the advantage of using a bridge vs. using just a divider

A5: Sensitivity calculation – team effort



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1. What is the sensitivity of this circuit? PART B: Thermistor Part B-1: Build bridge circuit, individual effort, report on one result

1. Both voltage measurements with +5V and-5V supplies, warm and cool 2. Both voltage measurements with +5V and-4V supplies, warm and cool

This is a checkoff for 2. ______________________________ Enter “Y” for each student who was checked for the line above. Student 1 Student 2 Student 3 Student 4 Student 5 Student 6

3. Explain the advantage of using bridge. 4. Question 1 and 2

Part B-2 Voltage difference with difference amplifier – team effort

1. Both voltage measurement, warm and cool. ___________________ 2. Questions 1-4

PART C: Oscillating Beam C1: All team members find something that can be used as a cantilevered beam. C2: All team members find a way to support their beam. Include a picture of a beam from each team member. C3: Accelerometer Measurements - Team chooses one beam (or 2 if you prefer) to move forward. This will be used for Project 2 also.

1. Have a TA see a picture of the chosen beam. ________________ 2. Analog Discovery/M2k Plot of accelerometer for a pluck of beam ______________

PART D: Oscillating Circuits

1. PSpice plot of output from the oscillating circuit, with parameters and equation 2. M2k/Analog Discovery Plot of oscillating circuit, with

parameters_________________ 3. PSpice Plot of Energy, with explanation Questions 1-3

Member Responsibilities Summary/Overview

Documents

Experiment 5 – Online version Bridges, Potentiometers, and ......Note: For Experiment 5 and Project 2 will work in with your full team of ~6 students. Submit a single team report