Lab2_ECE3710_MrC

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Georgia Institute Of Technology *

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3710

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Electrical Engineering

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Feb 20, 2024

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© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 1 Student: _____________________ Sign-off: __________________ Date: ________________________ ECE 3710 Lab 2: Resistor Networks and Wheatstone Bridge Objective: To reinforce understanding of • Solution methods for electrical circuit voltages and currents • Potentiometers • Sensors and Wheatstone Bridges Table of Contents: Materials Needed 1 Pre-Lab Assignment 1 Background 1 Systematic Solution Methods 1 Potentiometer 2 Wheatstone Bridge 3 Lab Procedures 3 Part A) Circuit 1 4 Part B) Circuit 2 4 Part C) Potentiometer 4 Part D) Position Sensor Using Wheatstone Bridge 6 Appendix 8 Materials Needed • 100Ω rotary potentiometer • 950Ω resistor • 4 x 1kΩ (1% tolerance) resistor • 2 x 2kΩ resistor Pre-Lab Assignment 1) Solve the circuits in the Appendix for the voltages and currents requested. Turn in your prelab with the rest of the lab and include all of your calculations. Circuit 1: i 1 = _____________, v 2 = _______________ Circuit 2: i 1 = _____________, v 2 = _______________ Da Cal Mr.

© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 2 2) Read the Background section of this laboratory exercise. Background: Systematic Solution Methods Several different solution methods may be used to solve for voltage and currents in a circuit: Mesh Analysis, Node Analysis, Thévenin Equivalent circuit, and Norton Equivalent circuit. Both Mesh and Node analysis result in a set of simultaneous algebraic equations. • Mesh Analysis introduces intermediate variables called “mesh currents” and systematically implements Kirchhoff’s Voltage Law to solve for those mes h currents. • Node Analysis introduces intermediate variables called “node voltages” and systematically implements Kirchhoff’s Current Law to solve for those node voltages. • Thévenin and Norton Equivalent circuits replace a portion of a circuit with a simple source/resistance circuit that has the same current and voltage provided by the original circuit. Using Thévenin Equivalent and Norton equivalents, source transformation is a graphical method to replace a schematic with a simpler schematic in a series of substitutions. Potentiometer(or pot) A potentiometer is a variable resistor that varies its value proportional to the rotation of the shaft (rotary potentiometer) or a distance that a slider has traveled (linear potentiometer). Pots typically have three leads: two end points and the wiper . There is an externally adjustable trim that adjusts the position of the wiper with respect to the ends of the internal resistor. The symbol for a pot is shown on the left below; on the right is the equivalent circuit. Potentiometer Position Sensor The three potentiometer leads are used when the pot is to be used in a voltage divider circuit as shown in the figures below, a linear pot on the left and a rotary pot on the right. In the voltage divider configuration, one lead is to be attached to +v s , one lead is to be attached to ground, and the other lead is connected to the wiper (or pick-off point), v o .

© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 3 v s v o + y (m) v o  v s + Linear potentiometer Rotary potentiometer Wheatstone Bridge A Wheatstone Bridge is used commonly to measure small voltage resistance changes from a nominal value. In the figure below, - + v s R 2 R 1 R 3 R x b a When balanced, V ba = 0v and 2 1 3 R R R R x = . When R x increases, then V ba increases. When R x decreases, V ba decreases (becoming more negative). Lab Procedures To help build and troubleshoot circuits, lay out a circuit on the breadboard the same way it is drawn in the schematic. An example schematic and breadboard layout is shown below to emphasize this tactic. Do not build this circuit. The groups along the side rails are all connected in a long row to make a giant node.* Wider gap

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© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 4 • On some breadboards, there is a wider gap between some of the groups in the side rails. This wide gap indicates that those two groups are not connected, as shown in this breadboard. Part A) Circuit 1 Build Circuit 1 from the Appendix and verify that you get the same answer from your analysis done in the prelab. (hint: to measure i 1 , it is easiest to measure the voltage across R 1 and divide by R 1 . ) Circuit 1 (Measured): i 1 = _____________, v 2 = _______________ Compare your results determined analytically from the Appendix. Circuit 1 (Analytical): i 1 = _____________, v 2 = _______________ Verify that the experimental and computed values are approximately equal. If not, ask an instructor to check your analytical answers to determine where the problem lies. Part B) Circuit 2 Repeat Part A) with Circuit 2 from the Appendix. Note that you just have to add one resistor to the circuit built for Part A) Circuit 2 (Measured): i 1 = _____________, v 2 = _______________ Compare your results determined analytically from the Appendix. Circuit 2 (Analytical): i 1 = _____________, v 2 = _______________ Verify that the experimental and computed values are approximately equal. If not, ask an instructor to check your analytical answers to determine where the problem lies. Part C) Potentiometer R2 To voltage supply R1 Each row is a node You need to have an instructor sign off for one of the parts to this lab.

© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 5 Objective: be able to use a potentiometer in a circuit. Review the background information on potentiometers. An image of a rotary pot placed in a breadboard is shown below. Notice the white trimmer on the top that allows you to adjust the resistance with a screwdriver. This particular type of pot is often called a trimpot . Look for the three wires coming from the pot. The leads in the image below match the equivalent circuit schematic of a pot given in the background section. To be used as a variable resistor, use the connections between Point a and the wiper, or between Point b and the wiper (leaving the other end point unconnected). Connect a 100 Ω pot in the breadboard and measure the resistance across the pot between Point a the wiper as you turn the trim in the clockwise direction starting from all the way on the left to all the way to the right. Starting resistance____________ Ending resistance _____________ Repeat the procedure for the connection between Point b and the wiper. Starting resistance____________ Ending resistance _____________ Verify that these resistances match the behavior in the equivalent pot schematic shown in the background section, that is, that the resistances match Rp and RT-Rp where RT is 100 Ω. Put the 100Ω rotary pot in series with a 950Ω 1% tolerance resistor (blue in color). You can use either the Point a – wiper leads or the Point b – wiper leads for the pot resistance, which is placed in series

© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 6 with the 950 Ω resistor. Measure the total resistance of pot plus the resistor as you rotate the pot trim from one extreme to the other. Max R ____________ Min R _________________ This configuration allows us to have a small varying resistance to a nominal fixed resistance. Part D) Position Sensor Objective: build a position sensor using a Wheatstone Bridge. Build the Wheatstone Bridge in the Background section where R 1 = R 2 = R 3 = 1000Ω (with 1% tolerances, so blue resistors). Put the series combination of 100Ω rotary pot and 950Ω resistor in the place of R x . Layout the circuit on the breadboard in the same way it appears in the schematic (to help with troubleshooting). For example, it can be built as follows. The schematic on the left is equivalent to the wheatstone bridge schematic in the diamond formation shown in the background section. Balance the Wheatstone Bridge by adjusting the pot so that V ba has the smallest value possible (this is the voltage from a to b). This trim position becomes the “Zero Angle Position.” A n angle sensor that uses a Wheatstone Bridge is often calibrated by taking voltage readings with known angles. To do a rough calibration: • Set the DMM to “Auto” in order to auto scale the measurements • Do the measurements to fill in the following table.

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© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 7 All rotations are measured with respect to the Zero Angle position. For comparison sake, you are asked to record V b as well, that is, the potential at node b with respect to the negative side of the source voltage. Angle V ba V b -90 o counterclockwise rotation -45 o counterclockwise rotation Zero Angle Position +45 o clockwise rotation +90 o clockwise rotation Which has better resolution for determining the angle-voltage relationship, V ba or V b ? Why? To finish calibrating your sensor, use the results in the table to plot a line of the angles vs voltages (voltages being on the x axis). From your plot, determine the angle if the V ba voltage measurement is 100 mv: ____________ V ba Angle (deg)

© ECE3710, School of Electrical and Computer Engineering, Georgia Tech 8 Appendix: Circuit 1: R 1 = R 3 = R 5 = 1000Ω; R 2 = R 4 = 2000Ω; Circuit 2: R 1 = R 3 = R 5 = R 6 = 1000Ω; R 2 = R 4 = 2000Ω; i 1 - + 15v v 2 R 5 R 4 R 1 R 3 + - R 2 i 1 - + 15v v 2 R 5 R 4 R 1 R 3 + - R 2 R 6

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