p1 EE1050 Norton / Strain Lab

Norton equivalentTo calculate the Norton equivalent on paper:1) Disregard the load and calculate the short-circuit

current. This is the Norton current (IN).2) Zero all the sources. (To zero a voltage source,

replace it with a short. To zero a current source,replace it with an open.)

3) Compute the total resistance between the loadterminals. (DO NOT include the load in thisresistance.) This is the Norton source resistance(RN). (Exactly thesame Théveninsource resistance(RTh)).

4) Draw the Nortonequivalent circuit andadd your values.

OR...1) Find the Thévenin equivalent circuit.2) Convert to Norton circuit, RN = RTh and IN =

VTh/RTh.

University of UtahElectrical Engineering Department

EE1050/1060

Norton, Source Resistance, & Strain GaugesA. Stolp, 1/31/00

rev, 2/3/00

Objectives1.) Make a Norton equivalent circuit.2.) Measure the source resistance of a battery.3.) Observe and measure strain gauges in a bridge configuration.

Check out from stockroom:! Wire kit! APPA 95 digital multimeter! EE 1050 kit, optional, if available.

Parts to be supplied by the student:These items may be bought from stockroom or may be in the EE 1050 kit.! Two 100 S, Two 390 S, 560 S, and 1 kS resistors! 4.7 S, 10 S, 47 S, 120 S resistors! two trim potentiometers (100 S to 500 S)! Proto-board and wires! 0.22 :F capacitor (cap)! LM317T Adjustable voltage regulatorNote: The last three items on this list mayalready be on the proto-board in the EE1050 kit, and may already be wiredtogether to make an adjustable currentsource. In that case leave them alone fornow.

Experiment 1 , Norton equivalent In the box at right you’ll find a review ofthe steps you use to find a Nortonequivalent circuit on paper. In theprevious lab you performed most of thesesteps on two different circuits. Refer backto that data now. You’ll find short circuitcurrent readings and resistancemeasurements made with the source(s)zeroed. You have all the data you needto make Norton equivalent circuits of thetwo circuits you built last time. Today youwill do exactly that for one of them.

p2 EE1050 Norton / Strain Lab

Part 1 Make current source: All you need now isan adjustable current source. It turns out thatcurrent sources are more theoretical than practicaland you don’t find them very readily— not likevoltage sources. So we’ll have to make our own. This should already be built on your proto-board. Ifnot, build the circuit at right. There are two picturesof this circuit, use whichever you find easier tofollow. Connect this circuit up to the second B&Kpower supply and turn up the power supply to 30 V. Now you’ve built a nifty little adjustable currentsource. (Note: your circuit may have an extraresistor if I substituted a 1 kS pot for the 500 S.)

Part 2 Test current source: Short theoutput of the current source with theammeter and adjust the potentiometer(pot) to get about 20 mA. Select someload resistors between 0 and 2 kS. Make the circuit shown in the schematic. IS is the current source you just built andRL is one of your load resistors. Becareful, the LM317T part and the loadresistors may get hot. Take somemeasurements at various loads toconvince yourself that this is a goodcurrent source, at least as long as RL is smaller than about1.4 kS. Above that, the output voltage would have to behigher than the B&K supply voltage. Comment in yournotebook about the quality of this current source.

Part 3 Build Norton circuit: Pick one of the circuitsthat you made in the last lab and use your data todetermine the Norton equivalent circuit.

Short the output of the current source with theammeter and adjust the potentiometer (pot) to getyour IN. Adjust a second potentiometer to the value of your RN. Construct the Nortoncircuit shown and test it just like you tested the Thévenin equivalent circuit in the last lab. That is, take a set of readings with each of the following loads; RL = 0 S (short circuit), RL =100 S, RL = 390 S, and RL = 4 S (open circuit). Compare measurements to your previousmeasurements from the original circuit. You may compare them in a plot or in a table. Comment on the agreement in your lab notebook.

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Experiment 2 , Source Resistance So far we’ve conveniently ignored one important aspect in the construction of Théveninand Norton equivalent sources— the internal source resistances of the B&K and thecurrent source. It turns out that that these internal resistances are negligible because bothof these sources are regulated supplies. That means that electronics within each deviceare actively keeping the output constant, regardless of the load. Most sources are not sowell behaved. To illustrate that point, I want you to find the source resistance of a AAbattery.

Place an AA battery in the holder as shown. If you put thebattery in the right spot the black lead will be the negative sideof the battery and the spring connection shown will be thepositive. Use a couple of the clip leads from your wire kit toconnect the ammeter and the voltmeter to the battery in thenormal way. Take a set of readings with each of the followingloads; RL = 4 S (open circuit), RL = 47 S, RL = 10 S, RL =4.7 S. (Note: If the voltage sags noticeably when RL is connected, thebattery is very dead. Get another battery or measure fast.) Plot thesedata points on a graph and draw a straight line through yourpoints. Use the line to find an RS for this battery.

RS for a fresh battery can be well under 1 S. RS increases asthe battery is used. Comment on the freshness of your battery.

Experiment 3 , Strain Gauges Strain gages are used to detect the deformation of materials— their resistance increasesas they elongated. The resistance of a conductor is given by:

Where D is the resistivity of the material and A and l are itsdimensions as shown. Elongation of a strain gauge makes itsconductors both longer and thinner, increasing their resistance. Thatis how a strain gauge works.

Part 1 Strain gauge resistance: Your TA will have some flexiblebeams set up somewhere in the lab. These beams are on loan fromthe Mechanical Engineering department, please be careful with them. Examine the onethat doesn’t have wires attached to it. You’ll find four large strain gauges glued to themetal, two on top and two on the bottom. That’s enough to make a full bridge like the onementioned in your homework. If the beam is flexed downward the two on top will stretchand the two on the bottom will compress. The resistance of the ones on top will increaseand the resistance of the ones on the bottom will decrease.

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Use an ohmmeter to measure the resistance of one of the top strain gauges. Flex thebeam downward as far as it will go. Measure the new resistance and calculate a %change. You’ll have to make good connections and hold them steady during this processor changes in the contact resistance will be greater than the change in the gauges.

Part 2 Voltage divider: Now turn your attention to one of the beams that is all wired up. Hook a power supply across two of the strain gauges, one on the top and one on thebottom of the beam. The strain gages should be wired in series so that they make avoltage divider. Your TA will probably have this set up, ask. Turn up the supply to 5 V. Measure the voltage between the power supply negative and the point between thegauges. Flex the beam, measure the voltage again, and calculate a % change. Noticethat the changes have been very small so far.

Part 3 Full bridge: Now create a full bridge. R1 and R4 are straingages on top of the beam, R2 and R3 are gages on the bottom. Again,this will probably be set up for you. Connect it to the same supply (VS)and measure the voltage between the two sides of the bridge (Vab). Flex the beam downward about as far as you did the first one. Measure the new voltageand calculate the change. (% change no longer makes sense here because the unflexed voltage shouldideally be zero). Comment on the effectiveness of the bridge circuit compared to our earlierattempts to measure the stain gages. (That is, say something about the size of the changerelative the unflexed voltage).

A perfectly “balanced” bridge would show a 0 V output when the beam isn’t flexed. Canyou devise a modification to the bridge circuit that would allow you to use a smallpotentiometer to “balance” the bridge? This is a tricky question. Think about it, and whenyou’ve thunk enough, ask your TA to show you the trick.

Part 4 Output resistance: The source resistance of something like a bridge circuit isusually referred to as its output resistance or output impedance. For this bridge circuit of120 S strain gauges the output resistance should be 120 S. Confirm this by hooking a120 S resistor across the output of the bridge (from a point a to point b) and repeating thevoltage measurements of part 3. With this added load the voltage change (unflexed toflexed) should be half as big as it was. Do your measurements confirm this?

Theoretically confirm that the output resistance of the bridge is 120 S. (Calculate theThévenin resistance). This may be done later.

Part 5 Play: Finally, your TA will hook the strain gauge bridge to an oscilloscope anddemonstrate a few things.

ConcludeAs always, get your lab instructor to check you off.

Write a conclusion in your notebook. Make sure that you touch on each of the subjects inyour objectives. Say something about the usefulness of the bridge circuit. Mention anyproblems that you encountered in this lab and how you overcame them.