Experiment # 3 The Wheatstone Bridge—Practical Applications.ENGN/PHYS 207—Fall 2012 Foreword The goals of this lab are to: • Build a Wheatstone Bridge, and understand why it is able to make sensitive measurements. • Utilize the bridge to measure deflection of a beam (a very practical setting!). • Enjoy a first introduction to the wonderful world of amplifiers. 1 1.1 The Wheatstone Bridge Introduction The Wheatstone Bridge 1 , (WB) is the circuit shown in Figure 1. This typical configuration of the WB consists of four resistors in a series-parallel configuration, a constant voltage source (“excitation” to the WB), and a voltage gage (“output” of the WB). Excitation is supplied by your power supply at nodes a and d. The output is obtained by reading the potential difference between nodes b and c: Vout = Vb − Vc The WB is basically a very sensitive resistance measurement device, owing its high level of sensitivity to the fact that it is basically a difference amplifier. Thought it was invented circa 1833 (people have been clever for a very long time...), it still finds widespread use today in many engineering applications—mechanical, aerospace, and civil engineering, to name a few. The basic idea is that the resistance of one of the bridge legs can vary with time. This leg of the bridge could be a thermocouple. If the temperature changes, then the resistance changes, so the output changes accordingly. Or one of the bridge legs could be a strain gage2 . If the structure to which it is attached deflects or vibrates, the bridge will report this motion as a change in its output voltage. Clearly, then, it would be fun (and instructive!) to build and analyze one. 1.2 Theoretical Considerations 1. The bridge output is defined as the voltage difference between nodes b and c: Vout = Vb − Vc . On which respective nodes would you place the (+) and (-) probes of the DMM? 2. Show that: Vout = 1 R1 R4 − R2 R3 Vs (R1 + R2 )(R3 + R4 ) (1) Interesting historical side note: Wheatstone didn’t actually invent this circuit. Credit for the first description of the circuit goes to S.H. Christie; but Wheatstone is the one who found widespread practical use for this circuit. 2 A strain gage is basically a variable resistor. It essentially consists of long, thin piece of metal patterned in a shape designed to detect specific types of deformations (stretching, compressing, twisting). Changing it’s shape basically changes the values for A and L in R = AρL 1 Thus. Then let R4 increase its resistance by a relatively small amount: R4 → R4 + ∆R. R4 when the bridge is balanced? 4. Assume all resistors in your WB are equal R1 = R2 = R3 = R4 = R. The bridge is said to be “balanced” when Vout = 0. Explain how you interpret the meaning of the slope of this line? 6. Hint: Vb and Vc nodal voltages are be easy to compute. Vout is indicative of the strain in the beam. changing the value of R4 will make Vout = 0. The voltage source Vs provides excitation at nodes a and d. R4 might be a strain gage.Figure 1: Basic Wheatstone Bridge Circuit. what is good and bad about having this ratio be R really small (<< 1)? What is good and bad about having this ratio be relatively large (≈ 1)? 2 . What is the relationship between the resistances R1. For the case that ∆R << 1. Imagine you build a WB circuit to measure the deflection of a beam in a building during an earthquake. flexible resistor—anything that transduces one physical property into a change in resistance. show that: R Vout ≈ ∆R Vs 4R (2) 5. ∆R. R2. In practice. Once you get them. Vout is in the bag. thermocouple. R3. Make a quick sketch of Vout vs. Starting in a balance. The bridge is said to be “balanced” when Vout = 0. 3. What are some inherent trade offs with the setting the proper ratio of ∆R ? In other words. so your bridge is balanced (Vout = 0). R4 might be a strain gage whose resistance changes as the beam flexes. The output (gage reading) Vout is measured across as the difference in voltages between nodes b and c. Devise an mechanical/fluid analog to the WB. crappy reruns here. As we’ve oft discussed in class. in about 50–100 Ω increments. 2(b)).. you might examine the response of an airplane wing to an impact. Therefore. just barely large enough to see on your oscilloscope. very useful piece of electronics called an instrumentation amplifier . and R3. we’ll make use of a very. Make a plot of Vout vs. 4 Amplifiers are kind of like cars. Just good ole plain useful circuits. Where would you do something similar in real life? There are many examples! For instance. How do your measurements compare to the expected result developed in question 3 above? 2. We’ll simulate this for now by turning the dial on the 2 kΩ pot. we’ll discuss how its inner workings.. R2. 3 (3) No Dawson’s Creek. the resistance will change by an amount ∆R..pdf 3 . Describe this analogy in terms of what it would mean for your mechanical/fluid system to be “balanced” or “imbalanced”. To do so. 2(a)) configured as a Wheatstone Bridge to measure deflections in a beam (e.7. The datasheet for the INA 126 is available at: http://www.g. We’ll use the model known as the INA 1264 Later in the term. Now build the bridge (see Fig. Is the graph linear? Everywhere? Or are there seemingly non-linear regions? In your analysis/discussion. If the wing flexes upor downward. Imagine R4 to be a strain gage element attached to an airplane wing to measure its vibrations during flight (as you might do in a real engineering project one day!). Carefully measure and record the resistance of the pot with your circuit balanced. What would you use in place of a voltmeter to measure any imbalances in your fluidic bridge? 2 Experiment I: Getting Acquainted with the WB 3 1. 3 Experiment II: Real-life Application of the WB Now you will use actual strain gage elements (see Fig. Analyze and discuss your result in the context of Eqn 2. ∆R. let’s think about what the mechanical/fluid analog of the WB would be. see Fig. general category is automobile (amplifier). or other half-baked. the output of the amplifier is given by: Vamp = 50Vout . you just need to know that it amplifies the input signal by a gain factor G. Your amplifier will be wired for a gain G = 50. (Remember to carefully measure and record the actual resistance of each of these. Carefully measure and record Vout for each setting. (I did promise that circuits is actually useful. For now. 3. you might test the structural integrity of a bridge with a strain gage in a WB bridge configuration. The output of strain gage bridge is quite small (approximately 2–20 mV). 1). Buffy the Vampire Slayer. before we finish this exercise. Sweep the pot through a range of resistance from about 500 – 1500 Ω. By analogy.hopefully this helps convince you).ti. Fully explain how your proposed fluid/mechanical measurement system is analogous to the WB. Balance your bridge. and so on. a specific model is a Honda Civic (INA 126). Use 1 kΩ resistors for R1. carefully consider the validity of the assumptions made when deriving Eqn 2. you might test how earthquake isolated a building is.com/lit/ds/symlink/ina126. We will amplify this signal to make it easier to see and measure. use a 2 kΩ pot.) For R4. So. electrical circuits can often be thought of in terms of their analogy to mechanical or fluid system. Set Vs = +5 V. • Measure the amplified bridge output: You an oscilloscope to do it! The positive scope scope should connect INA126 pin 6 (the amplifier’s output). • Route bridge output to amplifier: Connect INA126 pin 2 to the White conductor of the bridge. Detailed instructions how to wire your circuit are as follows: • Bridge excitation: Connect the Red wire to +10 V. connect the ground probe to INA126 pin5 (the amplifier’s ground). This sets the gain to be G = 50. 4 . Connect the Black wire to GND.5 V (much easier to cleanly read on a scope). The resistance changes when thin metal film “comb” shape deforms. In a non-stressed state. if your bridge has an output Vout = 50 mV (possible to read. the gage typically has a resistance of a few hundred ohms. (b) Building undergoing vibration. Connect INA126 pin 3 to the Green conductor of the bridge. Additionally.de/resources/vibration-measurement/building-vibration. • Provide a reference for the amplifier: Connect INA126 pin 5 to GND. the amplifier will multiply this by a factor of 50 and output Vamp = 2500 mV = 2.(a) (b) Figure 2: (a) Strain gage.html where Vout is the output of your strain gage—which is also the input to your instrumentation amplifier. but difficult with scope). For instance. Strain gauges can be used to measure and record deflections vs time. Image credit: http://w-ave. • Route power connections to your amplifier: Connect INA126 pin 4 to -10 V and pin 7 to +10 V. • Setting the gain of the amplifier: Connect a 1780 Ω resistor between pins 1 and 8 of the INA126. with the chip properly oriented. investigate how response of the beam changes depending on the size of the mass attached to it. a bridge sags when cars and trucks are loading it. and k is the effective spring constant of the beam. • Use a C-clamp to fasten your the beam. What is the slope of the best-fit line to your data? What should it be according to simple-harmonic oscillator theory? In this context. If you have time. or it might simulate changing the overall design of the airplane wing. Therefore. simulate an impact on the beam.Figure 3: Pinout of INA126. 5 . with attached strain gage sensors to the bridge. • A beam can be modeled as a spring. Note that pin 1 is in the upper left corner. At any rate. Hopefully this portion of the experiment convinced you that knowing a little circuits really does pay off no matter what field/discipline you ultimately work in. the eyelet for loading your bridge at the distal end. analyze and discuss the result you obtained. It is easiest to use the digital multi-meter for this task. • With your beam firmly fastened to the table. Wrapping up. This might simulate changing the design for load-bearing beams in buildings. Measure the • Modify your beam by adding weight in reasonable increments to the end of the beam with a mass m. bridge output (voltage). you could make a plot of applied load vs. and—as you will recall—a spring-mass simple harmonic oscillator obeys the equation: k x+ x=0 ¨ m where x denotes the vertical position of the beam. Orient your beam so that the strain gauges are near the table. say. View the resulting signal on the oscilloscope to determine the frequency of oscillation. the frequency of oscillation should be inversely proportional to the square root of the applied load: 1 f∝√ . or on a car chassis. m is the mass/load applied to the end of the beam. Repeat for at least 5 different loads. make a log-log plot of frequency of oscillation (f ) vs the applied load (m). note that you could also measure static deflections as a result of loading your bridge. m How does your data compare with this theory? To investigate this question. sine they are best suited to measuring dc voltages. This leads to a solution of: x(t) = A cos(ωt + φ) where the natural frequency is ω = k/m. This plot would serve as a reference if you wanted to measure how much. 3. 5 The Write-Up Your report will consist of 3 main parts: 1. say what system you are studying. Please be sure to run your idea by the instructor before beginning—we’ll make sure the project is feasible and of appropriate technical scope. please include a brief Intro and Methods if you opt for your choose your own adventure. Section 1. and describe your setup in sufficient detail that a Circuits-knowledgeable friend could replicate the experiment. There must be a technical element of experiment with some theory to which you can reference your results. 4(b)). You should feel free to invent your own quick study/application. By no means is it the only one. ∆R is the center piece. Hard numbers are golden. (a) (b) Figure 4: (a) Airplane wing: come fly the friendly skies. note that a bat’s wing might work well in such a configuration.2 (Theoretical Considerations): Be sure to complete questions 1–7. 4. make a quantitative comparison. We have thermocouples (changes resistance upon changing temperature). The figure of Vout vs. Section 4 (Application: Choose your Own Adventure): In addition to Results and Conclusion/Discussion. see Fig. Write the Results and Discussion/Conclusions section. Let’s hope none of us ever see an airplane wing doing that! However. 2. (b) Flexible sensor: the resistance increases as the sensor is bent. 6 . Section 3 (Application to Beams): No need to write an Intro or Methods. why it is important (and/or cool and fun). Section 2 (Experiment I): Be sure to address all all questions in 1–3. This also means you must use your data to st back up any claims you make. Be certain to address the following: What did theory predict? What did you measure? How do those compare/contrast? Regarding this last point. flex sensors (kind of like a flexible potentiometer. Basically. and you should write a brief discussion to explain/interpret what you saw (something like 1 paragraph should be sufficient).4 Part II: Alternate—Choose your own Adventure The beam oscillation experiment was just one example application of a Wheatstone bridge.