Utilizing A Strain Gage Circuit To Measure Weight As Function Of Changing Resistance
Utilizing a Strain Gage Circuit to Measure Weight as Function of
Changing Resistance
John C. Greavu III
University of Minnesota, School of Physics and Astronomy
I. INTRODUCTION
Operational amplifiers can be combined with gages to accurately measure mechanical properties as functions of electrical variables of a circuit. Here, we used two strain gages on the inside and outside of a load cell to measure the mass of hanging weights as a function of voltage. As the resistance of a wire is proportional to its length, forces that deform the gages will be directly proportional to changes in their resistances. Creating a Wheatstone bridge with the strain gages allows for measuring a differential voltage, which is then amplified by an instrumentation amplifier. Strain gage circuits like this one are used widely, from bathroom scales to measuring structural changes in bridges. We calibrated our strain gage circuit and provided an in-depth analysis of it and the aforementioned circuit topics.
II. THEORY & SETUP
An instrumentation amplifier, or “in-amp”, is a difference amplifier with a unity gain buffer attached at each voltage input. A buffer, shown in Figure 1, is an op-amp that has its output wired to its negative terminal. Since there is negative feedback, and as long as the voltage to the positive terminal ?! is less than the voltage to the op-amp’s power lines (?!! , ?!! ), we can apply the “golden rules”: ?! = ?! =
?!"# . The buffer effectively makes a copy of the voltage input (to ?! ) at the output. Since the op-amp has infinite input impedance, this isolates the output and input, and helps prevent the measurement from disturbing the circuit that is producing the voltage.
Figure 1: A unity gain buffer. If ?! ≅ ?! , then ?!" = ?!"# .
A difference, or differential, amplifier (Figure 2) amplifies the difference between two arbitrary voltage points, provided they are between ?!! and ?!! . To solve for its transfer function (6.1.1.), we
assumed
Changing Resistance
John C. Greavu III
University of Minnesota, School of Physics and Astronomy
I. INTRODUCTION
Operational amplifiers can be combined with gages to accurately measure mechanical properties as functions of electrical variables of a circuit. Here, we used two strain gages on the inside and outside of a load cell to measure the mass of hanging weights as a function of voltage. As the resistance of a wire is proportional to its length, forces that deform the gages will be directly proportional to changes in their resistances. Creating a Wheatstone bridge with the strain gages allows for measuring a differential voltage, which is then amplified by an instrumentation amplifier. Strain gage circuits like this one are used widely, from bathroom scales to measuring structural changes in bridges. We calibrated our strain gage circuit and provided an in-depth analysis of it and the aforementioned circuit topics.
II. THEORY & SETUP
An instrumentation amplifier, or “in-amp”, is a difference amplifier with a unity gain buffer attached at each voltage input. A buffer, shown in Figure 1, is an op-amp that has its output wired to its negative terminal. Since there is negative feedback, and as long as the voltage to the positive terminal ?! is less than the voltage to the op-amp’s power lines (?!! , ?!! ), we can apply the “golden rules”: ?! = ?! =
?!"# . The buffer effectively makes a copy of the voltage input (to ?! ) at the output. Since the op-amp has infinite input impedance, this isolates the output and input, and helps prevent the measurement from disturbing the circuit that is producing the voltage.
Figure 1: A unity gain buffer. If ?! ≅ ?! , then ?!" = ?!"# .
A difference, or differential, amplifier (Figure 2) amplifies the difference between two arbitrary voltage points, provided they are between ?!! and ?!! . To solve for its transfer function (6.1.1.), we
assumed