Experiment 5 Part A: Bridge Circuits Part B: Strain Gauges Part C: Oscilla

Experiment 5  Part A: Bridge Circuits  Part B: Strain Gauges  Part C: Oscilla www.phwiki.com

Experiment 5 Part A: Bridge Circuits Part B: Strain Gauges Part C: Oscilla

Goth, Greg, Freelance Business Writer has reference to this Academic Journal, PHwiki organized this Journal Experiment 5 Part A: Bridge Circuits Part B: Strain Gauges Part C: Oscillation of an Instrumented Beam Part D: Oscillating Circuits Part A Bridges Thevenin Equivalent Circuits Wheatstone Bridge A bridge is just two voltage dividers in parallel. The output is the difference between the two dividers.

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A Balanced Bridge Circuit Thevenin Voltage Equivalents In order to better underst in addition to how bridges work, it is useful to underst in addition to how to create Thevenin Equivalents of circuits. Thevenin invented a model called a Thevenin Source as long as representing a complex circuit using A single “pseudo” source, Vth A single “pseudo” resistance, Rth A B A B Thevenin Voltage Equivalents This model can be used interchangeably with the original (more complex) circuit when doing analysis. The Thevenin source, “looks” to the load on the circuit like the actual complex combination of resistances in addition to sources.

The Battery Model Recall that we measured the internal resistance of a battery. This is actually the Thevenin equivalent model as long as the battery. The actual battery is more complicated – including chemistry, aging, Thevenin Model Load Resistor Any linear circuit connected to a load can be modeled as a Thevenin equivalent voltage source in addition to a Thevenin equivalent impedance. Note: We might also see a circuit with no load resistor, like this voltage divider.

Thevenin Method Find Vth (open circuit voltage) Remove load if there is one so that load is open Find voltage across the open load Find Rth (Thevenin resistance) Set voltage sources to zero (current sources to open) – in effect, shut off the sources Find equivalent resistance from A to B A B Example: The Bridge Circuit We can remodel a bridge as a Thevenin Voltage source A A B B Find Vth by removing the Load Let Vo=12, R1=2k, R2=4k, R3=3k, R4=1k A A B B

To find Rth First, short out the voltage source (turn it off) & redraw the circuit as long as clarity. A B A B Find Rth Find the parallel combinations of R1 & R2 in addition to R3 & R4. Then find the series combination of the results. Redraw Circuit as a Thevenin Source Then add any load in addition to treat it as a voltage divider.

Thevenin Method Tricks Note When a short goes across a resistor, that resistor is replaced by a short. When a resistor connects to nothing, there will be no current through it in addition to , thus, no voltage across it. Thevenin Applet (see webpage) Test your Thevenin skills using this applet from the links as long as Exp 3 Does this really work To confirm that the Thevenin method works, add a load in addition to check the voltage across in addition to current through the load to see that the answers agree whether the original circuit is used or its Thevenin equivalent. If you know the Thevenin equivalent, the circuit analysis becomes much simpler.

Thevenin Method Example Checking the answer with PSpice Note the identical voltages across the load. 7.4 – 3.3 = 4.1 (only two significant digits in Rth) Thevenin’s method is extremely useful in addition to is an important topic. But back to bridge circuits – as long as a balanced bridge circuit, the Thevenin equivalent voltage is zero. An unbalanced bridge is of interest. You can also do this using Thevenin’s method. Why are we interested in the bridge circuit Wheatstone Bridge Start with R1=R4=R2=R3 Vout=0 If one R changes, even a small amount, Vout 0 It is easy to measure this change. Strain gauges look like resistors in addition to the resistance changes with the strain The change is very small.

Using a parameter sweep to look at bridge circuits. PSpice allows you to run simulations with several values as long as a component. In this case we will “sweep” the value of R4 over a range of resistances. This is the “PARAM” part Name the variable that will be changed Parameter Sweep Set up the values to use. In this case, simulations will be done as long as 11 values as long as Rvar. Parameter Sweep All 11 simulations can be displayed Right click on one trace in addition to select “in as long as mation” to know which Rvar is shown.

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Part B Strain Gauges The Cantilever Beam Damped Sinusoids Strain Gauges When the length of the traces changes, the resistance changes. It is a small change of resistance so we use bridge circuits to measure the change. The change of the length is the strain. If attached tightly to a surface, the strain of the gauge is equal to the strain of the surface. We use the change of resistance to measure the strain of the beam. Strain Gauge in a Bridge Circuit

Cantilever Beam The beam has two strain gauges, one on the top of the beam in addition to one on the bottom. The stain is approximately equal in addition to opposite as long as the two gauges. In this experiment, we will hook up the strain gauges in a bridge circuit to observe the oscillations of the beam. Modeling Damped Oscillations v(t) = A sin(t) Modeling Damped Oscillations v(t) = Be-t

Hard Drive Cantilever The read-write head is at the end of a cantilever. This control problem is a remarkable feat of engineering. More on Hard Drives A great example of Mechatronics.

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