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# exp05 - Electronic Instrumentation Experiment 5 Part A...

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Electronic Instrumentation Experiment 5 * Part A: Bridge Circuits * Part B: Potentiometers and Strain Gauges * Part C: Oscillation of an Instrumented Beam * Part D: Oscillating Circuits

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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. B A out S B S A V V dV V V R R R V V R R R V - = = + = + = 4 1 4 3 2 3

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A Balanced Bridge Circuit 0 2 1 2 1 1 1 1 1 1 1 1 1 = - = - = + = + = V V V V dV V K K K V V K K K V right left right left
Thevenin Voltage Equivalents In order to better understand how bridges work, it is useful to understand how to create Thevenin Equivalents of circuits. Thevenin invented a model called a Thevenin Source for representing a complex circuit using A single “pseudo” source, Vth A single “pseudo” resistance, Rth RL 0 Vo R4 R2 R1 R3 Vth 0 Rth Α Β Α Β

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Thevenin Voltage Equivalents This model can be used interchangeably with the original (more complex) circuit when doing analysis. Vth 0 Rth The Thevenin source, “looks” to the load on the circuit like the actual complex combination of resistances and sources.
The Battery Model Recall that we measured the internal resistance of a battery. This is actually the Thevenin equivalent model for the battery. The actual battery is more complicated – including chemistry, aging, … V1 10.2V R1 0.4ohms 0

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Thevenin Model Vs RL Rs 0 Load Resistor Rth Vth 0 RL Any linear circuit connected to a load can be modeled as a Thevenin equivalent voltage source and a Thevenin equivalent impedance.
Note: We might also see a circuit with no load resistor, like this voltage divider. R2 0 R1 Vs

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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 Vth 0 Rth A B
Example: The Bridge Circuit We can remodel a bridge as a Thevenin Voltage source RL 0 Vo R4 R2 R1 R3 Vth 0 Rth Α Α Β Β

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Find Vth by removing the Load RL 0 Vo R4 R2 R1 R3 0 Vo R4 R2 R1 R3 A A B B Let Vo=12, R1=2k, R2=4k, R3=3k, R4=1k V B k k k V = + = 1 1 3 1 2 3 V A k k k V = + = 4 4 2 1 2 8 V t h V A V B V = - = - = 8 3 5
To find Rth First, short out the voltage source (turn it off) & redraw the circuit for clarity. 0 R4 R2 R1 R3 A B R3 R4 R2 R1 A B

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Find Rth Find the parallel combinations of R1 & R2 and R3 & R4. Then find the series combination of the results. R R R R R k k k k k k 1 2 1 2 1 2 4 2 4 2 8 6 1 3 3 = + = + = = . R R R R R k k k k k k 3 4 3 4 3 4 1 3 1 3 3 4 0 7 5 = + = + = = . R t h R R k k = + = + = 1 2 3 4 4 3 3 4 2 1 .
Redraw Circuit as a Thevenin Source Then add any load and treat it as a voltage divider. 0

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