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First Order RL and RC Circuit 7.1-7.4,7.5, 7.7

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Natural Response Definition: The currents and voltages that arise when stored energy in an inductor or capacitor is suddenly released to a resistive network

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RL Circuit The switch opens at t=1S

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Switch Setting The switch opens at t=1 Name of switch: sw_topen ROPEN=1 Mohms RCLOSE=0.01 Ohms

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Transient Simulation Run a transient simulation from 0 to 10 s

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Use Probe to Measure V

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Simulation Results For t<1S, current (1A) flow through L1, generating a VIN and VOUT=0. At t=1S, the current through L1 is 1A, so Vout=1V. At t>1S, VIN=-1V. What if you increase R2 by 10 times?

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R2=1 Ohms R2=10 Ohms

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L/R Constant The rate that Vout drops to zero is related to L/R time constant. – The smaller the L/R time constant, the faster Vout drops to 0. – R2=10Ohms results in a circuit that drops to zero faster than R2=1 Ohm

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Natural Response of RC Circuit C1 is charged until about t=2. C1 starts to charge at t=5.

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Simulation Results VX=Vout after t=5! VX does not discharge between t=2-5S.

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Purposely Discharge C1 Between Switching Events

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Step Response Definition: The currents and voltages that arise when energy is being acquired by an inductor or capacitor due to the sudden application of dc voltage or current source.

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Step Response of an RL Circuit

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Vout & Vin t=0

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Measurement Result

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Step Response of a RC Circuit

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Step Response of an RC Circuit Note that the voltage across the capacitor is initially zero because Q can not change instantaneously.

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C=1 F C=2 F V=Q/C

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Experiment 1 (Large) No Voltage divider

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Experiment 2 (change to 3) (Takes longer go charge, Less current is available)

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R5 At DC, the op-amp is not able to provide feedback. Thus V- is not equal to V+. A resistor should be added in parallel of C1 so as to provide feedback at DC.

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Select value of R5 This term should be minimized.

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Choice of R5 R5=330 Kohms C1=92 nF R5=1 Kohms C1=92 nF

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Exam review Inductors, EM oscillations

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