First Order RL and RC Circuit

7.1-7.4,7.5, 7.7

Natural Response

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

RL Circuit

The switch opens at t=1S

Switch Setting

The switch opens at t=1

Name of switch: sw_topenROPEN=1 MohmsRCLOSE=0.01 Ohms

Transient Simulation

Run a transient simulation from 0 to 10 s

Use Probe to Measure V

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?

R2=1 Ohms

R2=10 Ohms

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

Natural Response of RC Circuit

C1 is charged until about t=2. C1 starts to charge at t=5.

Simulation Results

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

Purposely Discharge C1 Between Switching Events

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.

Step Response of an RL Circuit

Vout & Vin

t‘=0

Measurement Result

Step Response of a RC Circuit

Step Response of an RC Circuit

Note that the voltage across the capacitoris initially zero because Q can not change instantaneously.

C=1 F

C=2 F

V=Q/C

Experiment 1

(Large)

No Voltage divider

Experiment 2

(change to 3)

(Takes longer go charge,Less current is available)

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 providefeedback at DC.

Select value of R5

 

This term should be minimized.

Choice of R5

R5=330 KohmsC1=92 nF

R5=1 KohmsC1=92 nF