Write the differential equation for the circuit above and obtain the characteristic
equation. Solve the characteristic equation and determine the type of damping.
Solve the differential equation for Vo assuming that Vi(t) = 5u(t). Determine the time constant.
Use MatLab to plot the solution for Vo. (Don't do this.)
Determine the resistor value required for critical damping.
Repeat steps 2 and 3 for this critically damped circuit.
Use PSpice to perform a transient analysis of this critically damped circuit. Use
Probe to plot Vo. Represent Vi with a constant 5 V source and a switch that closes at t = 0. You will need to set
the initial condition of the inductor and the capacitor.
Replace the resistor with a resistor half the value of the critically damped circuit
to produce an underdamped circuit.
Repeat steps 2, 3, and 6 for this underdamped circuit.
Equipment and Parts:
Signal Generator
Oscilloscope
Resistor: ~820 Ω
Capacitor: 0.56 μF
Inductor: 27 mH
Procedure:
Measure the internal resistance of the inductor. Choose a resistor so that the total
series resistance in the circuit produces the critically damped circuit.
Create the critically damped RLC circuit from the preparation on a proto board.
Use square wave generator for Vi. Set the amplitude for a 5 V step. Set the frequency so that half the period is greater
than five time constants. Record the frequency.
Observe Vo using the oscilloscope. Draw the waveform in your book.
Create the underdamped RLC circuit from the preparation on the proto board. Again,
use a resistor so that the total series resistance in the circuit is correct.
Use a square wave generator for Vi with a amplitude of 5 V. Set the frequency appropriately.
Observe Vo using the oscilloscope.
Conclusions:
Compare the theoretical, predicted (simulated), and measure waveforms and time constants.
If there are significant differences, suggest reasons why.
