University of Central Oklahoma: ENGR 3324L
Lab 3: Linear Time Invariant Continuous System (LTIC)
(Two Weeks Lab)
Lab objective:
1- Learn how to derive the mathematical expression of the system impulse response,
2- Learn how to calculate and measure the system total response to a step function input,
3- Examine the effect of circuit components on the system response.
Prelab:
System response in the time domain of a unit step input (Mathematical Analysis)
For the system shown in Fig. 1 find the following:
a) the impulse response h(t),
b) plot the impulse response
c) the total output y(t), if the input x(t) is the unit step function 5u(t) and y(0-) = dy(0-)/dt = 0,
d) repeat parts a to c when the value of the resistor is 0.2 KΩ.
e) What is the effect of L, R, and C on the characteristic roots and the system response?
f) What is the value of R that will minimize the time constant and does not cause the output to oscillate?
Suggestion: To answer f, I suggest you to express the mathematical equation for the impulse response h(t) in
terms of R, L, and C, and then plot h(t) for different values of R and determine which value of R that makes h(t)
decay to zero at faster rate without oscillation.
Hint in Matlab: You can use Matlab to find the characteristic roots for any differential equations.
Example: You can find the characteristic roots for D3 + 5D2 + 44D + 40 = 0 as
>> r = roots([1 5 44 40])
R
L
x(t)
+
Fun.
Gen.
_
R = 5 KΩ ,
C = 100 nF,
L =100 mH
+
y(t)
_
C
Fig. 1
Lab Procedures:
Task 1: System response in the time domain of a unit step input (Multisim Simulation)
Simulate the circuit shown in Figure 1 using Multisim for R = 5 KΩ and 0.2 KΩ. The input to the circuit
x(t) is a square wave with 5 V amplitude and 60 Hz frequency.
a) Plot the outputs for R = 5 KΩ and 0.2 KΩ.
b) What is the effect of R on the characteristic roots and the system response?
c) Measure the time constant of the system for R = 5 KΩ and 0.2 KΩ. Remember the time constant is
the time it takes the output to reach 63% of its final value.
d) Find the oscillation frequency of the output when the resistor value is 0.2 KΩ.
e) Compare the time constants and the oscillation frequency with the values calculated from the
mathematical expression found in the prelab section.
Task 2: System response in the time domain of a unit step input (Physical Circuit)
Build the system shown in Fig.1 with the following components values R = 5 KΩ, C = 100 nF, and L = 100 mH.
1- With the equipment in our lab we can’t generate a unit step function. However, if we apply a pulse using
the TTL output of the function generator with a long period (T > 5 * time constant of the system), then the
moment the signal change from zero to 5 volt resembles a unit step function 5u(t). Set the frequency of
the pulse wave to 60 Hz.
2- Use channel 1 to display the input and channel 2 to display the output y(t). Plot the output y(t) for the
positive cycle of the input x(t). Make sure to label in your plot the voltages of the output at 5 different
instants of time.
3- Does the output y(t) in step 2 agree with the mathematical expression of the output found in part c of the
prelab. Compare the two plots. Compare the measured and calculated time constants.
4- Change the values of the resistor to 0.2 KΩ and repeat steps 1 and 2. What causes the output to oscillate?
What is the frequency of oscillation? In the prelab you found the mathematical expression of y(t) for the
0.2 KΩ resistors. What is the mathematical variable that determines the oscillation frequency?
{In your lab report include only the work of the prelab and task 2. You need to draw the circuit, inputs,
and outputs waveform. Answer all questions in the prelab and task2.}
Lab 03
Linear Time Invariant Continuous System (LTIC)
INSTRUCTOR VERIFICATION SHEET
Turn this page in with your lab report to your Instructor.
Name:
Date of Lab:
Task 1: Plot the output for R = 0.2 KΩ and indicate the time constants and the frequency of
oscillation.
Verified: ______________________________
Task 2: Plot the output for R = 5 KΩ and indicate the time constants and the frequency of
oscillation.
Verified: _________________________
Part 2: Plot the output for R = 0.2 KΩ and indicate the time constants and the frequency of
oscillation.
Verified: _________________________