ELEC 320, Fall 2006
Profs. Wismer & Kozick
Impulse Response: Analysis, Measurement, and Matlab Simulation
The main objective in lab this week is
to learn about the impulse response
of continuous-time, linear, time-invariant systems.
You will determine the impulse
response of an RC circuit two ways,
analytically and experimentally.
Then you will use the analytical unit impulse response expression in
Matlab (or another computer programming environment)
to simulate the unit step response of the RC circuit, using
the properties of linearity and time invariance.
Please work in pairs on these lab exercises.
Lab Reports: Each pair of
students is required to
submit a report explaining your answers to items 1 and 2
at the beginning of your next lab meeting on
October 2 or 4.
- Consider a series RC circuit driven by a voltage source,
with the output voltage measured across the capacitor.
We will use R = 10 kohms and C = 0.1 microfarads.
- Analyze this circuit and derive the expression for
the unit impulse response, h(t), which is defined as the output
that occurs when the unit impulse function, delta(t), is applied
at the input.
In your analysis, consider applying a rectangular pulse that gets
briefer and briefer while maintaining a constant area.
Prof. Kozick did this in lecture, but you should repeat the analysis
and make sure you understand all of the steps.)
- Devise a procedure to experimentally measure the impulse response
of the circuit.
Hint: Use the pulse-mode of the function generator and adjust
the amplitude, duty cycle, offset, and frequency appropriately to make
pulses that are much shorter than the time constant.
Try using pulses with area on the order of 0.0001 volt-seconds.
- Measure the impulse response of the circuit using the
What happens to the measured impulse response when you reduce
the input duration by one-half and double the amplitude, so that
the area remains constant?
Next we consider the unit step response of the RC circuit.
- Obtain the analytical formula for the unit step response.
You did this in ELEC 225-226 in the context of "closing a switch" and
solving the differential equation.
This will give you a chance to review how to solve those problems.
- Measure the unit step response by applying a square wave input to
the circuit, and compare with your analytical formula.
- Write a Matlab (or other) program to simulate the unit step
response using the unit impulse response.
You can do this by dividing the unit
step function into a sum of rectangles, where each rectangle is
an amplitude-scaled and time-shifted impulse function.
Then use the
fact that the RC circuit is a linear and time-invariant system.
In Matlab (or Excel), plot the numerically approximated unit step response and
compare it with
the analytical unit step response on the same graph.
You may use a programming environment other than Matlab
(such as Java, Excel, or something else) if you prefer, but we may
not be able to provide as much help with other environments.