E11 Lab #5
Second Order Time Domain Response
This lab requires a formal lab report.
If you are having a lot of trouble with part of the report,
please come see me. I don't want the writing of the lab report to be an
exercise in frustration, so if you get stuck, please don't hesitate to ask for
help. Also, if you find you are missing some data, or it just doesn't make
sense, please talk to me before finishing your report.
Be sure to include in your report:
(you should think quite hard about the organization of the
Derivations of differential equations for the two
circuits (RLC and op-amp).
Solutions of the differential equations; one for ζ<1 and one for ζ>1.
All pertinent oscilloscope data.
All the Multisim simulations that you performed (in a way
that can be easily compared to corresponding oscilloscope outputs and
- Calculations and plots of the expected response
(using the expected values of ω0 and ζ).
Compare the expected response to the screen shots (e.g., show them side
by side). Compare expected and experimental values of α and ωd for the
cases where R=100 and R=1000 Ω.
- A best fit of the data collected from the oscilloscope. From
the fit determine ω0 and ζ, and compare to the
expected values (note: you can use the expected values as the
initial guess for the fit). You should also compare the
best fit parameters with values of α and ωd taken directly
from the step response (by measuring period and decay of oscillations) for the
cases where R=100 and R=1000 Ω, and for the op-amp circuit.
You will get one point of extra credit for each successful curve fit.
- In either case, note that the form of the equations representing the
output are different for ζ<1 and ζ>1.
- Direct comparison of theory and experiment whenever possible.
- Describe the qualitative effects of varying C and R in first circuit
(and give a brief explanation).
It may be helpful to recall that the Wavetek function
generator can be modeled as shown (where Vs is an ideal source):
Grading sheet for
(increased points for theory and results)
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any particular difficulties with this lab.