# Electronics bootcamp II: feedback systems

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--Steven Wasserman (talk) 21:14, 27 October 2018 (CDT)

20.309: Biological Instrumentation and Measurement

## Time and frequency response of a feedback system

In the second part of the boot camp, you will build the circuit below and characterize its time and frequency response.

Overdamped Critically damped
Slightly underdamped Underdamped
1. Find the transfer function of the RC network inside the feedback loop (not including the amplifier). Use an appropriate approximation to dramatically simplify the algebra.
2. Find the transfer function of the entire system, including the amplifier, as a function of the amplifier's open-loop gain, A.
3. Build and test the circuit in the diagram.
4. Connect the output of a signal generator to channel 1 of an oscilloscope and also to the input of your circuit.
5. Connect the output of your circuit to channel 2 of the oscilloscope.
6. Set the function generator to produce a 100 Hz, square wave output with an amplitude of 100 mV.
7. Adjust Rgain (between pins 1 and 8 of the AD622 instrumentation amplifier) so that the system response is slightly overdamped.
8. Measure the frequency response of the system as you did in part 1 of the electronics bootcamp (Assignment 6).
9. Find the transfer function, the undamped natural frequency, and the damping coefficient.
10. Plot the data and transfer function (as you did in part 1)
11. Adjust Rgain so that the circuit is critically damped and repeat steps 6-8.
• To achieve critical damping, start with an over damped response and vary Rgain by turning the potentiometer until there is a slight overshoot in the response. Then turn the potentiometer back until the overshoot just disappears.
12. Adjust Rgain so that the circuit is slightly underdamped (two or three overshoots) and repeat steps 6-8.
13. Adjust Rgain so that the circuit is underdamped with at least a dozen or so overshoots and repeat steps 6-8.