E11 Lab #5
In lab
2008

Before you start this lab, be sure to read the lab rules.

Second Order Time Domain Response
The rise (and fall) of the inductor

## Procedure:

Setting up the function generator

Connect a Wavetek signal generator directly to the oscilloscope.  Set the output of the signal generator to give a square wave that goes from 0 to 1 volt (the frequency isn't important for now).  If you don't get this correct your analysis will be more difficult.  If you are not sure you have it set properly, ask me.  If you don't recall how to do this, refer to the first lab.  After setting the amplitude and DC offset, don't adjust these knobs for the remainder of the lab.

### Part 1: A 2nd order RC circuit.

Remember: Don't change amplitude or DC offset of function generator!

Connect the circuit below with Vi coming from the function generator, R=100Ω, C=0.01μF, and L=112mH.  Set the frequency to about 100 Hz, then adjust it such that the circuit comes to equilibrium before the output changes.  For this circuit it is easier to use the large resistor and capacitor boxes than it is to use the breadboards.

1. Set the triggering so that a rising edge of the input is at the center of the screen (trigger on the input, slope set to rising edge)  and set your scales as large as is convenient so that you can get an accurate measurement.  Measure and record a screenshot showing the input and the output of your circuit.  You may also want to download the output data from the scope so you can do a curve fit (optional - a bit more work, but you'll get better results - and one extra credit point per fit).
2. From this data estimate α and ωd by measuring period and decay of oscillation.
3. Qualitatively observe how the behavior of the circuit changes if R is increased from 100Ω.  Is this what you expected?
4. Put R back to 100Ω and qualitatively observe how the behavior of the circuit changes if C is changed.
5. Put both R and C back to their original values and repeat part a for R=300, 1000, 3000 and 10000Ω.  It may be necessary to adjust the input frequency on the signal generator and the time scale on the oscilloscope so that the circuit comes to equilibrium.
6. For R=1000Ω estimate α and ωd by measuring period and decay of oscillation.
7. With R=100Ω, set the input frequency to about 4.6 kHz and describe what happens (no need to collect data).  Try to find the frequency for maximum output amplitude.
8. Simulate the circuit with R=100Ω and R=1000Ω with Multisim (when the input is a rising edge).  This needn't be done in lab.

### Part  2:  Eliminating the inductor

Remember: Don't change amplitude or DC offset of function generator!

Because the inductor is the least ideal component (and it is also very big), let's get rid of it.  Consider the circuit shown below.

It can be shown (i.e., you will do it for the write-up) that the circuit is defined by the differential equation:

This is the same form as the differential equation for the RLC circuit you built.  Not surprisingly, it behaves the same as well (with no inductors at all!).

Build the circuit with R1=1.2KΩ, R2=9.1kΩ, C1=0.1µF, C2=0.001µF.  Be neat with your wiring, and don't forget to connect power to the op-amp.

Repeat "a" and "b" from part 1 of the procedure.  The output should closely match one of the responses from the first circuit you used in the lab (which one?).

Simulate this circuit with MultiSim.  This needn't be done in lab.

## Before You Leave

Make sure the lab is cleaned up, and that you have all the information you will need for your report (see below).  Make sure the resistors are put back in the proper drawers -- either measure them with an ohmmeter, or read the color-code ( how to read the color-code).

Things you need for your report.

email me with any comments on how to improve the information on this page (either presentation or content), or to let me know if you had any particular difficulties with this lab.