Unit 3: Linear Circuits, Sinusoids, and Frequency Response

Previous Laboratory Experiment, Spring 2019

This project primarily gets the students comfortable with measurement and resulting analysis of second-order dynamics in linear circuits.

Resistive Divider
Figure 1: Circuits for lab measurement. (a) Basic op-amp circuit being used as a follower circuit, a circuit that has a gain of one. This circuit isolates the circuit from the sourcing electronics. (b) Test circuit to measure the follower circuit. (c) RLC second-order circuit for this laboratory exercise.

This project we will use the op-amp, but only as a buffer. First, the op-amps, or at least approximations of them, are actually physical devices, typically made from transistor circuits. As you remember from class, an op-amp is configured as a buffer by connecting the - terminal to the output terminal. Then the + terminal is the input, and the output terminal is the output. The key is for your op-amp chip to find pins for the positive and negative inputs and output terminals. Remember the circuit requires power supply pins. Either +5V, -5V or +15V, -15V will work.
You need to make sure the pinout you are using for your op-amp. There are standards, but you need to know which one you are using. Pin 1 is marked by stamp or mark near that pin.
081 series op-amp is a single op-amp in a package. The inputs are on pin 2 (-) and pin 3 (+), and the output is pin 6. V_dd+ is pin 7 and V_dd- is pin 4.
082 series op-amp is a dual op-amp in a package. V_dd+ is pin 8 and V_dd- is pin 4. The inputs of op-amp 1 are on pin 2 (-) and pin 3 (+), and the output is pin 1. The inputs of op-amp 2 are on pin 6 (-) and pin 5 (+), and the output is pin 7.
Validate your op-amp circuit setting up a circuit in Fig. 1b, and measure the output voltage as a function of input voltage. Find the slope through a curve fit and include a plot with these details. Explain any other aspects you might notice (e.g. offset).
Set up the second-order filter circuit in Fig. 1c. We will use this circuit for a number of experimental measurements. A short test of this circuit would be to notice that the output is nearly equivalent to the input.
Start by measuring the step response of this circuit. Having an input step from 0.5V to 1.5V would be appropriate. Are the roots of this physical differential equation real or complex? How do you know? What are the roots or center frequency and quality factor? On the plot, identify key regions of this graph.
Frequency response . First, choose a single frequency near the center frequency and show the resulting sinusoidal output and input signals as a function of time. You might want to try a couple of different frequencies to see the difference and see the amplitude and phase changes. Take a frequency response of this circuit. The tool will have an automatical way of inputing a sinusoid of one frequency, and measure the result with some accuracy. You need to find the right frequency for sweeping the frequency to optimally see the dynamics. Compare the results of this graph, and find center frequency and resonance from the graphs.
Next, we will take two additional curves. You will want to look at the behavior initially as step responses, and when we have a good step response, we should take a frequency response. In one case, replace the 1KOhm resistor with a 50Ohm resistor. In the second case, replace the resistor with two terminals of the trimpot, and tune the pot to see different responses. Have fun moving through the different step responses. Have all frequency responses (3 together; if more than three, maybe they could be in two curves) that show the effect of changing R while keepin L and C constant. Compare center frequency to L and C.
Older documentation and problem assignments . You don't have to complete any of these items explicitly, although they might be helpful for what is required by this assignment, as well as some documentation on creating these measurements.