Unit 3: Linear Circuits, Sinusoids, and Frequency Response

Topics

These are the core topics for Unit 3. These topics are what what would be covered in the exam for Unit 3.

• Fourier Transform and Frequency Response
• Sinusoids and Linear Circuits
• Designing R, L, C circuits (e.g. Filters)

This project focuses on the dynamics of a second-order low-pass circuiti (Fig. 1). The time constant for the main resistor, R, and main capacitor, should be 2-5ms resulting in a corner frequency around 100Hz. The value for R is recommended to be in a range of 100kΩ. R_a should be set with a potentiometer to allow for a range of resistances and/or a number of different resistor values. If one has a small resistance potentiometer, the two resistors in the amplifier with R_a can also be smaller with no issue.

The project writeup will be limited to three pages.

The writeup should not be a repeating of this document and filling in a sentance along those lines.

The project must be done as a group of two unless given previous approval by the Professor.

You need to have the analytic solution for the step response and for the frequency response to find the right values and have the right analysis when using this circuit.

Op-amps, or at least approximations of them, are actually physical devices, typically made from transistor circuits. 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.

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.

It will be valuable to look at the projects from previous years. Previous year projects ( 2019 , good examples a & b ) and ( 2020 ). The good writeups were not perfect, although they were good examples of the better writeups for that semester.

Figure 1: The second-order circuit for this experimental project. Three op-amp circuit with a tunable resistor, Ra. All of the resistors are identical. The other two resistors (R) with the inverting amplifier with Ra could be modified if that helps finding a desired tunable potentiometer.

First, build the ciruit (Fig. 1) initially without the op-amp that has R_a.

• Analyze for the transfer function, step response, and frequency response for this circuit.
• Step Response : Measuring the step response of this circuit. Having a 0.5V input step on a reasonable constant voltage level is recommended. Curve fit (need a semilogy( ) curve fit) for the circuit timeconstant(s).
• Frequency Response : Take a frequency response of this circuit. Ideally one should use a tool will have an automatical way of inputing a sinusoid of one frequency, and measure the result with some accuracy. Show the curve fit measurement agrees with expected theory.

Next, build the ciruit (Fig. 1) initially with R_a a tunable resistor such as a potentiometer (that you can measure separately). For some measurements, you might want to use an explicit resistor for R_a.

• Analyze for the transfer function, step response, and frequency response for this circuit.
• Repeat the Step Response , and Frequency Response measurements for at least three different Q values that are greater than 1, and have one value greater than 4. Compare the measurements with analytical results. What are the complex roots for each Q? Does the center frequency change significantly? Does the passband gain change significantly?