Performance-Based Assessments for AC Circuit Competencies

Here, students must calculate values for C₁ and R₁ that will produce the V_out waveshape specified in the “Given conditions” oscilloscope plot. The input signal, of course, is a square wave.

If the chosen circuit is a differentiator, students must calculate the time constant of the circuit (τ) such that the pulse fully decays within the pulse width (half-period) of the square wave. With 5 τ being the accepted standard for full charge/discharge of a time-constant circuit, this is an easy calculation.

If the chosen circuit is an integrator, students should be able to show mathematically why the time constant of the integrator (τ) must be 69.3% of the waveform’s half-period. Instructors, note: the calculations for this circuit, with V_out = ¹/₃V_in, are exactly the same as for a 555 timer circuit, because 555 timers also cycle their capacitors’ voltages at peak-to-peak values equal to one-third of the supply voltage.

There are many different combinations of values for C₁ and R₁ possible for any given square-wave signal frequencies. The purpose of this exercise is for students to be able to predict and select practical component values from their parts kits.

An extension of this exercise is to incorporate troubleshooting questions. Whether using this exercise as a performance assessment or simply as a concept-building lab, you might want to follow up your students’ results by asking them to predict the consequences of certain circuit faults.

The longer the cable, the better the coupling between the motor conductors and the other conductors. I have found that this exercise is practical with just a few feet of four-wire telephone cable.

It is very important to use a battery for this exercise, and not an AC-DC power supply. The filter capacitors in an AC-DC power supply naturally decouple the motor’s noise voltage, making it difficult to measure any at all!

Noise voltage should be measured with an oscilloscope set to AC input coupling, and recorded as peak-to-peak volts.

You may use an audio frequency impedance matching (1000:8 ohms) transformer or a step-down power transformer for this exercise. In either case, students need to know or figure out the turns ratio before proceeding with the experiment. If you are using an audio transformer, use a sine-wave signal generator for the voltage source, but avoid frequencies below 1kHz. If you are using a power transformer, use a Variac to provide adjustable primary voltage.

An extension of this exercise is to incorporate troubleshooting questions. Whether using this exercise as a performance assessment or simply as a concept-building lab, you might want to follow up your students’ results by asking them to predict the consequences of certain circuit faults.