Performance-Based Assessments for AC Circuit Competencies

Use a square-wave function generator for the AC voltage source. I have built this circuit using resistances of approximately 4.7 kΩ and capacitances of approximately 0.1 μF, and achieved good results with a square-wave (fundamental) frequency of about 300 Hz. Of course, the R₁ resistance calculation is more challenging if the two capacitor values are unequal!

Incidentally, this circuit may be used to comparatively measure reactive components such as capacitors and inductors, since the square wave signal will be faithfully reproduced only when the R₁/R₂ ratio equals the X_C1/X_C2 or X_L1/X_L2 ratio. To be honest, the idea was not mine. I found it in an old book, the Electronics Manual for Radio Engineers, by Vin Zeluff and John Markus, first edition (1949), page 427. Apparently, the inventor of this ingenious impedance measurement technique was an employee of Allen B. DuMont Lab., Inc. named Peter S. Christaldi, who obtained a patent for the technique on October 15, 1946 (patent number 2,409,419 for those who are interested).

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.

When presenting this as a performance assessment for a group of students, you will need to show the voltage/current waveforms as part of the “given” conditions. A good way to do this is to use a PC-based oscilloscope to measure the waveforms, and then display the image using a video projector.

I have found that small synchronous AC motors such as those used in clock mechanisms and in some appliances (microwave oven carousels, for example) will run satisfactorily at 24 volts AC. Small shaded-pole motors such as those used in household bathroom fans and household appliances (microwave oven cooling fans, for example) may be operated in a relatively safe manner from low-voltage AC power by stepping the voltage up through a power transformer connected directly to the motor. Use a “step down” power transformer operating in reverse (as a step-up unit), with the higher voltage wires connected and taped to the motor so that the only “loose” wire connections are on the low-voltage side. Here is a power supply circuit I recommend for the task:

This circuit ensures the motor only receives about 60 volts, reducing shock hazard somewhat and allowing the use of capacitors rated for 100 volts (a common mylar capacitor rating). The smaller the motor, the less capacitance will be required to correct for power factor. Remind your students that the capacitors used in this exercise must be non-polarized, since they must operate on AC and not DC!

A shunt resistor value of 1 ohm is recommended, but not absolutely required. You just need a low-value resistor that will provide a ready point of measurement for current (with the oscilloscope) without imposing too much series resistance in the motor circuit.

This is a very simple yet effective exercise in demonstrating the effects of reflections in cables where the termination resistance (R_pot) is unequal to the cable’s characteristic impedance (Z₀). It is also an easy way to measure Z₀, by adjusting R_pot until a match is shown by an undistorted square-wave between points A and B.

I’ve used ordinary “zip cord” type speaker wire for this experiment. You can also use household extension cords or lengths of coaxial cable if you prefer. Coax has the benefit of already being rated for a specified impedance, unlike the other cable types listed. A length of 100 feet works well to produce time delays easily measurable with inexpensive oscilloscopes.

The purpose of resistor R₁ is to “swamp” the square-wave signal generator’s own Thévenin impedance, so it does not become a significant factor in the system. The maximum resistance of rheostat R_pot is really not that critical. I’ve easily achieved a match on speaker cable with Z₀ ≈ 136 Ω using a 10 kΩ potentiometer for R_pot. A 1 kΩ potentiometer would probably be best.

If you wish your students to be able to accurately predict the length of their cable from the waveshapes displayed by the oscilloscope, you need to determine the cable’s velocity factor beforehand, and write that value in the “Given conditions” section. Otherwise, you could have students infer velocity factor from cable length and oscilloscope measurements.