AC Electric Circuits

Impedance Matching With Transformers

19 questions By Tony R. Kuphaldt

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Question 13 of 19

Suppose you were using a 600 watt, 120 volt electric heater to pre-heat the oil in a hydraulic system, but determined later that this heater delivered too much heat to the oil. A 400 watt heater would be more appropriate for the task, but unfortunately another heater is not available in that power rating.

You realize that the power output of this 600 watt heater could be reduced by supplying it with less voltage. You also realize that a transformer could be used to reduce the AC voltage delivered to the heater without incurring the large power losses of a voltage-dropping resistor.

The following transformer types are available to use for the task:

Design a circuit that uses one or more of these transformers to reduce the line voltage (120 VAC) down to an appropriate level so that the 600 watt heater will only output (approximately) 400 watts.

Reveal answer

You should have calculated a heater voltage of 98 volts necessary to produce 400 watts from the same heater that outputs 600 watts at 120 volts. It is possible to reduce 120 volts down to approximately 98 volts using the transformers shown here. Perhaps the most direct solution is to connect one of these units in a “bucking” configuration.

There is more than one possible solution to this problem using the transformer types available. You should realize, though, that there is more to consider than just getting the right voltage. Equally important to the solution is the transformers’ ability to handle the current demanded by the heater.

Notes:
A problem such as this is very realistic: having to engineer a solution to a practical dilemma with a limited choice of components. Let your students know that solving problems in real life involves creativity just as much as it involves mathematical calculations and other “closed form” (single right answer) methods.
Question 14 of 19

A simple pair of audio headphones makes a remarkably sensitive and useful piece of test equipment for detecting signals in a wide variety of circuits. Even very small DC voltages may be detected with a pair of headphones, if you listen for a “click” sound when contact is made or broken between a voltage source and the headphone’s test probes.

Yet, a plain pair of headphones is unsuitable for many test applications for two reasons:

Electrical safety

Low impedance

It is generally not a good idea to place your body in a position where it may come into direct contact with a live circuit, especially if that circuit harbors substantial voltages. Being that headphones are worn on a person’s head, with the potential for electrical contact between one of the speaker elements and the wearer’s head, this is quite possibly unsafe.

Secondly, the impedance of a high-quality headphone set is generally 8 ohms. While being a common audio speaker impedance, this low value would place far too great of a “burden” on many types of electronic circuits if directly connected. What is desired for a piece of test equipment is 1000 Ω or more.

Explain how a transformer may be inserted into the headphone test circuit in such a way as to address both these problems.

Reveal answer

Follow-up question: even though a pair of headphones used in this manner cannot provide quantitative measurements of signals, there are some qualitative features which a skilled user may discern from the sounds produced. Describe what features of an AC signal may be detected with headphones, and how this compares to the information obtained from an oscilloscope.

Notes:
This question reviews both the principles of impedance matching and electrical isolation, in addition to exposing students to a novel and inexpensive piece of test equipment they can build on their own. I highly recommend making the construction and use of one of these devices a lab project in your curriculum. I use a headphone test set regularly in my own experimentation, and I have found it very useful in understanding AC phenomenon (especially if you do not have your own oscilloscope).

The circuit I recommend for students to build is this:

The 1 kΩ resistors and 1N4001 rectifying diodes provide protection against hearing damage, by limiting the voltage which may be applied to the primary winding of the transformer. The potentiometer, of course, provides volume control, while the transformer steps up the headphones’ impedance and provides electrical isolation. I recommend a 120 volt power transformer for the task because it is rated for line voltage, and will surely provide the necessary isolation between circuit and headphones necessary for safety. A regular 8:1000 ohm “audio transformer” is not necessarily rated for the same (high) levels of voltage, and therefore would not provide the same margin of safety. For best performance, use a pair of headphones with the greatest “sensitivity” rating (measured in dB) possible.
Question 15 of 19

This is an interesting application of a transformer:

With this circuit, power to the AC load may be controlled by the variable resistor’s setting:

Calculate the amount of series impedance the transformer places in the load current’s path, if the variable resistor is set to a resistance of 15 ohms, and the winding ratio is 20:1.

Reveal answer

0.0375 Ω

Follow-up question identify any potential safety hazards associated with using a transformer in this capacity.

Notes:
Ask your students to think of a practical application for a circuit like this. Also, challenge them with this question: if the resistor were to open fully (∞ ohms), would current to the load completely stop? Why or why not?