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Impedance Matching With Transformers
19 questions By Tony R. Kuphaldt
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Question 10 of 19
An audio power amplifier with an internal impedance of 8 Ω needs to power a set of speakers with a combined total impedance of 1 Ω. We know that connecting this speaker array directly to the amplifier’s output will not result in optimum power transfer, because of the impedance mismatch.
Someone suggests using a transformer to match the two disparate impedances, but what turns ratio does this transformer need to have? Should it be used in a step-up configuration, or a step-down configuration? Explain your answers.
Reveal answer2.83:1 winding ratio, step-down.
Notes:Students should know at this point how to calculate the impedance transformation ratio from a transformer’s winding ratio. In this question, they are challenged to calculate “backwards” to find the winding ratio from the impedance ratio.
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Question 11 of 19
A mechanic goes to school and takes a course in AC electric circuits. Upon learning about step-up and step-down transformers, he makes the remark that “Transformers act like electrical versions of gears, with different ratios.”
What does the mechanic mean by this statement? What exactly is a “gear ratio,” and how does this relate to the subject of impedance matching?
Reveal answerJust as meshing gears with different tooth counts transform mechanical power between different levels of speed and torque, electrical transformers transform power between different levels of voltage and current.
The concept of “impedance” is just as valid in mechanical systems as in electrical systems: a “low impedance” mechanical load requires high speed and low torque, whereas a “high impedance” load requires high torque and low speed. Gear systems provide impedance matching between mechanical power sources and loads in the same way that transformers provide impedance matching between (AC) electrical power sources and loads.
Notes:Not only is this a sound analogy, but one that many mechanically-minded people relate with easily! If you happen to have some mechanics in your classroom, provide them with the opportunity to explain the concept of gear ratios to those students who are unaware of gear system mathematics.
I normally do not elaborate this much in my answers, but in this case I believe it may be necessary, as this is quite a cognitive leap for some people. It is a leap well worth making, however, since it connects two (seemingly) disparate phenomenon in a way that provides a sound context for understanding the concept of impedance matching.
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Question 12 of 19
One of the practical uses of transformers is to adapt equipment to conditions not anticipated in their original design. For instance, a heating element (which is essentially nothing more than a resistor with an unusually high power dissipation rating) may need to be operated at a lower power dissipation than designed for.
For example, suppose you have a 1 kW electric heater rated for 208 volt operation, which you intend to operate at a reduced power dissipation of 750 watts. Calculate the proper amount of voltage you would need to achieve this reduced power dissipation, and explain how you could use a transformer to supply this reduced voltage to the heater.
Reveal answerThe necessary voltage to make this 1 kW heater operate at only 750 W is approximately 180 volts.
Notes:Some students may struggle in calculating the necessary voltage, because this problem does not exactly match most voltage/current/power calculations problems they’ve seen in the past. The necessary math is almost trivial, but the “trick” is applying well-known equations to something unfamiliar. This is an excellent opportunity to discuss problem-solving strategies, so be sure to have students share their ideas on how to solve for the necessary voltage.
