Explanation of Electrical Impedance
Date: 03/26/2004 at 17:47:51 From: Heather Subject: Impedance What exactly is impedance? I understand that it is the resistance of an AC signal. I just don't understand how it works or doesn't work and why or why not. For instance, we had a speaker blow and I was told that it was because of the impedance. I've been asking as many people as I know to explain it to me but no one can seem to explain it in a way I can understand. So, any help I could get here would be wonderful.
Date: 03/26/2004 at 21:55:16 From: Doctor Douglas Subject: Re: Impedance Hi Heather. Thanks for writing to the Math Forum. Impedance has the same units as resistance, but resistance is only one component (the "real" component) of it. There is another component that is 90 degrees out of phase (the "imaginary" component) that is called the reactance. Both components have units of "ohms". Roughly speaking, the impedance is the ratio between the voltage amplitude and the current amplitude. If these two quantities are exactly in phase (the current and voltage have their maxima simultaneously), then the ratio is purely real and is called resistance. But in general, these two quantities will not be in phase, and you need to use the impedance to completely describe the situation. For a mechanical analogy, consider riding a bicycle that has many choices of gears. If you are in too low a gear, your legs will spin with little effort, but you will move forward slowly. The pedals present a very low impedance to your feet. If you are in too high a gear, your legs will feel the "resistance" of the gears (high impedance), and you will move forward slowly because it is difficult to grind out any progress. But a gear that is not too big and not too small--just right--allows you to maximize the power transfer from legs to wheels, and allows you to make the greatest progress. Sometimes you want the driven system to have high impedance (e.g. an oscilloscope), sometimes you want the driven system to have low impedance (e.g. current-carrying coils), and sometimes you want the driven system to be well matched to your signal source (e.g. bicycles, or audio speakers) in order to maximize power transfer. Improper impedance matching can have damaging effects: for example, your speakers may have had a 4 ohm impedance, while your amplifier was expecting 8 ohms of impedance--if this were the case, the amplifier will have delivered a lot of excess current into the speaker coils, possibly heating something up and destroying the speaker. In the analogy of the bicycle, you may have spun the pedals so rapidly that the chain falls off the chainwheel, rendering the bike useless. I hope that this helps give you a better feel for what impedance is. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.