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/