[Noisebridge-discuss] Amplification Design

[Jake]

sure no prob rob!  i will do my best to make up a good answer.

impedance is what we call the "resistance" of a load _at frequency_.

so where a 5 ohm resistor is 5 ohms at DC (meaning a simple multimeter 
test shows it's 5 ohms) you could say that's its resistance, or you could 
say that's its impedance - either way.

BUT if you have a speaker, and you measure it with the ohm-meter, you 
might get any number - it will probably be near the 4-ohm or 8-ohm of the 
label, but that's not necessarily the case.  What you measure with the 
ohmmeter is the speakers' resistance.  What it acts like _at frequency_ is 
its impedance.

let's say you decide to measure the speaker's impedance at 5 KHz.  You 
take a ten-volt AC sinewave at 5 KHz and feed it through (in series with) 
a 1-ohm resistor to the speaker.  The speaker is making a deafening sound 
and you measure the voltage across the resistor and see 1 volt AC (RMS).

you know the resistor is 1-ohm and the resistor has 1-volt AC across it.
which means there is 1 amp (AC RMS) flowing through the circuit.
you know the supply is giving ten volts AC, so you subtract the 1 volt 
across the resistor and you say the speaker is doing 9V AC at 1 amp.
You know that 9 volts divided by 1 amp = 9 ohms.  The speakers' impedance 
at 5 KHz is 9 ohms.

Now let's say you go outside, and the air is denser with humidity.  Since 
the air is heavier, and the speaker has to do more work (more force) to 
move the same amount of air, it means the amount of current will go up - 
because current corresponds to force in an electromagnet.  So the same 
experiment will show the speaker taking 1.0000000000000001 amp instead, 
and you calculate that its impedance is now 8.99999999999999 ohms!

The speakers' impedance is affected by the air, because the speaker is 
passing through the power into the air.  same thing with a radio antenna, 
which at DC is just pieces of metal, maybe touching maybe not, but at 100 
MHz the impedance may be 50 ohms.

another thing about impedance - it can be a complex number.  what's the 
impedance of a capacitor?  or an inductor?  Well at DC a capacitor is 
infinite ohms and an inductor is 0 ohms.  But as the frequency goes up, 
their impedance changes... but only reactance, not resistance.

think of the real number of the impedance of something as the ohms by 
which energy disappears through that thing out of the circuit (a resistor 
radiates away heat, a speaker sends sound out into the world).  The 
complex number of the impedance is called the reactance, and is either 
capacitive or inductive.  A capacitor or inductor shouldn't get hot 
because it's not burning up energy, it's just redirecting it like a spring 
does - or a flywheel.

fortunately you can just model your speaker as a resistor for the whole 
audio band and forget everything i just wrote.. for now.  that means if 
you want to know how much loudness you're getting from your speaker, you 
can just measure the voltage across it and calculate the area under the 
curve.  Use ohms' law.

one thing you may not have realized though, is that the average voltage 
across your speaker must be zero.  otherwise the speakercone is trying to 
push out or pull in the whole time, and it's not able to move freely.  If 
one side of your speaker is tied to ground and the other side to a pin 
going only between 0 and a positive voltage, you should put a capacitor in 
series with the speaker.  That will fix the average voltage across the 
speaker.  If you want it to work perfectly across the whole audio band, 
choose a capacitor of infinite farads with zero ESR.  If you can't find 
that, just use something that, at the frequencies you are using, is a 
reasonably small number of ohms compared to the speaker.  You can 
calculate the impedance (in ohms) of a capacitor based on its capacitance 
and the frequency you're working at.  I forget the formula though.

if you use two gpio lines of your microcontroller, your speaker will see 
the difference between those lines.  If the lines are inverted of one 
another, and the speaker sees an average of 0 volts across it, you don't 
need the series capacitor.  another advantage of this is that the voltage 
across the speaker will be higher, if you think about it.  draw yourself a 
chart.  It's hard to look at it on the scope though, because the scope 
normally references its inputs to ground and if both wires of the speaker 
are moving relative to ground.. you see the complication.  So draw it out, 
and once you understand it that well, we can see how to get it on the 
screen of the scope (it can be done).

I hope this helps.  please write back with more questions.

-jake

On Fri, 13 Jul 2012, Robby wrote:

> Dear Jake,
> What's up? So I got the sound play back working that I described in the
> noisebridge discuss, but now I need to amplify it to play it out of a small
> 8 ohm 0.1 watt speaker. I used a darlington npn arrangement to sink the
> speaker and that worked to amplify.. just not as much as I need. I was
> thinking op - amp or some kind of transistor arrangement like an H bridge
> that "pull" on the speaker in both directions. On the tiny85, theres two
> complimentary pwm outputs that are inverses of each other. and it was much
> louder when I hooked the two speaker wires to the complimentary outputs than
> just one output to ground. Anyways, I think I need some analog design help,
> I might need to learn about impedance. But, I havent taken classes on these
> yet, I only know how to calculate resistor values like kirchoff's
> loop/current rules node voltage current loops and thevenin resistors. Do you
> think you could help me out in your free time?
> 
> 
> 
>