Re: Apple IIe speaker

[mjmahon@aol.com (Michael J. Mahon)]

Paul Schlyter wrote:

>In article <20030529211138.15080.00000785@mb-m14.aol.com>,
>Michael J. Mahon <mjmahon@aol.com> wrote:
> 
>> Dopefish asked:
>> 
>>> I have an Apple IIe without a speaker and I need to buy a new one. Does
>>> anyone know the resistance that Apple II speakers had?
>> 
>> First, it's not the _resistance_ (DC) that matters, but the AC
>> _impedance_.  Most speakers will have very low DC resistances.
> 
>I disagree with you here!  Maybe this is the case for _some_
>loudspeakers, however all speakers where I've measured the DC
>resistance had a DC resistance not much different from the specified
>AC impedance.

Good point, Paul--I should have looked this up before responding.  ;-)

The stated impedance of a speaker is typically about 1.3 times its
DC resistance, since it is most usefully characterized in the midrange
of frequencies.

>Presumably most of the AC impedance is this DC resistance.  And this
>could be a way to try to make the AC impedance fairly independent on
>frequency.  If it was, as you claim, that the DC resistance is "very
>low", then the AC impedance would be an almost pure inductive
>impedance, and as such the impedance at 20,000 Hz would be some 1,000
>times larger compared to the impedance at 20 Hz.  And this would pose
>a significant problem to manufacturers of hi-fi amplifiers.
> 
>In real-world loudspeakers, the AC impedance is fairly constant up to
>perhaps a few 1000 Hz, and above that it starts to rise significantly.

This would be so if the voice coil were immobilized.  A speaker is
a motor, and it generates a "back EMF" as a result of its motion
whose phase depends on whether it is excited below or above its
primary resonance.  Below resonance, it is inductive, and above
resonance, it is capacitive.

These effects, which are significantly affected by the accoustic
loading of the enclosure, lead to a quite complex impedance
characteristic for real-world speakers.

You are certainly, correct, however, that the impedance in relevant
frequency ranges is dominated by the DC resistive component.

Thanks for inducing me to do a little research on this.  It turns out
to be quite relevant to driving a speaker with ultrasonic PWM
waveforms, as my DAC522 Apple II software DAC does.  At high
frequencies, the impedance is approximated by a series RLC
circuit, with R the DC resistance, L the voice coil inductance, and
C the capacitive component of speaker cone impedance above
resonance, primarily attributable to cone mass.  This RLC equivalent
circuit is responsible for attenuating the 22kHz PWM frequency so
that it is virtually inaudible, allowing the midrange PWM modulation
(the audio signal) to be clearly heard.

In the case of the Apple II, it's a shame that a lower impedance
amplifier was not used, since it would have given the Apple a much
stronger "voice".  Of course, powered external speakers connected
through an added headphone jack make a fine addition.

-michael

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