NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/rec/audio/19054

Text File | 1993-01-21 | 3.3 KB | 78 lines

Newsgroups: rec.audio
Path: sparky!uunet!gatech!news.byu.edu!eff!world!DPierce
From: [e-mail] (Richard D Pierce)
Subject: Re: power amps blowing tweeters
Message-ID: <[e-mail]>
Organization: The World Public Access UNIX, Brookline, MA
References: <[e-mail]> <[e-mail]> <[e-mail]>
Date: Thu, 21 Jan 1993 21:25:28 GMT
Lines: 67

In article <[e-mail]> Richard S D'Ippolito writes:
>
>In article <[e-mail]>, Richard D Pierce writes:
>
>>
>> No, it would be a little less, not a lot less. Even at 20 kHz, the
>                    ^^^^^^
>> inductive component of the inpedance of most reasonable tweeters might
>> account for as much as maybe 20% of the total impedance (phase angle of
>> the impedance at that point about 10 or 12 degrees.
>
>OK, "much" or "little"?
>
>With your data, here is what I calculate:
>
>freq    wL    tan(th)    theta    Z    cos(th)    Power    SigmaP(n)
>
>20kHz    0.2R    0.2    11deg    1.02R    0.98    ~P(nom)    1.0P
>
>60    0.6R    0.6    31    1.17R    0.85    0.24P    1.24P
>
>100    1.0R    1.0    45    1.4R    0.71    0.10P    1.34P
>
>140    1.4R    1.4    54    1.7R    0.58    0.05P    1.39P
>
>Now, using Mr. Frith's base of 20 watts, your impedance ratio data, and
>assuming an amplifier power response to 140KHz, we see diminishing
>contributions by the fourth term and a "square" wave power of only 27.8 watts
>(40% more) compared to the theoretical maximum of 40 (100% more) and his rough
>calculation of 37.
>

Well, ok, except for several facts. First, it's seldom a 20 kHz sine wave
that clips an amplifier, it's more like stuff much lower and more complex,
so that splatter is much denser and lower frequency then your table would
have us believe. So while the table above is interesting in an academic
sence and certainly correct only as far as it goes, it is a poor
approximation of reality.

Secondly, you've made an assumption about how the impedance rises above 20
kHz which is simply not correct. The standard model for voice coil
impedance which consists of a single linear inductor in series with a
single linear resistor is to simple to the point of being seriously flawed
for just this kind of example (not your fault, the literature seldom gets
it right also).

In fact, both the resistive part and the inductive part of the model are
highly frequency dependent, with the inductance, for example, decreasing
roughly as the square root of frequency (not the inductive component of
the impedance, but the inductance itself). The net result is that
impedance rises much more slowly than your model accounts for, and the
phase angle is consequently less than your model predicts, by almost 50%
at the high end (typically the phase angle seldom exceeds 30 degrees at
any frequency below a couple of hundred kHz).

Sure, some of the energy then goes into heating the metal parts
surrounding the voice coil due to induced eddy currents, etc., but the
excitation current still has to flow through the voice coil anyway.

In short, the physical reality is more complex than you're allowing here,
and the differences are enough to make the substantial difference between
"much" and "a little" less, as I stated in my post.
--
|                Dick Pierce                |
|    Loudspeaker and Software Consulting    |
| 17 Sartelle Street   Pepperell, MA  01463 |
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