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When AR-3a tweeter pots are removed – why don’t we see a resonant peak?


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John started a recent thread, which now has over 40 replies and is getting little hard to follow. Anyhow, in that thread John posted the Spice model below, which shows the 3a tweeter will experience a rather “large, ugly resonant peak” (Ken's words) in both the MAX position and when the tweeter pot is removed.


Shortly after John posted this model, I got out my scope to see just where this peak occurs and its magnitude. Please bear in mind that it’s normal for deviations to occur from theoretical models as those models contain average values. My AR-3a’s, of course, have specific components and I was curious to see where this “peak” occurred and how much it deviated from speaker to speaker. In my case the peak is exaggerated to the fullest, because I have completely by-pass the tweeter pots (that is, those pots dissipate ZERO energy).

From the graph above, I was looking for a peak where the voltage would more than DOUBLE! Those of you who have used scopes know that this should be a fairly easy thing to find. I mean, it would be hard to miss!

We first hook a signal generator to our amp and then measure the amp’s output WHILE driving the AR-3a’s. What we are trying to determine is whether the amp’s output voltage changes over the frequency range of interest. (In my case, the amp was very stable over this range and very flat.)

Next, we hook the scope up to the tweeter and watch the scope as we “sweep” from 3000Hz on up to 20000Hz. What we are looking for is a frequency or any frequencies where the displayed signal DECREASES. That’s what a peak is. Voltage goes up, but then comes back down. In this case according to John’s model, we should see the signal drop to approx HALF of its value.

Well, after measuring for about an hour on both speakers, I can report that I can find NO peak, no “blip” …. NOTHING! The initial signal at 3000Hz is fairly low, but rises quickly and by 5000Hz is more than double the original value. So far this looks like what the model predicted! All I have to do is continue increasing frequency and wait for the signal to decrease. Surprise! That never happened! As I increased frequency …. the signal increased. The signal hit a plateau around 11000Hz and stayed fairly level until about 18000Hz, where I saw a very slight downward trend.

Now, this pattern was IDENTICAL in both speakers.

My next step was to see what happens if we simulate a pot in parallel with the tweeter. I put a 10 ohm resistor across the tweeter and the only change I could detect was the signal level across the tweeter was reduced. The signal, however, followed the identical pattern of doubling by 5000Hz and plateauing around 11000Hz.

So, what’s going on here? Is John’s analysis incorrect?

I’ve been in contact with Dick Pierce, an expert in speakers. He thinks the problem is John’s choice of a model for the tweeter. John’s simulation assumes the tweeter can be represented by a FIXED resistance and a FIXED inductance over this entire frequency range. That clearly is NOT what happens in a real speaker. Let me quote Dick:

“And remember that TWO things are happening:

1. The tweeter inductance is going roughly as the

reciprocal square root of frequency, and

2. The tweeter resistance is going roughly as

the square of frequency,

The inductance is going down and the resistance is

going up as frequency goes up, in other words.

There's a further complication: the figure of 0.115 mH, where

did that come from? The problem with a simple model like

that is that the inductance of loudspeaker voice coils is frequency-

dependent. It might be 0.115 mH at, oh 1 kHz, but you'll find

that if you measure the impedance of the tweeter of a wide

range of frequencies, it won't match your simple model.

Instead of the impedance rising and asymptotically approaching

a doubling with frequency, it in fact asymptotically approaches

something more like rising with the square root of frequency.

And the phase does not approach 90 degrees, more like 45


Electrically, you find that the inductance is going DOWN as

frequency goes UP, and that the effective resistance of the

voice coil goes UP as the frequency goes UP. So, while the

inductance might very well be 0.115 mH at 1 kHz (and that

seems a might high anyway for a tweeter), you'll find that it's

probably on the order of about 0.04 mH at 10 kHz.

The reason is that the higher in frequency you go, the more

easy it is to generate eddy current in the metal parts surrounding

the voice coil, like the pole piece, for example. That eddy current

is actually doing work, heating the metal. And when work is done,

electrically the effect is increased resistance and reduced

reactance (The reactance happens because the element can

store and return energy: as a charge in the capacitance or as

a magnetic field in the inductance). But when that energy ends

up heating something up, it's no longer available electrically.

The result is a reduction in the reactance, in this case, the

inductive reactance of the voice coil.”

So, where does all of this leave us? Well, for one it would be great if others could independently verify my measurements. It doesn’t take much; a scope, a signal generator and an AR-3a (with pots removed or at MAX).

In the meantime, I think it’s fairly safe to assume that running your tweeter pots at MAX or removing entirely will NOT cause any resonance induced peaks. Chuck McShane said that removing the tweeter pot in a 3a will boost the tweeter output by approx. 1 db and I believe that is fairly accurate assessment.

I further believe that this 1db is a very welcome addition!



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Several tweeters are en route to me, courtesy of Roy. I run comprehensive measurements, both electrical and acoustical, to try and settle this. I did some very quick simulations last night, and found that the crossover was right on the edge between max flat and underdamped. It is very possible that different generations of tweeters will show a peak, or not, depending on their exact impedance. We shall see within about 10 days!



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Hi, Ken

Do you have the ability to measure the inductance at different frequencies (say 3000, 5000, 7000, 9000, 11000)?

Same question with the "pure resistance" at those frequencies?

This will help a lot in determining where and when any electrical resonance effects can appear.

Lastly, with a tweeter you can actually look, as I did, for an underdammped resonant problem. All you'll need is a 6 mfd bi-polar. Right??



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Not sure I fully understand the second question... I will measure the Q (1/"damping") of the tweeter by itself. No other components are needed. This is done by using a constant current amp to drive it, and observing the terminal voltage.

I'll measure R and L components at a least a few different frequencies. Of course, my main interest is to determine the actual behavior of the crossover and drivers in question. I don't want to spend too much time on details that won't yield practical information. I'll leave the Volterra Series expansions as an exercise for the reader....



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>Not sure I fully understand the second question... I will

>measure the Q (1/"damping") of the tweeter by

>itself. No other components are needed. This is done by

>using a constant current amp to drive it, and observing the

>terminal voltage.


Yep! My question was NOT very clear.

All I was asking, Ken, is whether you'll attempt to duplicate the AR-3a xover for the tweeter. For me, that entire xover consists of a 6 mfd cap and … the tweeter.

Once duplicated, measuring voltage across the tweeter as we scan from 3000 to 20000 is fairly easy. What would also be nice is if you could simultaneously measure the SPL while scanning. I’d love to see how severely the tweeter “rolls off”.

This is just one of those interesting tidbits that really won’t impact me. I know I can’t hear anything above 10000.



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