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Re: From Wayne Parham - Re: Patentable claim

Hi Wayne

1. How does the Unity act as an acoustic transformer, i.e. provide horn loading over the bandwidth generated by
three audio subsystems?

2. How does the Unity manage to correct the movement in time over the span of frequencies within the overlap band
of drivers in the crossover region? You have said, "generally a first or second order crossover gives the best results"
in this design. The difference in time generated by these two networks is a factor of two. So which is it?

Think about an exponential horn, it is a high pass filter who's low frequency cutoff is a function of the expansion rate
(and if acoustically small, its length).
A 30 Hz horn would have an area which would double every 24 inches or so a 300 Hz would expand 10 times faster
doubling about every 2.4 inches.

When one drives a big conical horn from its apex, the driver couples into a part of the horn where the expansion is
very rapid and so, such a horn has poor lf response compared to an exponential of similar size.
If one slices up a conical horn and looks at each slice, what one finds is that the expansion rate is greatly variable and
that for example the same 16 1/2 inch mouth conical horn that would only allow flat response down to ~1Khz driven
from the apex, now with appropriate drivers, connected where the expansion rate is slower, can go down to 300 Hz.

This probably sounds weird but get your self some paper or keyboard and plot the distance it takes to double in area
as a function of distance from the apex. What you see is that it starts as a high frequency horn and as it gets larger it
becomes a mid or even low frequency horn, all dependent on the rate of expansion.
Think about making the T&S parameters of the mid driver "right" for that throat area where the expansion is correct
for that frequency (making them larger in area and at lower internal SPL than a compression driver)

At the low cutoff, one finds that there is still a main 1/4 wave resonance which is included in the design and as a result
except for defining the low cutoff, it is not evident in measurements. Driving the horn from a point forward of the
actual apex is also not an issue as the free volume rearward of the mids is in the model as well.


First, lets define time and how I measure it.
Set up a sine sweep that is some fixed rate, say from the below the low cutoff of the speaker under test to the above
the high cutoff of the speaker under test.
You place your microphone some distance away, say 1 meter.
The output of the microphone and the test signal go into a modulator (multiplier) which outputs a sum and difference
frequency.
Since it takes some time for the sound to get to the microphone and the sweep rate is constant, there is a difference
frequency produced, when the output of the sweep is viewed as an FFT, one see's an Energy VS time display which
shows not only the reflections in the room but also the shape (distribution in time) of the direct energy from the
speaker.

Once the time is entered, the acoustic magnitude and phase can be measured by in effect making a tracking filter
analyzer which is the right number of HZ behind and this rejects reflections because by the time they get back to the
microphone, they are too far behind to be passed by the filter.
*I should say the TDS process is more complicated but it is sort of like a frequency agile radio which is tuned into the
direct arrival frequency.

Since in a horn the acoustic paths are intermingled, the raw magnitude/phase measurement and time of each section is
done with all the drivers in place.
As you have identified, it is a pain to make a crossover with a real speaker as a load.
In my case, I have to have a crossover which also EQ's the power response of the compression driver and horn
and makes the "phase" happy in the region of interaction.

I use a proprietary "spice like" filter design program, TEF and an HP network analyzer.
I take the upper and lower drivers response and phase and its impedance and phase measurements and use one as a
"series response" filter file and the other as a specified impedance load file.
I arrange a circuit topology which seems suitable and leave most of the components as open variables.
I assign the filter output to be "in series" as well and then have it curve fit to a flat response or what ever curve I asked for.
If the circuit topology permits it, this will find values that give the best fit shape of the magnitude and phase.
Just as in your spice simulator, one can define any topology high pass, low pass, all pass and combinations of all of them and then have it solve for what ever you asked for (magnitude and phase)

Often there is more than one solution and then one has to decide which way to go, sometimes you have to manually change something to get it out of a local minimum in the math somewhere.
Sometimes it takes 5 minutes of solid
crunching to find the best fit, often it takes a day or two of fiddling to get something good.
In the beginning, this process took a week or more.

It does make a lot of things easier, like the equivolent circuit models for drivers. One need only feed in the impedance curve data
setup the elements arangement with ball park values and then curve fit the impedance of the measured speaker letting the computer find exact component values.
The last compression driver model had 19 elements FWIW.

One last thing, remember that the response curves we are matching up have a slope that is both acoustic AND
electrical and the part that matters is the region where they interact with each other which is to maybe -10 or 12 dB
or so on each side of center (-10 would be 90% from one driver and 10% from the other in power~ about 1 dB
error). By having the phase slope in the neighborhood or even right on, one can make the upper/lower driver
distances correct in the transition range.
All this combining takes place at an acoustic dimension which insures that the sum is still a point source in the horn,
there is no "array" related directivity at crossover etc.
When the distances are correct, one see's only one ETC arival and the acoustic phase has no clue as to there being a crossover or more than one driver.
I have a cube (which has a smaller 16.5 inch 2 way Unity horn) apart in the other room, when it is together, I'll send you a TEF measurement of the magnitude and acoustic phase of the horn part if you wish.

Tom

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