Horn loading for Idiots

[ra7]

(At the risk of sounding ridiculous)

The greatest power is transferred when the impedance to the force being applied is equal to the force itself. To put it another way, imagine yourself punching air. Yeah, how does it feel? Now trying punching underwater? Tougher, huh? Need more power? If there were a medium which could perfectly "accept" the power in your punch, 100% of your energy would be transferred to that medium. When punching air, you'd be just burning up some muscle (or fat).

You can take this and pretty much apply it to loudspeakers. Horns create that extra pressure to allow a greater transfer of (sound) energy from the diaphragm to the air. Otherwise, the diaphragm is just "punching" air.

And no, no bending of physics laws is happening here. Not yet, anyway!

Enjoy!

[chris661]

This thread has helped a lot - Thanks All.

Chris

[danielm]

Originally Posted by Tom Danley

Hi

Personally I find most idiots are loud enough without horn loading, in fact too often that seems to be a defining feature.

Seriously I do know what your asking, just not sure how to answer the most understandably.

A piston vibrating in air feels a resistance to it’s motion (it's velocity), this is related to the sound which radiates away and does not return.
For a fixed frequency, the larger the piston is the more resistance it will feel (up to a point).

Since mass and spring forces are not dissipative (not resistive, no work is done) sound power is not radiated here.
I mentioned ‘to a point” what I mean is that when you look at a Radiation resistance curve for a piston (fig 3 in this link), you see that in the left most region, the radiation resistance increases as the size of the radiator approaches a dimension where it is approaching a half wavelength across.

http://www.aikenamps.com/speaker.pdf

Above that frequency, the resistance is essentially unchanging with respect to piston size.
For a woofer, one has a radiator which is much smaller than the wavelength so it operates far down on the left side of the graph.
AS you might guess, a larger piston can be more efficient as it feels more load from that radiation resistance. This is also why two separate woofers placed less than ¼ wl apart, become twice as efficient as one alone, it has in effect doubled it’s area and so has twice the load and so does twice the “work” radiating compared to one.

A “horn” is used because it provides a way to couple the large area at the big end of the horn to a comparatively tiny driver at the small end or in other words, to couple the high resistance part of the curve to the tiny driver which operates at the far left of the curve, thus greatly increasing the radiation efficiency (produces more SPL for a given electrical power input). In reality, a horns radiation resistance curve is somewhat different, the ideal or flat portion of the curve is reached at about 1 wavelength in circumference.

Some like to use the analogy of an impedance matching transformer which is vaguely correct in some cases.
A more accurate analogy is a three terminal “T” resonant impedance matcher if you deal with antennas.
About half way down on this link is such a circuit.
Impedance Matching Network Designer

The ideal is you make the impedance point at the center, the square root of the input times the output impedance.

With sound, resistance is related to area and if you examine a simple exponential horn, one finds the center resistance between the ends and actually at any points you examine, is the square root of the small end times the large end.

An electrical circuit like these in the link has one set of values and works only at one frequency BUT a horn is still different. Consider a large proper horn.

The electrical circuit is obviously resonant and has a narrow bandwidth BUT a horn is a variable device. At it’s low cutoff, the entire horn is working but as the frequency goes up, the horn becomes acoustically larger and longer and one finds the operation portion of the horn moves towards the driver and the mouth end is no longer involved with the impedance transformation as it is already on the flat part of the resistance curve.
If a horn has the area’s consistent with the source and load resistances, the fact that it is resonant is fully masked and in that case really does appear to be a transformer or like a gear ratio and not resonant.

I real life it is nearly impossible to make a horn large enough to act like this so bass horns operate in a strange in between world.

An additional complication is horns have a “high pass” filter effect related to how fast the area expands along it’s length. For a simple exponential horn, if you want a 30Hz horn, the area needs to double about every 24 inches, for a 60Hz horn its every 12 inches and so on.
Why is this?

In a horn one has a momentum transfer from one air molecule to another.
Picture a huge airhocky table with a zillion pucks all touching ( a 2 dimensional analogue)
If you hit the middle of this array of pucks you will see that like sound the pressure spreads in all directions. Only a small amount of the energy will be released in the same direction as the initiating puck.
The goal of the horn is to prevent the pressure from escaping to the sides like a duct would do except that by allowing the area to expand slowly, one can couple the energy to a large number of pucks and have them all go in one direction, like a single large piston would do.
Now, keep in mind that the wavelength comes into this too, the wavelength describes the natural change in pressure at different parts of the wave as it progresses down the horn.
Thus, one finds the expansion rate ties into how low in frequency this momentum transfer can be accomplished.

I have skipped over a great deal here for simplification and have used some descriptions, which are analogies I like, which I hope make things easier to envision.
These are not part of any text book explanation if you can find such a thing but is based on how I have come to see a horns operation as of today.
Hope this helps.

Tom Danley

Tom, I've matched many RF devices via qtr wave stubs and fully understand what is happening there. However, I'm having a tough time wrapping my head around the horn analogy.
Can you explain what represents the matching network's lumped C and L equivalants in the horn?
Thanks.

[Tom Danley]

Hi

Well how that ties in requires a more complicated answer.
For an efficient horn, the length has to be a half wavelength at the low corner.
This is because the driver has to be at the velocity maximum and the exit has to be at the other velocity maximum.
In that case, the horn is like a T network because the center point impedance is set to be the geometric center of the input and output.
For a horn, Area equates to the impedance /resistance etc and in an exponential horn, one sees the area at the half way point is also the geometric mean.

In practice we are forced by the size to make the horn a quarter wl at the low cutoff instead and this greatly reduces the impedance span the system can adapt to.
One finds that the driver parameters needed to be efficient above the low corner are much different than those you need when the driver is at the velocity minimum.
AS a result, the quarter wave horn, when you examine its impedance, you see that it isn’t optimally efficient until it’s a half wave long.
Like the antenna, it is the ratio of the reactive to resistive parts which govern the standing wave.
With the horn, one is concerned with the resistances at both ends as well if these are dominant, the appearance of a resonant system is lost.

In the antenna world, there is a useful analogue to a horn at it’s low cutoff, the Biconical antenna. At the low corner, it’s entire length is in use but as the frequency climbs, the amount of the antenna “in use” is less and less.
Here, the geometry is “correct” or close, for any frequency within it’s operating band.
An acoustic horn propagates pressure axially however its active region retreats down the horn as you rise above the low corner.
In the acoustic horn, the horn segment which is past the impedance matching region is not exactly gone though, it continues to define the horns radiation pattern up to some still higher frequency.
Hope this helps,
Tom Danley

[danielm]

I would have thought, in an acoustic horn, impedance transformation took place at one quarter wl. I keep associating it with the 1/4 wave transmission line stub, in the rf realm, goes from max voltage, min current to min voltage, max current at 1/4 wl down the line. A shorted line appears Hi Z at 1/4 wl away from the short. Getting old ain't helping me getting a grasp on the horn analogy.

I've built Hi Q RF duplexer filters using 1/4w stubs and achieved a massive notch with a recovery (passband) above or below by adding shunt C or L.

But, dang this broadband acoustic spew has me baffled.

Thanks Tom.

[Tom Danley]

Hi

Ah, acoustic spew, yes.

Think of the horn in terms of the passive 3 element T network. The center impedance etc.

The quarter wave resonator is similar but it is the > half wave horn that is “efficient”.

To make a quarter wave horn efficient, requires a different set of driver parameters, one with a much stronger motor and greater mass and not so suitable above ¼ wl.

In other words like with an antenna a source with an impedance capable of driving at the current maximum and not voltage maximum.
With antenna’s the Voltage maximum is an impedance so high it is normally impractical to drive from anywhere near that end. The air around you presents much more of a load than the RF radiation resistance of free space if that helps.

In acoustics the concept of an equivalent circuit is also useful and valid although less used, if you used to antenna’s, I would say try that direction.
Look for Marshal Leach and others who have published on the Pspice equivalent circuits for drivers and horns.

Examine the conical antenna for the broad band nature, it is a quarter wave antenna at it’s low cutoff BUT is capable of operating above that because it’s aperture changes with frequency. Antenna’s by Krause has a good description.
Where the antenna works radially, the horn is axial, throat to mouth.

Lastly, this stuff is frustrating, hard to picture and most of all, it is not an age thing, it’s just not simple or obvious or described in terms that make sense immediately.


Understand too there are big differences between EM and audio it’s just that the wave nature makes for some useful analogies.

73's
Tom

[danielm]

Oh the speaker equivalent of the coaxial colinear array would be so easy if it wasn't for those so many octaves...

Thanks Tom, I enjoy the challenge.


73's
Dan
N5MRG

[thoglette]

Originally Posted by danielm

Oh ...if it wasn't for those so many octaves

There's one of the problems in understanding audio - a "wideband" antenna might do a tenth of an octave whereas audio we're looking at many octaves.

My brain works best in considering a horn not as a T circuit, (which relies on discrete discontinuties and a single frequency) but as a transmission line whose impedence changes along it's length.

The nasty bits are getting the impedence change well behaved over the desired range while also matching the mouth & exit impedence and getting frequency independent directionality (dispersion)

[Tom Danley]

Hi

A real issue here is that the Q of a simple antenna or resonator governs it’s usable bandwidth.
In airborne sound, the Q is partly set by he area and frequency and the highest Q one can get in a horn is far lower than an antenna. Like any passive element matching network, the bandwidth is inversely related to the impedance span one is trying to bridge.

Search out “antenna’s” by Krause which treats several wide band antenna designs like the biconical and others in chapter one and especially in chapter 8.

Antennas j d kraus 2rd edition solution - Rapidshare Search

These are a “variable” antenna, not like a log periodic which has discrete nodes, and being omni directional, have no forward gain, just a broad band behavior.
Some can be very wide band too;
HF Broad Band Conical Monopole Antenna

Keep in mind for an acoustic horn, the efficient range of operation is more like an octave or two, in order to make one horn be efficient over a larger bandwidth, takes different drivers suited to the frequency range in question.
We make such a horn, perhaps the explanation for it will help, go about half way down;
http://www.danleysoundlabs.com/pdf/danley_tapped.pdf

Again, keep in mind that the horn is an axial thing while the conical antenna radiates radially.
Lastly, it may be that you will have better luck dealing with the equivalent circuit of a horn and driver, here are a few places to start.
Analogous Circuits for Acoustic Horns

W. Marshall Leach, Jr.

SpringerLink - Book Chapter

http://www.acoustics.hut.fi/teaching...ogies_2009.pdf

Hope that helps.
Tom Danley

[danielm]

OK, I think I just found some unobtainium. There's no way could I explain it though.

There's a complex juggling act going on in Tom's head.

Thank you Sir.