The phase plug will usually protrude into the horn.  This will affect the initial part of the horn which will have to have a diameter equal to the outer diameter of the ring.  Thus, the horn walls will have to expand due to the presence of the tapered plug.  That part of the horn will then have a ring taper, the area of which will expand according to that of the flare rate constant, b, which is determined by the low frequency cutoff, f_c of the horn.  This was  done in the early seventies when a Wharfedale Super 3 tweeter was horn loaded with an f_c of 400hz.  The need for the plug was circumvented by using an initial taper/adapter to go from a circular throat to a rectangular throat of the same aspect ratio of the horn and also maintaining an exponential flare during this length, which was 3/4 inch.  Of course, there was no way then to measure actual frequency response but they sure did sound good in conjunction with the horn loaded W15.  There are two pages on that for the curious.  horn-g   and   horn-h

There is also the handicap of working with wood as, to achieve the above, a lathe is required and the use of very hard woods as hard woods can be machined to better tolerances than soft woods; soft woods will absorb high frequency energy.  The pressure exerted on a horn loaded diaphragm is greater than that of a direct radiator.  The horn is an acoustical transformer, matching the high impedance imposed at the front of the diaphragm to the much lower impedance of the air in the room. Hence their efficiency.  It's much the same as connecting an 4 ohm speaker to the 8 ohm tap of an amplifier; the power transfer is compromised to the tune of 50%.

The Usual Suspects

The rear chamber.  The piece with the rounded corners hole is the spacer.  With the speaker front loaded, the speaker gasket is just about 1/2mm above this plate, allowing a seal when the horn is bolted on

The internal volume is larger than the 8.5 cubic inches to allow for the wool to be stuffed in.  This was deemed necessary as the box is square, 3.25" on the sides.  This corresponds to a wavelength of 4187hz.  Of course, the presence of the magnet assembly may have prevented that

Accounting for magnet assembly displacement, the internal volume of the back chamber is about 15 cubic inches

The speaker gasket is about 1/2mm above the surface of the spacer which provides a good seal to the horn flange.  A gasket of 1.5mm thickness was added to the speaker gasket to increase the distance between the annulus and the horn flange.  This will allow for a 1mm excursion at 250hz, which is an octave below the crossover filter and will produce an SPL of 87.3dB at 250hz

The total volume, V_fc between the surface of the cone and the horn flange is now 1.5 cubic inches

The crossover is first order 2-way and the polarities of the speakers are reversed with respect to each other

This isn't common practice for a first order crossover but the reason will be explained later in photo 10

This was placed here just to have a look-see into the horn.  the woofer is a Wharfedale W12RS in a 3 cubic feet sealed enclosure

Clicking on these last three photos, 5, 6 and 7 will produce a larger image

Just to show the whole test setup

This is the high frequency speaker without the horn.  This will be explained later in the conclusion section

This is the current rear chamber.  The red rectangle is the front baffle, onto which is front loaded the speaker. The blue outlined rectangle above it is the spacer.  The speaker gasket rises above this by about 0.5mm to provide a seal to the horn flange, which is the top rectangle

The red area is the proposed additional spacer onto which would be placed a ring, shown by the inverted triangles.  the blue area is the same size as the horn throat

The idea was to decrease the front cavity volume but that idea went to hell in the proverbial handcart, PDQ. (Pretty Darn Quick)  The volume would have been reduced by a about only 20% because the additional volume of the blue throat would have partially offset the volume reduction of the ring

A phase plug (green) can be added to further reduce the volume but this would have to be designed in conjunction with the red ring encircling the throat to obtain the correct throat area, meaning a circular ring throat.  This method was used in some ring radiators.  One that comes to mind because I had a pair and swapped them with a musician for the ElectroVoice T-350 units is the JBL-075 tweeter (aka ring radiator)

Considering this, it was deemed to be a waste of effort. It was decided to carry on with the original design and let my ears do the critique followed by the CLIO, in that order so as not to be biased by a response curve.

The final crossover.  A second order was considered but this worked very well.  Besides, it was easier to juggle the component values.

Juggle??  After seeing the initial horn response with a wide peak of several dB between 400hz and 800hz, and knowing the woofer output would exacerbate that, it was decided to spread the crossover points (Juggle)

After several attempts, a low pass of 5mh in the woofer and a high pass of 5.6uf in the upper section, the red  response curve of fig 1 was obtained.  Initially, the system honked.  So the crossover points were spread apart, first starting with the woofer, then the tweeter.  When the honking stopped, a response curve was run and tweaked a little further in an attempt to smooth the response between 500 and 2khz.  See fig 3

This didn't have the effect I desired so the tweeter polarity was reversed, going from the black trace to the red one in fig 1

The grey trace at the bottom is the THD, less than 1% above 100hz

The added flange which made no difference

The purpose of this is described in the section titled "Mouth Reflection Dip" at the bottom of this page

1w1m  5mh 5.6uf   BLK = TWT norm pol; RED = TWT rev pol; GREY = THD

It was later discovered that the dips at 450hz and 600hz and the rise centered at 750hz can be considerably reduced by elevating the horn by about 6 inches or moving it back by the same

This dip at 600hz is reminiscent of what Klipsch referred to as a mouth reflection dip.  This will be explained at the bottom of this page.

Click on pic for larger image

This figure was removed but the cell was left to avoid having to find and correct references to subsequent figs after renumbering them

1w1m RED = horn only; GREY=THD

This shows the response of the horn loaded speaker only, no woofwoof.  The signal was electronically second order filtered at 200hz to control diaphragm excursion. That is one reason for the rapid drop below 200hz.  Another would be the small box volume

The high THD in the lower register is likely due to the excessive loading of the very small box.  The optimum volume for a smooth response to 168hz is 63 cubic inches, according to BassBoxPro. However, no mention is made of distortion. This box about 15 cubic inches giving a smooth response to about 191hz, the knee of the filter, -3dB

Considering displacement of air due to the stuffed wool, the diaphragm excursion at low frequencies, however small, would cause deformation of the diaphragm.  The wool was added to suppress resonances at the higher frequencies when the wavelengths of those frequencies approach the internal dimensions of the chamber

The back chamber volume was recently reduced to 7 cubic inches by adding 4 wood blocks around the rear inside perimeter.  The wool was removed.  No noticeable change, graphic or aural, was detected

Click on pic for larger image

Z  RED = horn box w/o horn; BLK = with horn

One might expect to see the resonant point rise due to the horn throat being slightly smaller than the speaker cone area.  An attempt at explaining this is adjacent to fig 5

The vertical scale in fig 5 is different

Click on pic for larger image

RED=Z open air

ORANGE=Z in 15 cubic inch box

Black=horn attached to box

A speaker mounted in a sealed enclosure will exhibit a higher point of resonance.  This is due to the spring effect of the air trapped behind the cone.  The impedance magnitude is also reduced as in the orange curve

This phenomenon has been mentioned in technical papers but the writer, probably an engineer assumed the reader would also be an engineer.  I'm not, so it had me pondering this for awhile since at first glance it is counterintuitive. A suitable, although not necessarily complete or correct, explanation came up and lit the proverbial light bulb

The resonant point lowers with the horn attached (black) possibly due to the air in front of the cone, not being trapped, moves through the horn throat

This will also lower the impedance as can be seen due to the restriction of cone motion but that moveable air is also seen as an added mass on the cone, which will lower the point of resonance. With cone motion blocked, the impedance will approach the DC resistance but never reach it due to the reactance of the coil.

Click on image for larger view

Conclusion

OK.  So it looks good on paper but how does it sound and is there much, if any, difference between direct radiating and horn loaded?  Keep in mind that the following may contain some subjectivity regardless of how much effort is put into maintaining objectivity

A higher output than that of the direct radiator was expected but not realized.²  This is thought to be due to the very wide bandwidth for which the horn was designed.  One way to determine the suitability of a speaker for horn loading is by the EBP, )Efficiency Bandwidth Product) which is stated as, EBP=f_s/Q_es (Eq-12)  The general consensus is that for sealed enclosures, EBP should be less then or equal to 50 and for vented enclosures, greater that or equal to 100.  This particular unit  has an EBP of 17, making it suitable for a horn since a horn uses a sealed enclosure behind the speaker, V_b

Also, the slightly smaller throat will have a negative effect on the lower part of the band, imposing a heavier load on the diaphragm.  The response in fig 3 was obtained without the throat adapter, using the 2 inch throat of the horn.  Initially, it was thought that this would negatively affect the extreme high end but that proved to be incorrect, (red trace, fig.1).  The bump in the band between 400hz and 1300hz (fig 3) was flattened by spreading the crossover points, now 300hz and 2khz, first order.  A smaller front cavity and maybe a phase plug  (photo 9) may have helped increase the efficiency of the highs.  That modification hasn't yet been shelved.  The larger back chamber volume may also have contributed to this lower midrange rise.  The current back chamber volume will be reduced by adding wood blocks inside to get to the ideal 7 cubic inches from the current 15 cubic inches.  It was originally thought that the highly packed wool in that chamber would achieve this.  Replacing the wool with wood will verify that

Despite the lack of increase in efficiency, what was noticed was the presence of the mids.  It should be noted that efficiency and bandwidth are inversely proportional. Since the response is relatively linear, (red trace, fig 1) it was noticed that the horizontal dispersion widened.  Listening tests showed that the listener's position can move as much as 45^o off axis before an loss of the very high frequencies could be noticed.  This wasn't tested because of having to move the coffee table plus the stuff stashed under it

A couple of friends gave it a listen and were astounded at how well they sounded upon entering the room.  They were, at that point, about 12 feet from the speakers and about 45^o +/-5^o off axis.  Both agreed with my feeling that it sounded a little bright on axis but that was at better than 95dB SPL at several feet

So, in short, better horizontal dispersion was obtained with no loss or gain in efficiency.  A satisfactory tradeoff

FIGURE 6

These response curves are those calculated by Bas Box Pro, v6, re: the 3FE22.  They show the normalized response in an optimum sealed enclosure of 63 cubic inches (red) and the box for the horn, (orange) of 15 cubic inches and (yellow) 7 cubic inches.  This comparison was run to find out if such a reduction in volume would produce a bump.  There appears to be a 3dB to 4dB rise around 400hz, (orange) which may be a problem.  The yellow shows a 6dB rise in that region.  With a first or second order filter at 500hz, the rise at that frequency would be lowered by 3dB, the knee of the filter

Paul Klipsch describes this in very great detail, along with the solution in his paper titled "A New High Frequency Horn" ³

Briefly, a dip in the response of about 7dB was noticed at 480hz.  The solution was to install the horn onto a flange of area three times the horn mouth area.  This also resulted in being able to halve the mouth of the horn, thus shortening it by close to 3 inches. The flange (baffle) maintained a close aspect ratio of the horn mouth dimensions.

The dip noticed in my design may be the result of that or caused by the horn's proximity to the woofer.  Fig 6 shows no dip at 600hz with the woofer disconnected. Adding a baffle of 3 times the mouth area and the same aspect ratio to this horn made no difference.  The baffle measures 23" wide by 15" high  Photo 11

Footnotes

1  Consider a straight axis bass horn for the Faital 15PR400 with a modest low frequency cutoff of 47hz, like the Klipschorn.  It would have a mouth diameter of 24 feet and have a total length of 13 feet.  One must look with admiration upon the Klipschorn with its total length of about 4 feet

2  Suitability of Low frequency Drivers for Horn Loaded Loudspeaker Systems - Richard Small  Audio Engineering Society (AES) May 1977

3  Submitted, June 24, 1963, IEEE Transactions On Audio, pages 201-206

FIGURE 7  (click for larger image)

Many horns designed for midrange or full range cone speakers seem to deviate from horn theory, especially at the throat.   For a circular horn, it seems to be common practice to fit the loudspeaker at the throat which has a diameter equal to the inside diameter of the speaker's front gasket.  If square or rectangular, the square may have an area equal to that of the above or the effective cone area. If the corners of this rectangle or square protrude beyond the circumference of the speaker, the rectangle or square will be adjusted to fit, resulting in a smaller area which, in actuality, me be closer to the correct throat area.

The crude figure below gives an example of such a design; it assumes a 6" speaker.  The length and mouth diameter is approximated from such designs seen online.  It assumes an exponential horn although they could be tractrix, which will result in a shorter length but the mouth area will be much the same as that is determined by f_c the low frequency cutoff.  This example uses inches.  The following is more readable than the chicken scratch in the figure below, from the top

We are given the throat diameter as per C.R.Hanna, D as 4/b or l/p and b=4pf_c/c  To the right of that is stated a 6" speaker being used with a 5" horn throat diameter.  Below that, is Keele's equation for throat area expressed in T-S parameters,  S_t=2pf_sQ_tsV_as/c  

Under Parameters we have the throat diameter and mouth diameter, D_t and D_m respectively and below them we have throat area and mouth area, A_t and A_m  respectively, followed by the horn length, L_h (which, to maintain the nomenclature previously used, should have been written as H_L )

Next we divide the mouth area by the throat area and get 16.028, which is equal to e^bx .  Taking the natural log of both sides, we get bx=2.774 and since the horn length, x=24", we get  b=0.1156.  Now, using the equation given above for b, by transposition, we get f_c=bc/4p=125hz. (The wavelength of 125hz is shown under that equation).  From this we can calculate the mouth diameter to get 34.6" which is 1.73 times larger than originally estimated.  This method is similar to a process known as reducto ad absurdum, whereby an initial statement being assumed to be true is proven false, assuming, of course, that the logic between is without fault.