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Thread: Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides

    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #1 of 9)

    This thread is an offshoot of the Handmade Ersatz M9500 thread, found at: http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3

    The thread evolved into a comparison of various horn contours, which included a pair of questions (from Rob H. and Ian Mackenzie) addressed to me. Rather than dilute the original thread with a long reply, I have opted to initiate a new thread dedicated to a discussion of the various factors which affect subjective sound quality of horns and waveguides intended for midrange and high frequency reproduction.

    In this, and subsequent posts, I will show that the goal of high quality sound reproduction using compression drivers appears achievable if sufficient attention is given to;
    - Holistic system design, including careful crossover parameters for optimum transducer integration,
    - Applying proper horn & driver equalization and frequency response tailoring,
    - Understanding the causes, and methods to attenuate, horn-honk
    - Employing wideband CD waveguides, designed to be tonally neutral,
    - And the value of using high quality transducers.

    The original question on sound quality was posted by Ian:
    Quote Originally Posted by Ian Mackenzie
    Jack, Correct me if I am wrong but what you are talking about is the sound quality of the horn itself……snip…… Ian


    Ian’s question summarized my intent correctly; my posts do concentrate on improved sound quality of horns/waveguides as a central theme. Taking a step back, I would also add that I’m probably more concerned with overall sound quality of the full reproduction system, including: source, electronics, loudspeakers and room. I view the set of equipment and components in all four of these categories as a single unified system, and the optimization of the sound quality from the whole system should be the goal of any design exercise.

    “Big Four Criteria”
    From my experience, there are four criteria which impact a reproduction systems ability to render an impression of a live performance (in order of importance):

    1) Flat frequency response, both on axis and total radiated power.
    2) Wide frequency bandwidth. (20Hz -20kHz is sufficient)
    3) Wide dynamic range, meaning realistic peak output SPL, with low electrical and mechanical noise floor.
    4) Low distortion (all forms of non-linearity)

    I’ll nickname this lofty set of goals as “the big four criteria”, for later reference. I won’t expand on any specific details of the big four criteria, because a thorough description of the quantitative measures, and measurement techniques to confirm performance would take a lot of time and space on this post. But I will mention that each time I have made an improvement in any of the big four criteria, I have subjectively noted a qualitative improvement in the sonic reproduction. For every measurable improvement I have managed on the one or more of these four criteria, I have always been rewarded with a system that sounds more realistic.

    Clearly the big four performance criteria are acoustically, mechanically and electrically all highly inter-related, and this is the primarily motivation for a holistic rather than a disjointed approach to system design. In other words, a particular transducer sub-system, such as a compression driver and horn, should be integrated into the larger reproduction system in such a way that it does not draw attention to itself, in either a good or bad way.

    I believe that the most important sonic aspect of any compression driver horn or waveguide combination is how well it can be integrated into the total system design, such that the outcome satisfies the big four performance criteria. For instance, the required performance characteristics of a horn aimed at use in a two way speaker deployed in a small well damped living room will be different from the requirement for a good mid or top unit in a fully horn loaded system of someone living in a house the size of a sports arena.

    It’s not mandatory that each system must have its own individually designed horn, as it may be entirely possible to use the exact same horn/driver in both the previously mentioned situations. What would need to change are the specific details of crossover and equalization in the two cases, so that the device in question could be best integrated with the cabinet and other transducers to achieve specific sonic performance goals. This process requires access to specific engineering performance data for the transducers, along with a systematic approach to the design work:

    A brief summary of the design steps for transducer integration:
    1) Measure (or obtain) and review the power bandwidth and distortion across the power bandwidth of each prospective transducer in the trial system design. Does each transducer provide acceptable distortion and dynamic range limits within the intended bandwidth?

    2) Will the chosen set of transducers (in the system configuration: 2, 3, or more way) provide sufficient frequency overlap between ranges above and below each preliminary crossover point? In the case of gaps, change transducers, or increase number of units and crossover bands. Can appropriate crossover frequencies and slopes be chosen to support adequate power handling, and restrict out of band distortion? In the case of a compression driver and waveguide combination, the crossover frequencies and slopes must restrict the bandwidth to operate above the cutoff frequency and below the band where diaphragm breakup causes excessive audible distortion.

    3) Measure (or obtain) and review the (on axis and power) frequency response of each transducer. Can appropriate equalization be applied while maintaining acceptable distortion and headroom? Is the equalization practical with the chosen crossover topology?

    4) Check the directivity (polar response) of each transducer at the preliminary crossover frequencies. Do the coverage patterns match correctly on either side of each crossover point? Do the crossover frequencies need to be adjusted to provide smoother directivity transition? Will the complete system provide good power response? Adjust crossover frequencies, slopes and/or change transducers to optimize.

    I’m just scratching the surface of the tip of the iceberg in terms of system design steps, but by now you are getting the idea that a particular driver/horn/EQ combination which can excel at matching the big four criteria will be much easier to use compared to a narrow band device with rough out of band distortion and poor directivity. (Common sense really). I am emphasizing the importance of transducer integration into the total system design, because small changes in the crossover frequencies, slopes, and transducer equalization can have dramatic effects on frequency response, which will impact subjective opinion on the system, or individual transducer performance.

    Compression driver attributes:
    The preceding comments could be generically applied to almost any type of transducer; however horn/driver combinations have four acoustic aspects that definitely set them apart in terms of sonic characteristic (in order from best to worst):

    a) The highest reference efficiency of any transducer type.
    b) A wider range of designs for improved directivity control, compared to cone or planar transducers (arrays excepted).
    c) Some requirement for equalization (either electrical tailoring, or by choice of horn contour).
    d) The undesirable tendency to support longitudinal (and higher order mode) internal reflections within the horn/waveguide cavity.

    High efficiency, along with high power handling can be used to build a system with prodigious peak acoustic output capability, and wide dynamic range. Careful use of constant directivity waveguides can also be used to configure a system that produces a flat frequency spectrum, and total power response in the final listening venue, however this depends on how well the compression driver & horn equalization is rendered.

    In my experience, the equalization step is probably the most critical aspect of integrating a horn/driver combination into a loudspeaker design. Even though I use a full DSP crossover, with comprehensive EQ capability, calibrated by a laptop based acoustic test and measurement system using ETF software, (along with my own white/pink noise based spatially averaged spectral analysis technique), it still takes hours and sometimes days to use EQ for optimum response tailoring.

    Errors in EQ and gain settings among and between transducers will negatively impact the sonic character of the system, moving further away from the most important goal of the big four, namely flat frequency response. Improper EQ does not necessarily mean that the horn/driver combination is at fault, it’s just that it takes time, and a certain amount of trial and error to sort out the interaction between equalization settings, crossover frequencies & slopes, and the effect on the overall frequency & phase due to the summation across the crossover overlap zone between various drivers in the system.

    end of part 1 - Jack Bouska

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #2 of 9)

    Horn vs. Waveguide comparisons and the importance of EQ:
    Considering the difficulty in optimizing crossover and EQ settings for a horn/driver in a given system, I maintain a healthy skepticism towards any subjective reports of “horn shootout” comparisons posted on the internet. While I have no doubt that swapping horns and drivers in a particular system will lead the listener(s) to conclude that one particular horn/driver combination dominates in sonic quality, I have my doubts about the validity of the comparison in those cases where the audition was performed by disconnecting one driver and replacing it with another (using an L-Pad or resistor divider for approximate level setting).

    From experience, I know that changing a horn, (and/or driver) generally requires a complete re-design of the crossover (passive, active, or DSP) with attention to proper EQ of the frequency response, (in the listening room). This includes adjustment of crossover frequencies and slopes to best account for any changes in bandwidth, cutoff, distortion, etc. between different driver & horn combinations. I have occasionally taken the “lazy man’s” device-swapping approach to tweeter-tasting, with only a quick RTA based level adjustment prior to auditioning and forming an opinion regarding the “winner”, only to discover later, when I had the chance to do a proper job integrating each device with the system, that the differences between devices was much less prominent, and in some cases my established opinion of the “winner” was overturned.

    Given the difficulty in re-designing the crossover (and in some cases the baffle) for each new device in a time limited “horn-tasting” session, it’s possible that a CD waveguide might be swapped into a system which originally used an exponential, Tractrix or radial horn, however without proper HF EQ, the CD waveguide would be judged as “dark” or “mid-rangey”, by comparison, leading to a bias against such devices.

    While I don’t want to discourage any forum member from trying different horns or waveguides, and reporting on the audition conclusions in subsequent posts, it would be useful to also have a description of what crossover or system modifications were used for each different horn, and if any throat coupling converters were in use, etc. I would hate to see a particular device get a bad reputation, when some other aspect of the system, such as the crossover topology may have contributed to underperformance. When the crossover and EQ are carefully adjusted for each device, it should provide a more level playing field for comparison, so that the underlying sonic character of the horn/driver can be evaluated.

    Limitations of EQ:
    Using EQ to correct & flatten frequency response leaves two additional aspects of horn/driver behavior which are both difficult to modify using electrical EQ, and only partially, and unsatisfactorily, addressed by crossover frequency selection.

    The first aspect is the horn or waveguides directivity index as a function of frequency. Essentially no amount of EQ will turn an exponential or Tractrix horn into a wideband CD device. The best that can be done is restricting the (HF) bandwidth to a range where the device does not beam too badly, however both those types of horns will always have a increasing DI (narrowing directivity) with increasing frequency (see posts #38-42 of the Handmade Ersatz M9500 thread http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3 ).

    I will discuss CD behavior at more length in a subsequent post in this thread.

    The second aspect (unaffected by crossover) is broadband distortion. In this category, I include both nonlinear distortions (e.g.: front compression chamber induced), and objectionable tonality caused by reflections from acoustic discontinuities at the mouth or within the horn cavity.


    Horn distortion due to internal reflections: “Horn-Honk”

    Quote Originally Posted by Ian Mackenzie
    Jack, …. Snip…..Issues of driver loading, throat impedance, the horn contour and mouth termination all seem to play a role in the subjective performance whereas there are numerous biradial CD horns that have technically good dispersion but are not subjectively that great. Ian


    In addition to the criteria of flat frequency response, I believe that the second biggest influence on the subjective quality of horns or waveguides is the unpleasant phenomenon known as “horn-honk”. This has been incorrectly attributed to a variety of causes, such as compression chamber and/or throat distortion, resonances in the horn cavity or walls, and even abrupt changes of DI between cone and horn transducers in a loudspeaker system. While the previously mentioned mechanisms can contribute to poor quality sound, the real culprit behind horn-honk is caused by poor mouth termination, and/or rapid flare rate changes within a horn or waveguide. In answer to Ian’s comment on subjectively poor performance of some CD horns, I note that many of the commercial devices on the market rely on diffraction slots and abrupt internal slope breaks (flare rate changes), while also displaying poor mouth to baffle impedance matching, all of which are responsible for imposing varying levels of horn-honk to the sonic character. Unfortunately, good CD does not guarantee good sonic performance.

    In post #5 (http://audioheritage.org/vbulletin/showpost.php?p=123500&postcount=5) of my thread: DIY Axially symmetric oblate spheroid CD waveguides, in solid Oak ( http://www.audioheritage.org/vbullet...ad.php?t=12126 )
    I briefly discussed the article: "Round The Horn" by Philip Newell and Keith Holland, (Speaker Builder, 8/94, and an excerpt was included in post #34 of the Handmade Ersatz M9500 thread referenced above). Dr. Holland concludes that the poor sonic quality of many horns is attributable to internal reflections between the mouth and throat. The horn-honk caused by these internal reflections can be easily detected as a distinct tonal aberration, similar to talking through a cardboard mailing tube, or a small tunnel. (Send me private mail if you are interested in this article.)

    Addendum: Please note that in Post #5 of my oblate spheroid thread, I incorrectly described this comb filtering effect as a resonance. I apologize if I mislead anyone by my use of that misnomer, as horn-honk is not caused by an internal resonance, but rather by one or more discrete reflections, between mouth and throat. In contrast, a typical fundamental resonance mode would exhibit a response peak much lower in frequency, which even for short horns would be below 500Hz. (eg: a 13” long horn would have a resonant frequency of 250 Hz, and a 7” horn resonance would be just over 500 Hz)

    The broad-band comb filter effect, associated with horn-honk, is created by reflection, and summation of delayed signals, which are added back into the primary acoustic output of the horn (with alternating polarity). The delay & addition of any broad-band signal with itself creates a comb filtering effect, which on a log scale amplitude plot appears as a sinusoidal ripple in an otherwise smooth response. The period of this sinusoidal pattern is related to the time delay of the reflection according to the equations:
    Time period = 1 / frequency
    (This period is measured between peaks on a linear frequency scale spectral graph).

    The comb filtering effect can be band limited in the case where the internal reflections are not broad band. In Tractrix or Exponential horns, the higher frequencies beam down the center of the horn, and do not diffract or reflect from the mouth edge, and so the response ripples will be limited to the lower octaves of the horn bandwidth (which is in the human voice range, where we are quite sensitive). In the case of CD horns, if the mouth has some form of flair, or radius, the high frequencies will be presented with a better acoustic impedance match, thus limiting the reflections to the lower octaves, similar to Tractrix and exponential horns. The reflection induced ripples in the horn frequency response have the same root cause as the impedance bumps which might be observed in the first octave or two above cutoff, these are attributed to improper mouth dimension for a given flare rate, as described by David Smith in the last sidebar of:
    http://www.audioheritage.org/html/profiles/jbl/4430-35.htm

    end of part 2 - Jack Bouska

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #3 of 9)

    Horn-Honk simulation:
    The first image in this thread (labeled fig 1) shows a time domain representation of two wavelets (actually two distinct single sample spikes), separated in time by 1.66ms, which is about equal to a path length difference of ~56 cm between the direct arrival and it’s 1st reflection (from the horn mouth). This is a two way travel path, (mouth-throat-mouth), which would correspond to a horn length of ~28cm measured along the straight horn walls. An impedance contrast at a horn mouth creates a negative reflection co-efficient, so the reflection is inverted polarity, and scaled in amplitude to mimic the internal reflections in real horns.

    This wavelet pair can be analyzed as a classic differentiator (high pass filter), with ripple caused by constructive and destructive interference within the HF pass band. The frequency spectrum of the wavelet pair are shown in the accompanying two graphs of fig 1, the upper graph rendered with the familiar log-log scale, and the lower graph using a linear frequency scale, which simplifies detection and estimation of ripple periodicity. The simulation of a single reflection makes the disturbance in the time domain compact, which means that the corresponding duration in the frequency domain transform will be long, and indeed we observe that the ripples extend over the full bandwidth of the high-pass zone. This is characteristic of reflections, while resonances appear to have long duration in the time domain (they ring), and short duration in the frequency domain (a narrow Q peak centered on the resonant frequency). Note that the individual spectrum of either wavelet (by itself) would be a ruler flat straight line (no ripples).

    The graphs in fig 1 are useful as comparison against spectra derived from measurements of various physical horn & transducers shown later in this post.

    On a linear amplitude scale, the interference pattern would be visible as a series of deep notches, however on a log amplitude scale the notches are compressed into sinusoidal ripple. The portion of the log spectrum which exhibits the strong sinusoidal ripples can also have a second pass of Fourier transform applied, to convert the values into the Cepstral domain, which would provide a direct readout of the offending reflection on a time scale. (Not required for this simple illustration)

    Also note that reflection induced horn-honk is not amplitude dependant (like harmonic distortion), and can be heard equally clearly at low or high amplitude levels.

    The simulation in fig 1 is illustrative of the problem, but over simplified because most real world horns, typically the slot loaded CD variety, have multiple sets of abrupt flare rate changes, with variable horn mouth termination, creating reflections with different path lengths along the horizontal and vertical walls. Multiple reflections will complicate any analysis which is reliant on frequency spectra. The reflections are also difficult to detect in real world time domain plots, as the reflection time is often shorter than the coda (tail) of the primary wavelet for band limited horn loaded transducers. Dr Holland used the Cepstral domain for analysis of complicated reflection patterns; however the examples I will show later in the post can be interpreted by simple inspection of the frequency spectrum. This ripple signature of horn-honk is often seen in various commercial frequency graphs, and can be used as a good indicator of how well the horn mouth is impedance matched to free space, and/or how much horn-honk will be audible in the device.

    Practical demonstration of Horn-Honk sound:
    In post #5 of my oblate spheroid thread (link given above), I made the comment:
    “For a practical demonstration of how important good mouth termination is for neutral tonality, simply take your favorite magazine, roll it up into a conically shaped "megaphone" then hold it up to your mouth and clearly utter the phrase: "this is the sound of horn-honk", (and you will be speaking the truth).”

    Ok, a question for those among you who read that post, please raise your hands if you actually did roll up a magazine and try the experiment I suggested? Please keep your hands raised while I count…1,2,3,4…… ok got the tally. It’s zero! (I’ll wager none of you out there in web space tried this at home!)

    I don’t blame you for not trying, if I was sitting at work on my lunch break surfing the net and read a post suggesting I talk out loud through a rolled up magazine, I wouldn’t do it either. But that’s your loss, because it’s such a simple way to hear exaggerated horn-honk, and the experience might better equip you to detect this type of distortion by ear on typical horn/driver combinations.

    Still not convinced it’s worth talking through a rolled up magazine? Read on:

    Rarely do we get a chance to perform such a relatively simple physical experiment that provides so much information about sonic character of a device. Seriously, this demo is right at the top of the “simple but mandatory” tests such as rapping your knuckles on the side of a speaker enclosure to check for panel resonances, or clapping your hands in a large, live room to check for flutter echo and/or estimate mid-band RT60 time. (Both of which I assume you have done many times in the past).

    To help entice you to try, I have extended the experiment, to include a test of your own voice using both a poor and good horn mouth termination.
    The supplies you will need are:
    1) a large size magazine (I used last months HiFi News)
    2) a large bath towel (dry)
    3) sticky tape and safety pins (optional, but handy)

    For examples of the construction, see fig 2, below.

    I suggest you can try talking through the magazine megaphone both with, and without the bath towel rolled and wrapped around the horn mouth. Without the towel the horn mouth is poorly terminated, and you will hear the expected honky-horn sound. When the towel is strategically positioned just straddling the mouth (without restricting the opening), it will provide some absorption and round-over radius for the mouth, which will in turn provide a better acoustic impedance match for the mid and high frequencies. The simple addition of this “towel cowl” (amazingly) suppresses a huge amount of the audible horn-honk.

    To try this, first talk through the magazine megaphone without the towel to gain familiarity with the honk sound. Then roll up the towel and wrap it around the mouth of the magazine megaphone, try to keep the mouth from collapsing (it helps if you have three hands). While talking through the magazine horn with the towel, it will sound flat or dead at first, but if you quickly remove the towel cowling, the honk returns instantly.

    After a few trials, it will become apparent that the sound with the towel is neither dead nor flat, but rather neutral and tonally smooth, especially compared to the naked magazine megaphone. It’s quite spooky to hear such a simple apparatus sound so clear and natural on human voice. I had the opportunity to demonstrate this at the recent LLDIYHiFi pub meeting a week ago, using a rolled up jumper (sweater) in place of the towel, and the club members were astonished at the audible difference in tone with and without the mouth treatment.

    end of part 3 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #4 of 9)

    Horn-Honk measurements and calibration:
    To help entice everyone to give this a try, I have decided to do the experiment for you, (just this once), in such a way that I can measure, and graphically illustrate the spectral changes. This provides a calibration dataset to study while testing the effect while using your own DIY magazine-megaphone, and towel cowl.

    In the second image of this thread: fig 2-A and fig 2-B, illustrate the rolled up magazine which is fixed in a cone shape using masking tape, along with a small computer speaker that I substituted for my own mouth and vocal cords. Fig 2-C shows the magazine horn with the bath towel that I rolled (into a long cylinder shape) and wrapped around the mouth (half on, half off). Dimensions of this apparatus are shown at the top of fig 2.

    The next three figures 3-5, show spectral analysis (log amplitude, linear frequency scales)
    Fig 3: the naked transducer,
    Fig 4: the speaker/magazine megaphone combination, and
    Fig 5: the speaker/magazine megaphone and towel cowl combination.

    Wideband white noise was used as an excitation signal, and the microphone was slowly traversed through a 6x6x6 inch volume approximately 8” in front of the horn mouth (closer for the raw speaker), to provide a modest level of spatial filtering, which attenuates some of the floor and table early reflections, so as to highlight the spectrum of the device under test. The driving amplitude and microphone gain was kept constant, although the microphone was placed closer (4”) to the raw driver than it was for the horn tests. The scale of the spectral analysis is the same for all three plots. (1 dB/division)

    Fig 3 shows the frequency spectrum of the raw driver. The graph illustrates some resonances and response aberration inherent to this transducer, and is included for baseline comparison. The driver is seen to have sufficient output in the upper octaves to be useful for this test.

    Fig 4 shows the frequency spectrum of the speaker driving the magazine megaphone. The increased level of sinusoidal ripple across the top 4-5 octaves of the amplitude spectrum is immediately apparent. This is attributed to the strong acoustic impedance contrast at the megaphone mouth, which causes a reflected wave to travel back down the megaphone, to be reflected again from the speaker (at the throat), back to the mouth. The reflected energy combines with the primary signal to form notches in the spectrum (comb filtering. This is directly comparable with the ripple seen in the graph at bottom of fig 1.

    The clarity and amplitude of the mouth reflection of this particular horn allows the comb filter notches, and associated reflection time to be obtained by direct inspection of the FFT spectral graph. In this case, the period between peaks (or troughs) along the frequency axis is approximately 600Hz.

    This 600Hz period corresponds to reflection with time T = 1/P = 1/600Hz = 1.66ms. This time corresponds to a 2 way distance of (334m/s x 0.00166 s) = 55.6cm. This distance corresponds closely with about double the axial length of the magazine megaphone.

    The graph in fig 4 clearly shows the characteristic oscillatory spectral shape associated with the distinct tonal coloration you will observe when speaking through your own version of the magazine megaphone. This graph helps you calibrate the sound you hear from the megaphone against this familiar (and common) spectral display. You can now use the rolled up magazine to train yourself to recognize what horn-honk sounds like, and you can use the graph in fig 4 to train yourself to recognize horn-honk using spectral analysis, such as frequency response graphs published by loudspeaker manufacturers.

    Based on the description of the mechanics behind the generation of horn-honk, it should be a simple matter to devise various schemes to improve the impedance match at the mouth of our magazine megaphone, in order to suppress the honk distortion. Flaring the mouth, adding a large radius, adding damping material would all work to greater or lesser degrees; however I chose to use the towel cowl because I assume the entire forum membership either has access to a towel, or could easily borrow one from a willing neighbor. When wrapped carefully around the mouth of the magazine megaphone, the towel cowl forms a partial radius, and provides some acoustic energy damping, both of which help to “soften” the abrupt impedance contrast discontinuity at the mouth.

    The measured results of the towel cowl are shown in fig 5. Notice the nearly complete suppression of ripple above 3 kHz, with weaker attenuation of ripple between 1-3 kHz. The evidence from this spectrum alone should be sufficient to convince everyone reading this post of the value in trying the magazine megaphone and towel cowl experiment at home (A gif animation is included below for ease of comparison between figs4-5)

    Comparing the two graphs in figs 4 and 5 aids in understanding the differences which can be heard between the megaphone with and without the towel. The addition of the towel audibly improves the sound from the horn, removing a huge proportion of the unpleasant honk, so reminiscent of standing in a small tunnel.

    If at this point, you want to understand more about horn-honk, I suggest you obtain a large magazine and bath towel and try this for yourself. Remember, you can’t learn to ride a bike by simply reading a book of instructions; you actually need to get on it and try. Reading this post, and viewing the graphs may benefit the visual learners among you, but trying the experiment yourself will tap into your kinesthetic learning capability, and better tune your ears into the sound of horn-honk, so that you are better able to detect, and suppress it in your own horn loaded systems.

    Criteria for suppression of Horn-Honk:
    In their speaker builder article, Newell and Holland suggest that axially symmetric horns are the best means to attenuate the sonic aberrations associated with internal reflections. I agree that a well constructed axially symmetric horn will achieve this; however that shape is not mandatory for good tonality, and rectangular shaped horns would be equally permissible, if they adhere to the following guidelines:

    a) The throat section should be unrestricted (no diffraction slots).
    b) The throat should smoothly taper into the compression driver exit aperture.
    c) The horn walls should be straight or slightly curved, without abrupt flare rate changes.
    d) The mouth requires a “bell section, lips, or curved radius” treatment, which will effectively flare out to a full 90 degrees from the horn axis, such that the final horn wall exit angle is flush with the front baffle.
    e) The horn flare should be accompanied by complementary radius of the front baffle
    f) The edges of the horn could alternately be treated with felt, acoustic foam, or any other absorbent material that would suppress the diffraction and reflection from the mouth.
    g) The axial length should be shorter than 12” (details to follow).

    The points a) through g) above could be applied to any horn or waveguide design to yield a system capable of suppressing both the acoustic impedance contrast discontinuity at the mouth and within the horn resulting in low levels of horn-honk.

    Clearly, points a) through d) are easier to achieve when constructing an axially symmetric horn, compared to a horn with a rectangular mouth. Newell and Holland tested a device called the AX2, (which appeared to be either exponential or Tractrix flair), and the midrange tonal quality of this horn was reported as nearly equal to that of a Quad electrostatic loudspeaker. The line drawing of the device showed a very wide mouth, and presumably good flare rate match into the front baffle. It seems then, that for best tonality, the contour is not important, and any of the exponential, Tractrix, oblate spheroid or conical types can yield equally low levels of horn-honk, so long as all the external and internal acoustic impedance discontinuities are minimized.

    Considerations for commercial and DIY horns and waveguides:
    Referring again to the directivity simulations in posts #38-42 of the Handmade Ersatz M9500 thread http://www.audioheritage.org/vbulletin/showthread.php?t=12390&page=3 I note that the Tractrix and exponential horn types exhibit strong narrowing of directivity with increasing frequency, (beaming). This means that only the frequencies in the lower range, with wavelengths comparable to the axial length of the horn, will diffract enough to engage the impedance discontinuity at the horn mouth. This may contribute to the generally good quality of sound (low level of horn honk) from the Tractrix flair type, and perhaps also in exponential horns with very wide mouths, where the final exit angle approaches 90°. Horns which are truncated in axial length will exhibit much higher levels of horn-honk.

    Commercial horns or waveguides intended for PA use, (in single or multiple array configurations), tend to have rectangular shaped mouths, allowing piecewise continuity of coverage for large venues. The home constructor can be less concerned with the need to specify different coverage angles in horizontal and vertical axes, and is free to build axially symmetric contours, which can be easily turned on a home workshop lathe. The axially symmetric coverage pattern is acceptable in a home setting, where the floor is generally carpeted, and for seated listeners, the ceiling is high enough above the horn and ear height so that the first reflection from the ceiling will bounce down to a point behind the listener, if seated in the front half of the room (near the speakers)

    end of part 4 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #5 of 9)

    Mouth termination in commercial horns and waveguides:
    Commercial horns and waveguides may also suffer from physical constraints associated with the need to be economical in terms of front baffle real estate. The requirement to provide good mouth termination, by either flaring the contour to 90° at the horn mouth, or providing a ¼ round radius edge around the horn/waveguide exit, mandates that the horn mouth might need to double in diameter. Earl Geddes states that the radius curve should be equal to ¼ wavelength at the lower cutoff frequency. For a 1.1 kHz cutoff, this adds almost 3” all the way around the horn mouth. Commercial horns often have cutoff frequency in the range of 550 Hz, requiring about 5” additional mouth radius, which could mean as much as 500% increase to the total front mounting surface area of a typical commercial horn. For example: a 7” x 7” horn with cutoff of 550 Hz and mouth area of 1/3 sq.ft. will require approximately an extra 5” wide radius edge around the periphery, making the final mouth area = 17” x 17” , which equals 2 sq.ft.! The size increase would not be very conducive to sales, especially if the horns are to be used in tight packed flying clusters or arrays. In practice, most commercial horns opt for compact size over good mouth termination, which is why horn-honk is still prevalent in commercial horn and waveguide offerings.

    It may be possible to modify the mouth termination of some commercial offerings to improve the tonal quality; however this should be accompanied by careful before-and-after testing and auditioning in order to verify the expected performance improvement. For internally generated reflections, modification is unlikely to improve the sound. For most DIY’ers the effort and complexity required to add a rounded cowl to the front of a commercial horn would justify building a new waveguide from scratch instead.

    Horn length impacts detectability of Horn-Honk:
    The blind testing, and subsequent analysis, of Newell and Holland also revealed that the time delay of the reflections was at least as important as the amplitude. In other words, short horns (less than 12” long) with poor mouth termination sounded better than long horns (longer than a foot) which had slightly lower amplitude reflections. This finding would encourage prospective builders to keep their waveguides as short as feasible in the axial direction.

    Human hearing is very sensitive to the time span between short period echoes. This is an important mechanism employed by our hearing system for spatial location of sound sources. Frequency response ripples (notches) are generated by directionally dependant reflection interference caused when a wave front reflects from the folds (pinnia) of the ear. Sounds impinging on the ear from different directions will illuminate different parts of the ear, changing the combination, and delay times of the resultant reflections. The sound reflected from the pinnia interferes with the direct arrival sound within the ear (at the eardrum) and the interference is detected in the cochlea as a series of notches, periodically spaced in frequency. The physical size of the ear, and the size, shape and spacing of the folds dictate that the frequencies of importance for spatial location fall in the 2khz to 6khz range.

    As evidence of our keen ability to recognize slight reflection timing differences, another simple experiment using cardboard tubes can be performed. These commonly available (bathroom roll) cardboard tubes (approximately 4” long by 1 7/8“diameter) are also illustrated in fig 1 D. After obtaining a pair of these, try cutting 1” off the end of one of them and speak through the tubes, switching lengths as you talk. Although intuition may guide otherwise, the difference between the tonalities of the two tubes is clearly audible, and although the tube lengths differ by only 1”, sonic preference goes to the shorter device. While swapping and talking, you can also try to put the two tubes end to end, and continue to speak through them both. This imparts an even more objectionable tone to the sound, yielding more horn-honk. The only variable in this experiment is the length of the tube, as all three cases have exactly the same level of acoustic impedance mis-match at the mouth, and the same loading property at the throat (your mouth). This experiment reinforces the notion that shorter horns will sound better than long ones.

    Some Horn-Honk is present in all horns and waveguides:
    The problems of mouth induced, or internally generated, reflections is a common problem among all horns and waveguides, professional or DIY alike, because the impedance matching between transducer and horn, and the horn and the room is never perfect. The best approach would be to build horns or waveguides following the guidelines in a) through f) above, followed with careful measurement and audition to ensure that horn-honk is kept to a minimum. For commercial horns or CD waveguides which exhibit honk, replacement with a better design is the best option for home use.

    As an example of how prevalent these internal reflections are in commercial devices, I include frequency response graphs from a pair of JBL speakers, which I happened to have handy. These are shown in the top part of fig 6, images: A & D. Both these graphs show clear ripple in the high frequency response. It’s a bit hard to see the periodicity because of the log frequency scale, but the time period for both graphs falls in the 600-800 Hz range, yielding a path length difference of 16 to 22 inches (corresponding to horn sidewall lengths of 8 and 11 inches). The ripple amplitude is fairly large; however the horn length falls under the magic 1 foot specification given by Newell and Holland. I have not auditioned these speakers myself, however early reports of the DD66000 sonic character are universally favorable. Despite this, the graphs don’t lie, and I suspect a critical listener would be able to detect some level of horn-honk in both devices.

    To my knowledge, the work of Dr. Holland has not received widespread attention in either of the pro-audio or HiFi fields, and so we are unlikely to see offerings from the pro-audio manufacturers for horns or waveguides specifically designed to address internal reflections, especially considering the requirement for mouth size expansion. This leaves the task to the DIY crowd, and a couple of examples from my workshop are shown in the lower half of fig 6, images: B & D. These are the same pair of axially symmetric Oblate spheroid waveguides which I described in the thread referenced earlier. The waveguide contours are compound, with the larger unit employing both a Tractrix mouth, and ¼ round radius at the mouth (this doubles the diameter). While the smaller unit utilizes a ½ round radius of smaller diameter, allowed by the use of a higher crossover frequency.

    The horizontal and vertical scales on all four graphs of fig 6 are identical, allowing direct comparison of ripple level between the four units. The DIY waveguides are seen to exhibit somewhat lower levels of ripple over the intended pass band compared to the commercial offerings. The ripple that is visible on the DIY spectra is longer period, which is consistent with the design of short axial dimension in these devices. The graphs are included not as a “shoot out” comparison, but simply to illustrate that a home hobbyist, armed with the knowledge of the mechanism which causes horn-honk, can build good sounding waveguides in their home workshop. Now, pick up a magazine, roll it up into a megaphone and talk through it, if you need further convincing that this is a worthy goal.

    Controlled Directivity in waveguides:
    On the “Erstaz.” thread, Rob posted a question addressed to me, on the subject of CD horns and diffraction:

    Quote Originally Posted by Robh3606
    Hello Jack, I have a question about both the Peavey horn and Earls…..snip…Rob


    The controlled directivity subject has a number of facets related to subjective sound quality of horns, which will require covering some background information in order to give a meaningful answer to the question.

    At the beginning of this thread, I listed the big four criteria for good sound reproduction, and I repeat the list here:
    1) Flat frequency response, both on axis and total radiated power.
    2) Wide frequency bandwidth. (20Hz -20kHz is sufficient)
    3) Wide dynamic range, meaning realistic peak output SPL, with low electrical and mechanical noise floor.
    4) Low distortion (all forms of non-linearity)

    Category #1), of the big four, lists the requirement for flat frequency response both on axis, and in terms of total radiated power. What that means is that an on-axis frequency response measured in an anechoic chamber should be flat, with no resonant peaks or troughs, no ripple, and no broad tilt or response variation (ruler flat is best). If the phase is well behaved, this will yield a good impulse response in the time domain.

    I additionally stated my criteria for flat response in terms of total radiated power, which relates to the requirement to generate both early reflections, and diffuse reverberant sound field with frequency response that mimics the direct arrival spectra. The spectra of the total radiated power could be measured in a “live” reverberation room at some distance from the speaker, independent of relative microphone-speaker angle.

    end of part 5 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #6 of 9)

    Why CD?
    My original interest in smooth power response was motivated by a series of articles which appeared over a number of years during the 1980’s, in an obscure Canadian magazine called Audio Scene Canada. The editor, Ian G. Masters, often reported on the research being conducted by Dr. F. Toole at the National Research Council (NRC) facilities in Ottawa. Dr Toole concluded that when frequency response, and other factors were held constant (and adequate), subjects in the extended blind listening tests reported strong preference for those speakers which exhibited the smoothest off axis response, and those that came closest to providing full omni directional response.

    Members of this forum will know of Dr Toole from his work with the Harman group of companies, and the strong influence that the NRC team has had on JBL home and pro-audio divisions. Dr Toole’s white papers on this and other subjects are mandatory reading
    http://www.harman.com/about_harman/technology_leadership.aspx (look under white papers).

    While I am not a fan of pure omni directional speakers (stereo image is too vague for my taste), I am a big proponent of using controlled directivity in the high frequency end of the spectrum to limit the adverse effect of early reflections, and improve the subjective tonality of the reverberant sound field in my listening room.

    For a reasonable synopsis of how this can be accomplished with CD waveguides, see the white paper written by Earl Geddes on the Summa loudspeaker and room placement:
    http://www.gedlee.com/downloads/Summa.pdf

    How to achieve CD:
    Under the assumption that CD is desirable for good room integration, the next question is: how do we simultaneously achieve both good CD, and good tone, in a driver & waveguide combination?

    Most waveguide designs require three features to achieve reasonable constant directivity performance:
    a) Conversion of plane waves into spherical waves via diffraction.
    b) Flare shape which guides the spherical waves without wave front distortion.
    c) Transducers which produce true plane waves over a broad range of frequencies.

    The full quote of Rob’s question is shown just below:
    Quote Originally Posted by Robh3606
    Hello Jack
    Quote Originally Posted by Robh3606
    I have a question about both the Peavey horn and Earls. In both cases the measurements stop at 10K. What actually going on above that frequency?? The 2344 used the diffraction slot width to determine the HF beam width limit in the horizontal plane. Both Earl’s horn and the Peavey don't have this feature so the smallest dimension is the throat diameter. In Earls I think it's a 1" throat while the Peavey is 1.6". Are the throat dimensions acting as a diffraction slot as far as the upper limit dispersion in concerned? Does the directivity change above 10K???
    Rob
    The peavey white paper that was referenced in the Ersatz thread can be found here:
    The Quadratic-Throat Waveguide (overview):
    http://www.installaa.com/downloads/pdf/qwp1.pdf#search=%22charlie%20hughes%20peavy%22
    and C. Hughes paper here:
    http://home.carolina.rr.com/charliehughes/Articles/QTWaveguide/QTWaveguide-Fr.html

    The first link gives a good historical review of CD horn design, and introduces the use of conical horns for defined coverage. The second link introduces the concept of: one parameter (1P) wave propagation, which turns out to be an important aspect of modern CD designs. 1P wave propagation is defined as an acoustic iso-pressure wave-front where the instantaneous pressure is a function of a single spatial coordinate.

    Only three types of 1P propagation exist for acoustic waves, namely: planar, cylindrical, and spherical waves.

    A planar wave travels along one of the three Cartesian coordinates, say X, while the instantaneous pressure is invariant over both the other coordinates, Y and Z. Think of a low frequency pressure pulse moving in a heating duct, or pipe, the pressure at the wave front is the same top to bottom, and side to side (width and height of the duct), and only varies by distance along the duct. The duct side walls act as perfect reflectors (acoustic mirrors), creating the same effect as if the wave was moving in open space.

    A cylindrical wave might be generated by a very, tall circular array of small ribbon transducers. In cylindrical coordinates, the low frequency components of the pressure pulse do not vary in the Z axis up and down the ribbon, or in the Theta angular axis, the pulse is invariant in circular arcs around the ribbons, so the pressure only varies with radius away from the center.

    A spherical wave, which might be generated from a very small omni directional transducer, has a low frequency pressure pulse that only varies by the radial distance from the center, so that pressure at a point in space is completely determined by the coordinates of time and radius.

    Perfect examples of 1P waves don’t really exist in the physical world, but if the frequency range is kept low enough, the approximations are close enough for wavelengths longer than any dimension of the transducer. For instance, PA line arrays are designed to emulate cylindrical wave generation.

    The motivation for discussing 1P waves is that compression driver phase plugs are designed to generate approximations to plane waves at their exit apertures. Modern CD waveguides work by launching sections of angle constrained spherical wave fronts. This trick requires a device that converts between 1P propagation types, by transforming plane waves into spherical waves. I know of three physical methods which can be used to change between plane waves and spherical propagation:

    1 – Reflection, such as the parabolic microphones used by birdwatchers and spies
    2 – Refraction, such as the acoustic lens discussed by Ausburger (http://www.lansingheritage.org/html/jbl/reference/technical/lens.htm )
    3 – Diffraction, as used by the majority of CD waveguides on the market

    Diffraction is in common use, because it really is the only practical method for converting the plane wave front from a compression driver exit, into a uniformly distributed sound field. There are other horn geometries, such as Tractrix, Acapella (or Avantgarde) "Kugelwellentrichter" shapes which are lumped into the category called “spherical horns”. Unfortunately, there is no magic flare rate, or horn shape which will convert plane waves into spherical waves. The “spherical” horn flares, or any other exponential, or hyperbolic, curve which has a large radius of curvature at the throat (slow expansion), followed by a smaller radius of curvature at the mouth (rapid horn diameter increase), will always exhibit increasing DI with increasing frequency. These horn types can only produce spherical wave fronts at the lowest frequencies, where the wavelength is equal or longer than the horn axial length. (Usually close to cutoff frequency). See discussion below for details.

    The majority of modern waveguides achieve broadband constant directivity by transforming the transducer generated plane wave to a spherical wave by passing the plane wave though some form of diffracting aperture, which expands into a (semi) conical horn flare. These CD waveguides need to have predominantly straight sided walls, which intersect with the edges, or center, of the diffraction aperture. The spherical wave front emitted by a diffraction aperture will always propagate perpendicular to straight sided (radial) walls. Any radical departure from straight sides will cause reflections and/or induce non-spherical (non-1P) expansion of the wave front, which will defeat the CD objective.

    end of part 6 - Jack Bouska

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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #7 of 9)

    Horn wall shape:
    Straight sided waveguides are fundamentally different from traditional flared horn contours. Imagine the layers (skins) of an onion represent the isophase acoustic wave fronts radiated from a tiny source at the onion center. Imagine poking a long thin needle directly towards the center, it will be perpendicular to each layer at the point of piercing.

    Now imagine using a sharp knife to cut the onion in half, directly though the center. Each of the layers comes to the plane of the cut at exactly 90°. If the plane of the knife cut does not pass through the center, the layers will not intersect the cut at 90°. Imagine the needle edges are sharp enough to carve out a cone (with the apex fixed at the center of the onion), you would also see that the onion layers remained perpendicular to the cut. Actually the needle could carve out a pyramid, or oval, or any other 3D shape into the onion, and as long as the tip of the needle stayed at the center, the cut would always be 90° to the onion layers.

    For spherically expanding wave fronts, (or any 1P wave), the guiding boundaries (horn walls) which are perpendicular to the wave front act as acoustic mirrors, and create reflected phantom images of the wave front (continuing the same curvature beyond the wall), which effectively cause the 1P wave to continue to propagate exactly as if it were in full 360° (3D) space.

    The majority of CD waveguides do not have perfectly straight sidewalls, for a variety of good reasons (some to be discussed), but they all use straight-radial bell sections at the critical point just following the diffraction aperture. (The Oblate spheroid is a slight exception).

    Diffraction from small apertures:
    In practical terms, diffraction requires that the aperture appear as a discontinuity in acoustic impedance. A low frequency plane wave traversing an aperture which has dimensions smaller than a wavelength will create a spherical wave front in the far field. The shape of the aperture is largely unimportant (square, round or rectangular) for long wavelengths, but will have impact on the radiation pattern for wavelengths close to, or shorter than the diffraction aperture dimensions. Rectangular apertures are convenient for driving waveguides with rectangular mouths, and round apertures best fit round mouth waveguides. Regardless, both shapes will produce diffraction patterns for the lower frequencies.

    Acoustic textbooks usually illustrate diffraction via a plane wave impinging on a thin, planar, barrier containing a small aperture, which produces semicircular (2D) or hemispherical (3D) waves on the other side. The thickness of the thin-plane-barrier should be less than ½ a wavelength; otherwise the higher frequencies will propagate within the aperture as if it were a short waveguide.

    Compression drivers feed the waveguide diffraction aperture from either an integral short cylindrical pipe (with low freq. Exponential taper), or directly from the phase plug (on modern compression drivers). Fortunately, the diffracting aperture works the same regardless of whether the impinging plane wave is infinite in scale, or guided via a circular conduit. (See paragraph above describing plane waves in ducts.) What is important is that the exit aperture of the compression driver emits plane waves across a broad band of frequencies. There is a high frequency limit to the plane wave assumption, as I will discuss later.

    In acoustic waveguides, and also in some horns, diffraction occurs at the point of rapid flare rate change, either at the exit of the compression driver, or in older CD waveguides, following a short exponential (or hyperbolic) tapered duct, (which may be required to provide low frequency loading for the transducer). The phrase: “rapid flare rate change” implies a short radius curvature change of the horn walls. For horns with continuous curves, diffraction effects are limited to a distance of about ½ of a wavelength (measured axially). This means that the angular coverage as a function of frequency will roughly conform to the tangent angle of the horn wall at an axial position which is ½ of a wavelength away from the beginning of the flare curve (usually the horn throat).

    Throat control over directivity:
    In post #9 of the waveguide comparison thread: http://www.audioheritage.org/vbulletin/showthread.php?t=12751 observe that the Huges-Peavy and Geddes-oblate spheroid waveguides both rapidly flare into the final angle coverage (about 26°), with most of the flare change occurring in the first 3” for the Huges curve, and within the first 2” for the Oblate spheroid curve. (This graphic is repeated below as fig 7, with 1:1 scaling for clarity). This would imply that the Huges waveguide will operate as a CD device up to about 9.1kHz (f=Vel/(1/2 lambda) = 13716ips/1.5”), and the Oblate waveguide will cease acting as a CD device above about 13.7kHz. (f=13716ips/1”) The directivity will gracefully narrow above those frequencies.

    For horns with exponential, or Tractrix flare, the most rapid horn wall curvature changes occur towards the mouth of the horn, with the sides exhibiting less curvature near the throat. This means that waves will only diffract into the full angular coverage, defined by the exit angles of the mouth, for wavelengths which are longer than the axial length of the horn. For shorter wavelengths, the coverage pattern approximately conforms to the angle of the horn walls at the ½ wavelength axial position. For most of the other horn curves in fig 7, the angles range from 8°-12° at an axial distance of 3”, meaning that these horns (exponential, Tractrix, hyperbolic and spherical) will be unable to support a beam width of more than +/- 10° at 9kHz and above.

    In contrast, the two oblate spheroid contours plotted in post #3 of my DIY Axially symmetric oblate spheroid CD waveguide thread:
    DIY Axially symmetric oblate spheroid CD waveguides, in solid Oak ( http://www.audioheritage.org/vbullet...ad.php?t=12126 )
    are both shorter devices (3.3 to 3.5 inches deep), with a wider angle of coverage (+/- 40°). Consequentially the initial flare is more rapid, with greater curvature near the throat. The 2” (49mm) throat device flares out to 36° (just 10% shy of the final exit angle) within the first 1.4” of the axial length. This would correspond to a CD bandwidth extending to a frequency of 19.6 kHz (f=13716ips/0.7”). The 1” exit oblate spheroid waveguide in post #3 flares out to 36° within the first inch of axial length, which would not start restricting a CD operation until upwards of 27.4 kHz (f=13716ips/0.5”).

    A cartoon graphic representing the frequency dependant directional effect of horns with curved walls compared to horns with straight walls is shown in fig 8-B. ). The graphs in Fig 8 are taken from an article found here: http://www.soundandcommunications.com/audio/2005_09_audio.htm
    The lowest frequencies, with wavelengths larger than the horn mouth circumference are seen to approach omni directionality, above the frequency of mouth-diffraction induced waist banding, the horns with straight walls have constant directivity, and the horns with curved walls have decreasing angular coverage. At the top end of the bandwidth, the aperture dimensions of the throat limit directivity in both types of horns.

    Throat reflections:
    Note that a pure conical flare, with an abrupt angle change at the throat, would have the broadest frequency bandwidth, unrestricted by horn wall curvature, albeit, with the associated penalty of inducing high levels of intra-horn reflections and associated horn-honk. The Huges (Peavy) quadratic throat mitigates this problem by introducing a radius curve transition (“quadratic throat”), which suppresses high frequency diffraction and reflections. For frequencies in the lower octaves, the radius will progressively appear as a sharp transition, which may present sufficient acoustic impedance contrast at the low frequencies to generate internal reflections.

    The Geddes oblate spheroid flare is a superior design which provides a continuously variable radius of curvature from the throat to the mouth, where the exit angle is asymptotic to the desired coverage angle. The advantage of this curve is that the highest frequencies are presented with a very short diffracting radius (which extends CD bandwidth upwards), while the lower frequencies see a “gradational-scale” radius of curvature, which reduces the impedance contrast over a much broader range of frequencies, all the way down to the horn cutoff. In my opinion, this is the true genius of Earl Geddes invention, a waveguide device which provides true broadband constant directivity coverage, via effective diffraction of 1P plane waves into 1P spherical waves, with the minimum of internal acoustic impedance discontinuities.

    end of part 7 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #8 of 9)

    Diffraction aperture dimensions:
    Rapid throat flare rate is a necessary, but not a sufficient condition for wide angle, high frequency diffraction, as the diffraction aperture must also be sufficiently small compared to the wavelength at the highest frequency in the CD bandwidth. The “piston in an infinite baffle” model is adequate to estimate the aperture directivity as a function of frequency, for plane waves emitted from a compression driver.

    Fig 8-A shows polar amplitude plots for various values of “ka” for a piston in an infinite baffle (ka= circumference / wavelength and a= diameter on these plots). See also:
    http://www.lansingheritage.org/images/jbl/reference/technical/inside-monitor/page02.jpg

    From these set of graphs, a value of ka=4 is estimated to have a CD beam width of +/- 40° at the -6dB SPL limits. At larger values of ka, the beam width narrows very rapidly: less than +/- 30° at ka=5 and about +/- 7° at ka=10.

    These charts can be used to estimate the upper frequency limit for diffraction into a (semi) conical waveguide flare.

    The formula for k = (2*Pi*f) / Velocity.

    Substituting ka = circumference / wavelength yields: ka = (Pi * d) / (Vel/freq.)

    Rearranging terms gives the equation for frequency (as a function of ka number):

    Frequency = (ka * Vel) / (Pi * a)

    We can calculate the upper frequency limit for both a 1” exit and a 2” (49mm) exit driver, with a conical waveguide flare of +/- 40°. Fig 8-A, shows that ka should be 4 or less for diffracting into a beam width of +/- 40°.

    For a 1” exit compression driver:
    (a=.00254m), Freq = (ka*vel) / (Pi *a)
    = (4 * 334m/s) / (3.1416 * .00254) = ~ 16.7 kHz.

    For a 2” exit: (a=.0049m), Freq = (4 * 334m/s) / (3.1416 * .0049) = ~ 8.7 kHz.

    In practice, the upper frequency limit of CD coverage will be somewhat larger than these calculations, owing to the contribution of some side lobe energy which is constrained within the waveguide throat radius, and reflected towards the mouth. This is more of a factor in waveguide designs with a narrow coverage angle.

    If the desired coverage angle is wider, say +/- 60°, then the value of ka needs to be lower, and we see from fig 8-A that a value of ka = 2 has approximately a -6dB amplitude at 60°. This will drop the upper CD bandwidth by a factor of two, meaning that a 1” exit driver will be limited to a constant directivity of +/- 60° for frequencies below 9 kHz, and a 2” exit will be limited to 4.5 kHz in a +/- 60° design. Waveguides designed for these broad angles of coverage invariably load the compression driver with a short tapered conduit which terminates into a narrow slot at the throat of the conical CD section. The slot is then adjusted to be sufficiently narrow to provide wide band diffraction into the desired coverage angle. These types of multi-segment CD horns are prone to suffer elevated levels of horn-honk due to internal reflections caused by the segment discontinuities.

    Waveguide DIY Tips:
    I would encourage any hobbyist constructor who is opting for a more acoustically neutral CD waveguide to try an axially symmetric, continuous curvature flare, such as the oblate spheroid, or quadratic throat designs. These waveguide designs are not fool proof, however, and sufficient care must be applied when choosing the various performance parameters to achieve optimum trade-off in the quest for good sounding CD:
    As a recap, the various parameters which must be considered are:

    1) Compression driver exit diameter (determines angular coverage for given upper frequency)
    2) Waveguide mouth exit angle (determines coverage angle, and impacts axial length and mouth size)
    3) Waveguide axial length (affects: throat curvature, mouth size, and degree of horn-honk)
    4) Compression driver bandwidth (power limited on low size, diaphragm breakup, or phase plug limited on high side.)

    Typically 1” exit drivers, loaded with a conical-derivative waveguide, employing a flare rate in the 40-50° range, can be built fairly compactly (6”by4”) while yielding good sounding CD coverage from around 1 kHz to over 15 kHz in a home setting.

    Midrange Cone transducers vs. horns and waveguides:
    I want to remind readers that compression driver distortion (2nd and 3rd harmonic) through the upper midrange (500 Hz to 2 kHz) is typically much higher compared to modern cone midrange transducers. As an example, see figures 9 and 10 in the jbl tech note V1#8: http://www.audioheritage.org/vbulletin/showthread.php?t=4410
    And compare this to the much lower distortion from the jbl 2012:
    http://www.jblpro.com/pages/pub/components/2012h.pdf


    Compression drivers with high compression ratio’s generate strong harmonic distortion when high acoustic amplitude levels exceed the capability of the air (trapped between the diaphragm and the phase plug) to act as a linear spring. High compression ratios do improve efficiency; however the penalty comes in the form of increased distortion.

    In the pre-war days of cinema sound systems, SET amplifier output was limited to a few watts, which forced the design tradeoffs more towards efficiency rather than considerations of distortion, bandwidth, or audience coverage. Early compression drivers were used in horns with cutoff frequencies around 300 Hz, and 500 Hz horns were in common use up until the end of the last century. These low frequency cutoff frequencies mandated the use of a driver with high compression ratio with good (exponential flare) low frequency loading. With availability of modern high power amplifiers, complimented by reasonably efficient, high power, low distortion, direct radiator cone loudspeakers, it is prudent to consider system designs employing a cone midrange to cover a much wider bandwidth, up into the kHz range, depending on the diameter of the cone transducer.

    The tech note and spec sheet referenced earlier show that the JBL 2012 cone transducer requires about 8dB more power for the same acoustic output compared to the JBL 2445 (15.5V vs. 6.3V), but exhibits 10-15dB less distortion over the midrange, for the same acoustic output!. Based on maximum power handling, the peak acoustic output of both a 2446 and 2012 would be about the same over the critical midrange frequencies, despite the fact that a 2012 would cost considerably less than a 2446 + large horn. The midrange cabinet for a 2012 would be also be much smaller than a horn with 500 Hz cutoff, and considering that direct radiators do not suffer from horn-honk, it appears increasingly difficult to justify the use of compression driver and horn combinations below 1 kHz.

    Above 2 kHz however, there are no direct radiators which are comparable to a large format compression driver and waveguide in terms of peak acoustic output and good directivity control. To achieve the goal of maximum dynamic range, and lowest distortion, a cone crossed over to a compression driver + waveguide somewhere between 1 and 2 kHz appears to be the optimum choice.

    end of part 8 - Jack Bouska
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    Factors Affecting Sonic Quality of Mid & HF Horns & Waveguides (Part #9 of 9)

    (This is the last post in this 9 part series, if you jumped to this thread here at the end, please go to the top and read all 9 parts in series, for continuity.)

    What about CD above 10 kHz:
    Returning again to Rob H’s question:
    Quote Originally Posted by Robh3606
    Hello Jack
    Quote Originally Posted by Robh3606

    I have a question about both the Peavey horn and Earls. In both cases the measurements stop at 10K. What actually going on above that frequency?? The 2344 used the diffraction slot width to determine the HF beam width limit in the horizontal plane. Both Earl’s horn and the Peavey don't have this feature so the smallest dimension is the throat diameter. In Earls I think it's a 1" throat while the Peavey is 1.6". Are the throat dimensions acting as a diffraction slot as far as the upper limit dispersion in concerned? Does the directivity change above 10K???
    Rob
    When I reviewed Earl Geddes graphs some years ago, I also noted that his measurements stopped at 10 kHz. I originally assumed this was because he was using an old 8 bit soundcard, or perhaps an uncalibrated microphone with poor response above 10 kHz, however it’s more likely that he did use instrument grade measurement gear.

    On his website, Earl comments that frequencies above 10 kHz are not as aurally important as those below, however I would personally raise that estimate to around 12 kHz at least, because most people, (even old rockers), have auditory response up to that frequency.

    Personally I can hear music up to about 13 kHz. I have tested this using my own system, while playing music with a laptop connected to my Behringer DCX2496 digital crossovers. I inserted a steep high cut filter at the top end, and used the mouse to slowly move the corner frequency downward. With my eyes closed, I could start to hear the filter cut into the music at 13k. When the filter corner frequency was above 13k, I could switch the filter in or out, and not detect a any difference. If my compression drivers stopped working at 14k and above, I would only be able to detect this with a microphone, but never with my ears!

    I continue to maintain that flat response up to 20 kHz is a reasonable target, considering that there are some people (mostly young ones) who can hear frequencies up that high. I’m somewhat more skeptical about adding super-tweeters which extend response beyond 20 kHz, unless of course your family pet is endowed with sophisticated taste in music. (I will defer this discussion on high frequency for yet another thread sometime in the future, as I have a backlog of material waiting to be posted) As a final comment, it is fairly easy to verify your own high frequency auditory response limit with a simple sweep test and some headphones (I have a .wav file available, send me private mail if you want to try this).

    Graphs of oblate spheroid waveguides above 10 kHz:
    The measurements that I made on my own oblate waveguides ( http://www.audioheritage.org/vbullet...ad.php?t=12126 ) indicate that the response will be well behaved up to 20 kHz for the 1” exit driver, (but only to about 10 kHz for the 2” exit device). I have found some additional frequency response and polar plots in a 1993 JAES article by Bauman, Adamson and Geddes. A copy can be found at: (http://www.exdreamnet.de/download/WgPractice.zip)
    I have copied the salient graphs in the previous post as figs 9 and 10.

    In Fig 9, the table lists the three types of horns tested, and shows comparisons of on-axis frequency response, using the same (titanium dome) compression driver. Fig 10 shows the families of curves measured at different angles to the axis (5° increment). Fig 10 also shows the polar plots at discrete frequencies for each device. While the diffraction horn shows the best overall CD behavior, the oblate waveguide is not far behind, and shows consistent performance on all the polar plots up to 16 kHz, with graceful narrowing of coverage angle at 20 kHz. This is consistent with my earlier estimates for diffraction coverage angles based on the assumption of a simple piston of 1” diameter.

    Compression driver plane wave assumptions:
    In practice, the CD performance at the high frequency extreme will also depend on the quality of the compression driver being used, and how well our assumption of 1P plane wave propagation is honored at the driver exit aperture, for the highest frequencies. The diaphragm material type, and phase plug design have a strong influence on the shape of the wave front at the uppermost octave. To generate a plane wave, the output of each phase plug slit must be in phase, and emit identical amplitude compared to its neighboring slit. Frequency dependant breakup modes will cause some parts of the diaphragm to radiate out of phase compared to other points, and the location of the breakup modes on the diaphragm will also modify the amplitude emitted from each of the slits in the phase plug. For short wavelengths, internal cavity resonances, internal reflections, and multi-path arrivals (sound emerging from multiple slits, with time delay) all begin to affect the wave front shape at the phase plug exit, causing various degrees of departure from the plane wave assumption.

    Compression driver and phase plug design are well beyond the scope of my expertise, and I have no means to measure the seriousness of this issue, nor have I seen any measurement data published which describes how high in frequency the plane wave assumption can be taken for a typical compression driver. At this point, I’ll simply speculate that a modern phase plug design, mated with a beryllium diaphragm, will produce plane waves higher in frequency compared to a driver with an older phase plug design, using aluminum or titanium. Regardless, my oblate spheroid waveguide design, with a 1” exit compression driver seems entirely adequate to deliver good CD performance well above the 13 kHz limit where most (older) folks hearing dies out anyway.

    Conclusions:
    The goal of high quality sound reproduction using compression drivers appears achievable if sufficient attention is given to; system integration, frequency response tailoring, CD coverage, internal reflections and diffractions, along with the use of high quality transducers.

    As usual, I invite your comments or questions.

    part 9 of 9 - Jack Bouska

  10. #10
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    Nice!

    Quote Originally Posted by jack_bouska View Post
    Waveguide DIY Tips:
    I would encourage any hobbyist constructor who is opting for a more acoustically neutral CD waveguide to try an axially symmetric, continuous curvature flare, such as the oblate spheroid, or quadratic throat designs.
    Build them and we will evaluate them.
    Quote Originally Posted by jack_bouska View Post
    I have not auditioned these speakers myself, however early reports of the DD66000 sonic character are universally favorable. Despite this, the graphs don’t lie, and I suspect a critical listener would be able to detect some level of horn-honk in both devices.
    Perhaps so. You'd have to do the listening yourself and draw your own conclusion. I'm not a horn fan, never have been, but the DD66000 is on the real short list of systems that I personally consider desirable. I'm always up for listening to what someone else considers to be an exceptional horn/waveguide design.
    Quote Originally Posted by jack_bouska View Post
    On his website, Earl comments that frequencies above 10 kHz are not as aurally important as those below, however I would personally raise that estimate to around 12 kHz at least, because most people, (even old rockers), have auditory response up to that frequency.
    Yeah, I'm not real sure about that whole 10 kHz thing. Speaking of graphs - here are a couple. Evidently B sounds better than A. I have yet to try it myself. The horn is a custom design of which only four exist. The details are not available.
    Attached Images Attached Images   

  11. #11
    Administrator Robh3606's Avatar
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    Hello Jack

    Nice post! On my way to work have to read it in depth later.

    Rob

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    Member jack_bouska's Avatar
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    Quote Originally Posted by Giskard View Post
    Nice!

    Build them and we will evaluate them. ......
    Construction details and flare contour graphs for 1" and 2" axially symmetric oblate spheroid waveguides are available on my thread: DIY Axially symmetric oblate spheroid CD waveguides, in solid Oak


    John W has built a pair of these 2" waveguides using my hybrid oblate spheroid-Tractrix "rams-head" horn shape. He has posted some images and early listening impressions on his Big Blue thread: http://www.audioheritage.org/vbulletin/showthread.php?t=12671&page=2

    Ken Pachkowsky is planning to visit John and they will use a DEQX to optimize crossover and EQ. The DEQX includes measurement capability, so I expect John will post some graphs, and update us on the sound quality of Big Blue and the Rams head horn, following Ken's visit.

    Jack

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    Very nice!

    Build a 1.5" so we can bolt a 435Be or 476Be to it.

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    Senior Member Ian Mackenzie's Avatar
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    Jack,

    Thankyou for the in-depth response to my question.

    Ian

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    Jack,

    thank you for your in depth analysis. Have you experimented with any materials like the LD open cell foam Geddes uses as a refractive sound plug to reduce HOMs further, or do you not feel it necessary for you design/threshold of audibility?

    thnx

    AJ

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