Baffle diffraction loss

Diffraction loss and room effects are independent and completely different effects.  The diffraction loss is nicely predictable whereas the effects of the room are highly variable, not only from room to room but also with speaker placement and room furnishing.  This typically means that each listening environment will be unique and will require unique compensation.

Spherical diffraction compensation is easily corrected with a high degree of precision, while other enclosures are a little bit less predictable and demand large amount of equalisation.

Regardless of where it is placed in the room, a typical hi-fi speaker system sees a half space load at frequencies from the midrange up as a result of the drivers placement on the
At high frequencies the speaker is radiating into "half space" i.e. it is only radiating into the forward hemisphere.  Starting in the midrange (depending on the baffle size) the system shifts from radiation into half space to radiation in full space at lower frequencies.  This transition from half space loading to full space loading results in what is commonly called the "6 dB baffle step",
At even lower frequencies, say from 100 Hz down, the wavelength of the radiated sound is such that the walls and cavity of the listening room begin to load the system in a way that results in a complex load that is less than half space and results in increased output from the system.  This effect in the low bass is called variously "room gain", "boundary effects", "room resonance", "frequency dependent radiation
impedance", etc.

The smaller the baffle the higher the transition frequency.

The shape of the diffraction loss frequency response curve depends on the size and shape of the enclosure. All enclosure shapes exhibit a basic 6 dB transition (or "step") in the response with the bass ending up 6 dB below the treble.  A spherical enclosure exhibits this transition clearly with a very smooth diffraction loss curve.  More "angular" enclosures exhibit the underlying 6 dB step along with a series of response ripples that are dependent on the placement of the speaker with respect to the baffle edges.  The worst case appears to be placing the driver at the center of a circular baffle so that it is the same distance from all diffracting edges.  Placing the driver on the baffle so that it is a different distance from each edge tends to minimize the response ripples and make the diffraction loss look more like the smooth loss of the sphere.  Because the spherical diffraction loss is a common element for the diffraction of all enclosure shapes and the response ripples are much more difficult to predict (and can be minimized anyway) it makes sense to approximate the diffraction loss of a loudspeaker as the diffraction loss of the equivalent sphere.

Q - What the hell!!?

A high Q indicates that for the amount of energy stored in a resonant system, the mechanisms that dissipate that energy are small. A high-Q system will tend to have a resonance that decays slowly, because the amount of resistance available to dissipate the energy is small compared to the amount of energy stored. Accordingly transient response of a high Q system is very bad. A low-Q system will tend to dampen the resonant motion quickly, because the energy is dissipated quickly and removed from the resonant system.

There are primarily two energy dissipating mechanisms available in a loudspeaker driver: mechanical and electrical (there is another, acoustical, but it is very small compared to the other mechanisms). The mechanical energy dissipation are primarily the frictional losses in the driver's suspension, and, to a lesser extent, acoustic absorption. There are, essentially, two electrical energy dissipations: the DC resistance to the voice coil and the output resistance of the amplifier. In almost all cases, the DC resistance of the voice coil completely dominates.

These two mechanisms, mechanical and electrical, determine, respectively, the mechanical Q (Q_ms) and the electrical Q (Q_es) of the loudspeaker driver. Their parallel combination determines the total Q (Q_ts) of the loudspeaker driver."

When we mount a loudspeaker driver onto a baffle system we also have to take into account the Q of the baffle system to arrive at the total system Q. To work out the total Q of the driver and baffle system you simply multiply the baffle system Q with the total Q of the loudspeaker driver. Closed boxes store energy that interacts with the loudspeaker driver in complex ways, especially in vented enclosures. Boxes themselves also have resonances. Normally a high-Q closed box is combined with low-Q loudspeaker driver to give a desirable total system Q. But when we mount a loudspeaker driver on an open baffle this situation is reversed. An open baffle stores no energy and has a low-Q of 0.2 and Carver chose to use a high-Q woofer with a total Q of 3+ to arrive at a desirable total system Q.

Carver's high-Q woofer was also chosen for another good reason to do with mounting a woofer on an open baffle. As we decrease in frequency or increase in wavelength, the system initially behaves as an infinite baffle. When the wavelengths are long enough to be a quarter of the baffle dimensions, the waves begin to cancel each other around the edges of the dipole baffle. The wave travels out to the edge (1/4) and back to the opposite side of the vibrating speaker cone, where it is exactly out of phase and cancels out. Quarter wave cancellation on an open baffle is a first order phenomenon - the roll-off occurs at 6dB per octave. When we reach the free-air resonance point of the high-Q woofer we add to this the second-order sub-resonance fall-off of the high-Q woofer to end up with a third-order or 18db per octave fall-off below the free-air resonance point of the high-Q woofer (this makes a good rumble filter in the Carver case).

In loudspeaker literature we can look at the family of curves for the frequency response of a loudspeaker driver on an infinite baffle as we decrease the frequency. Starting with the rolled-off curve when Q=0.5 (critically damped), then the Butterworth graph with Q=0.71 (maximally flat), then a little ripple at Q=1, then clearly a bumped-up graph at Q=1.4. When the Q is higher than any you can usually find in loudspeaker driver catalogues you start to get boosting above the resonance point of the loudspeaker driver, and a sufficiently high-Q will result in a slope of about 6dB per octave above the free-air resonance point of the loudspeaker driver. This increase of 6dB per octave of the high-Q loudspeaker driver can be used to counteract the 6dB per octave quarter wave cancellation to give a flat frequency response right down to the free-air resonant frequency of the loudspeaker driver. This is a much more elegant solution to the problem of quarter wave cancellation on an open baffle to that used by Celestion, etc of using a conventional low-Q woofer with electronic equalization since it does not involve additional amplifier power and the necessity of electronic equalization equipment. High-Q woofers are relatively easy to design/make. Both ways of overcoming quarter wave cancellation on a baffle entail the use of long throw woofers for the safe operation of the woofer.

unbridgeable gap between the Geeks with their slide rulers and the LL with their ears. Part of the problem seems to be in the misunderstanding of the use of T/S parameters.
The values of Qes, Qm, Qts were derived to assist in the design of the low frequency response of the driver for a particular box volume and alignment. These are dimensionless numbers that are based on driver primitives such as Mms (mass of the diagram including voice coil and air load), Cms driver's mechanical compliance ( surround and spider) and motor design factors Bl and Le and Re. Thus the primary applicability of T/S parameters are for the low frequency resonance frequency Fs. They can't predict the second frequency response limit, the 2nd. resonance that defines the high frequency attenuation slope. The HF slope Fh (2nd. resonance) is defined from the driver primitives such as Le, Bl and Re. It is much more difficult to compute since factors such as Re and Le effective reduction vs. frequency parameter has to be computed.
This is where the discussion of the Babb P6 response degenerates into nonsense. It is quite impossible to define the P6 high frequency response from T/S parameters. Alan makes a claim based on the proprietary design of the cone, spiderless suspension and coil Le. These are partially reflected in the impedance data as well as the Qes, Qms values. Note that the P6
Qes is unusually high and Le with frequency is unusually low and the phase unusually flat in the high frequency range. While these values by themselves are insufficient to support the claim of the unusually wide bandwidth of the P6, they should give pause that something out of the ordinary is going on and that especially T/S parameters should not be used to discuss the driver's high frequency response.

Fast Bass versus low Bass

The first thing we must know is that bass itself is not particularly fast. Virtually any woofer, even those with heavy cones can easily reproduce bass frequencies with every scintilla of speed present in that bass. So don’t buy a bunch of baloney about low-mass woofer cones leading to "high-speed bass" -- it just isn’t going to happen. If the woofer can reproduce 40Hz with low distortion, how fast the woofer starts is almost irrelevant (within reason of course). It only needs to accelerate fast enough to match the rise time of 40Hz at the fastest point along a 40Hz sine wave. If the woofer can do that, it is going as fast as it needs to in order to be as fast as fast can be -- at 40Hz. The woofer cone does not need to be able to accelerate at 20kHz velocities in order to produce instantaneous 40Hz energy and if you could build a woofer that "fast," 40Hz would sound exactly the same through a "slow" woofer.

Does this mean that there is not such thing as fast bass and slow bass? Absolutely not. It exists, just not for the reasons and explanations you have been hearing for years, and certainly not for the attributions you’ve read in the high-end press. There are reasons to use lighter, lower-mass woofer cones. They just happen to be different reasons than the ones you’ve read in print. Smaller woofers don’t make faster bass, but they do reproduce higher frequencies than larger woofers can reproduce, and this is all important when it comes to speaker design. You want the midrange driver and the woofer to integrate with sublime symmetry, with perfection and with nary a single problematic interaction throughout their overlap zone. This is why you want smaller, lighter, "faster" woofer cones -- not because they lead to faster bass. That overlap zone is so amazingly critical to your perception of bass speed that there is little or no tolerance for error. The null tolerance for integration error extends to phase, amplitude, frequency, and time. Introduce even slight variations between any part of the woofer and midrange (or panel) overlap zone and you get audible effects in the bass or midbass. This is where all of your perception of bass speed comes from.

In fact, bass speed is virtually 100% a function of how ideally the midrange and woofer are integrated. Bass linearity is greatly involved also; you may see a flat frequency-response curve, but the speaker can still sound like it has lumpy bass response because of less-than-ideal phase (or other) relationships between the midrange driver and woofer. Phase can often change with frequency. The woofer and midrange drivers can actually veer off in different directions, phase-wise. This is especially possible when you mix driver types like panels and dynamic drivers. But large dynamic drivers (woofers) operating at the top of their range and medium-sized dynamic drivers operating at the bottom of their range can often diverge significantly in their phase response. When phase (or other) errors happen, you get comb-filtering effects. This comb filtering results in the complex response of the loudspeaker (to music) being quite different than the response of the speaker when the input is something simple like the sine-wave sweep used to measure "frequency response."

To avoid comb-filtering effects that cause "beating" (reinforcement) and "cancellation" effects in the sound (both are usually partial effects), it is imperative for the phase, time domain, amplitude and frequency performance of the woofer and midrange driver to be "aligned." Get the midrange or woofer a little ahead of or behind the other driver, and comb filtering starts. You can do things to minimize it, but you can’t stop it with certain combinations of driver and crossover. It is fearfully hard to integrate a dynamic woofer with an electrostatic panel because the two drivers are so different from one another. Your absolute best shot is using an active crossover with infinitely variable phase/frequency, polarity, time domain and amplitude adjustments. Play with it long enough and you could dial in the response of the dynamic woofer and electrostatic panel to achieve perfection in their integration. Achieving the same thing using a passive crossover is incredibly difficult. Some designers are getting better as they learn from years of trying, but it is still one of the hardest things to do in audio that I can imagine. Just getting a dynamic midrange and dynamic woofer to integrate perfectly is enough of a challenge. You can hear even small errors show up as speed problems in the bass or midbass. These are the kinds of "character" that will remain with the speaker no matter where it is used.

How come one speaker has so much more bass detail than another? This too is strictly driver integration and NOT the quality of the woofer itself, as you may have heard. The fact is, bass detail comes from the midrange driver. But your ear/brain is so completely fooled by this complex interaction of midrange and bass sound that you believe that it is strictly a bass-related thing. It isn’t, and you can prove it by listening to something very boring but also very instructive. Listen to a subwoofer all by itself for a while. You won’t hear anything vaguely resembling speed coming from that slow, soggy-sounding, plodding subwoofer. It has no detail and no speed whatsoever when heard all by itself. Integrate it carefully with a nice set of main speakers, however, and suddenly the subwoofer has scads of detail, and if the integration is off a little, the bass will sound fast or slow too. All of that sense of speed and detail is coming from the main speakers, but from the midrange, not the woofer. That is why the integration of the woofer and the midrange drivers is so critical to getting a good-sounding speaker.

Another thing to bear in mind: live bass does not sound fast or slow; it just sounds like bass associated with whatever instrument or other source is creating it. The concept of "fast" or "slow" bass is a loudspeaker and audio-system-related thing. Oh, I suppose you could devise a live demonstration to show how the midrange of a string bass can affect the perceived quality of the bottom end of its range (and for all I know, the best musicians may use this to further extend their emotional reach in their playing). But in day-to-day listening situations when you hear live music, I doubt you’ve ever thought about the "fast" or "slow" bass that you were hearing. No, that’s something that happens at home in the reproduction chain, and it’s an artifact of integration errors. Remove the integration errors and the bass loses all sense of being fast or slow, just like live bass.

For you this means something profound. If you hear a system (hopefully not yours) that sounds "fast" or "slow" in the bass, enough that you have noticed anyway, that system has a problem. It might be fixable if the bass is coming from a subwoofer with lots of adjustments. But most of the time, it will take some minor or major change to remove the fast or slow character. A different footer can affect apparent bass speed because it changes the midrange of the electronic component or loudspeaker it is used under, not because it couples (or isolates) to the floor or shelf better. The different foot simply changes the character of the midrange a little bit, and because the midrange and bass quality are so tightly intertwined, the quality of the bass changes too, even though nothing specifically changed in the bass itself.

So there you have it, the symbiotic existence of bass and midrange, which are more tightly interwoven and interdependent that you may have thought.

distorsion

A formal study on the requirements for high quality reproduction recommended less than +/-2db, a performance that is absolutely unobtainable unless the room is designed for good acoustics and heavily treated even if the Transducer is perfectly linear. Most of us never get such listening conditions, so I would suggest that under domestic conditions +/-6db are acceptable for the 3m in room response within the 100Hz –10kHz range (the study recommended 40Hz – 15kHz). Note that this for the response at the listening position (hence not necessarily on axis), not just the raw Driver/Speaker anaechonic response.

Another Item is linearity. Now due the physical way our hearing works we have a quite high level of Harmonic Distortion “build in” into our hearing. This will mask a certain level of Distortion so that despite it’s presence it is not audible. This masking applies both to harmonic and intermodulation distortion and depends heavily upon the spectrum of the Distortion.

Without going into too much detail, I consider less than 3% 2nd Harmonic, 1% 3rd Harmonic, 0.3% 4th Harmonic and so on in a monotonic sequence to be essentially inaudible at a SPL of 96db (Patterson, Bekesy). The same holds for any intermodulation products that stem from the same non-linearities. Here it is much harder to apply weighting, but sidebands spaced closely to the main tones will be more audible than those spaced widely, corresponding to more audibility for IMD produced by nonlinearities producing primarily odd order Distortion. (Shorter).

So as long as our entire replay chain produces distortion lower than that we can consider it as being as “High Fidelity”. It is worthwhile that the study already mentioned suggested 0.25% THD for the entire replay chain to be the limit, I have no indication what spectrum of distortion was used and what the maximum SPL’s used where.

Anyway, with the above we have a good deal of info in order to “define” High Fidelity reproduction.

I personally would propose the following:

Reproduction shall be considered of High Fidelity for Music IF:

I. the Frequency response linearity is better than +/- 6db for the 100Hz –10kHz range with Sound produced outside this range being no more than 10db down on the average SPL in the 100Hz – 10kHz. The total response should cover at least the normal range of fundamental notes and overtones produced by Acoustic Instruments. For reference, the lowest note on the Piano Grand corresponds to 32Hz, the upright bass lowest fundamental is 41.4Hz. There is no specific limit at high frequencies, as many instruments contain overtones reaching beyond 60kHz.

II. the level of the 2nd harmonic overtone is no more than 3% and of the 3rd harmonic overtone is no more than 1% at a SPL Level of 103db/1m for a Mono System or 99db/1m for the individual speaker output of one spaeker in a Stereophonic System for the “critical” range of 100Hz – 10kHz. Outside this range levels of 10% and 3% respectively for 2nd and 3rd harmonics must not be exceeded at the same SPL’s.

III. the degree of compression over the medium term (10 Minutes) for a SPL of 103db (Mono) or 99db (1 half of a Stereo System) is less than or equal to 1db.

Note that I have not included the phase response here and that I have not mentioned time alignment per se, as in a mono-system quite substantial shifts will not be audible. Only very “rapid” shifts of the phase with frequency will become audible. Note that I have also not included the levels of background noise. Without going into too much detail we should have less than 30db background noise at the listening position with less than 20db above 500Hz. Furthermore, the issuse of step response, ringing and resonances and pulse fidelity has not been addressed.

In short we should add to the three above conditions:

IV. the phase of the system is not subject to severe and rapid phase-shifts in the “critical frequency range of 100Hz – 10kHz

V. the level of background noise is lower than 37db/1m overall and lower than 27db above 500Hz, the range between 500Hz and 50 (60) Hz showing rising slope to reach 37db at the lower point. This is for control settings that will produce the maximum operating SPL as discussed as above.

VI. the system shows a simple step response (showing one spike and then a fast and monotonic return of the pressure to normal) and good preservation of the Waveform for a Squarewave in the 100Hz to 10kHz range.

I believe that the above set does indeed describe quite well the requirements for “High Fidelity” Reproduction. It should be noted that all the above the conditions are to be taken within the Room the system is used in and include further environmental factors (for example the back ground noise levels include noise not generated by the replay system).

Note that is quite desirable to improve on the bare minimum conditions given above, however ideally one would avoid to improve one parameter on the expense of another. Furthermore the above makes no claim on comprehensiveness or completeness, there are many other factors present that are not accounted for here but have a strong bearing on the perceived quality of the reproduction.

It offers an ABSOLUTE BARE MINIMUM definition of High Fidelity Reproduction of SPECIFICALLY music, not speech or for example Cinematic sound. Any system NOT complying with the above conditions should not be considered as being capable of high fidelity reproduction. It is also worthwhile to note that by implication the entire recording side of the reproduction chain must comply with this, including Microphones and in the case of Records the Cutting Lathe, obviously also all involved electronics, cables and the like.

Due to the way most so called “Hi-Fi” and “Studio” Loudspeakers are designed and build they must sadly be considered incapable of High Fidelity reproduction as they tend to fail multiple of the criteria set out above. Much of this is down to basic Driver design more than anything else.

In the next instalment I shall be looking closely at some of the Issues in Driver-design, especially linearity and compression, the main areas where I feel substantial improvements are required with most commercially offered drivers targeted at "HiFi" and "Studio" applications.