Passive Crossover Frequency Selection

The “Systematic Growth” program employed and promoted by Bozak, Inc. (The R.T. Bozak Manufacturing Company) for more than 25 years, was a consumer-friendly concept that
allowed audiophiles to “build up” their loudspeaker systems as time and investment allowed, without sacrificing fidelity or quality. Bozak did not manufacture “economy” woofers,
midranges or treble speakers. Rather, they manufactured the highest quality drivers that technology and practical economics allowed. Bozak’s design philosophy was one that was
often stated as, “...our smallest loudspeaker systems utilize the very same high quality drivers as our largest systems—the differences are in wavefront power, dynamics, and the
ultimate bandwidth of the multiple driver systems.”
Paragraph extracted from: The History of Bozak Loudspeakers, by Bob Betts.)

The above is a preface to an explanation which attempts to define and explain the reasons for the selection of various different crossover frequencies for loudspeaker systems that
utilize similar drivers.
Typically, Bozak had a “Systematic Growth” program of three basic configurations. There were several others, but for the sake of illustrating the subject material, those shall be
ignored. There was the B-302A which was a single woofer system, and the most basic system in the “Concert Series.” Next came the B-305, a dual woofer Concert Series system and
the B-4000 family models, of the “Symphony Series.”  Finally there were the Concert Grands. This family of variants utilized four woofers and various midrange/tweeter configurations
in the B310A (and B-310B) and B-410 series.
As mentioned above, in order to address the specific topic of this chapter, we will only consider the B-302A single-woofer speaker and the B-410 four-woofer system. Both speakers
were 3-way systems, originally built with passive L/C crossover networks (later to be offered in bi-amped and tri-amped wiring configurations). The single-woofer speaker crossover at
800 and 2500 Hz, where the four-woofer system crossed over at 400 and 2500 Hz. Convertible crossovers were offered to accommodate those conditions.
The different lower crossover points of 400 and 800 Hz (between woofer and midrange, had technical foundations, even though the driver (or drivers) were of the exact same model
and design. This chapter attempts to clarify the technical reasons for these engineering decisions.

1. Steady State vs. Transients

Consider the geometry of a single-woofer, floor standing speaker enclosure of 4 to 6 cubic feet in volume, and about 2 or 2 1/2 feet high, and compare it to a large, freestanding
cabinet of about 16 cubic feet volume, and about 5 feet high. Obviously, the direct ray pattern of the more directional midrange and treble frequencies will be at a more desirable “ear
level” in the larger enclosure than in the smaller cabinet. This offers a much more comfortable listening condition for accurate tonal balance. It also allows the primary wave of these
upper frequencies to arrive at the listener’s ears with less effect from surrounding environmental surfaces, ambient acoustics, room reflections, and furniture and carpet absorbtion.
Due to mass loading and inertial reactance, the Bozak B-199A (12-inch) woofer is a less efficient transducer of complex signal energy than the B-209 (6-inch) midrange driver. In terms
of power conversion, from electrical to acoustical, they are very close to the same efficiency, but where they differ is in their ability to reproduce frequencies at the fringes of their
design bandwidth. What that means in the real world is that the midrange will respond to transient energy with greater efficiency below its crossover point than the woofer will above its
crossover point. Again, we are discussing the reproduction of complex signal energy—not sine waves. Most of this effect is due to rapid rise time and the lack of inertial impedance
(reactance from  mass).
The effect of all this is that with a single-woofer system, with a crossover one-octave higher (800 Hz) than a similar system will have more output from both drivers—woofer and
midrange combined—at frequencies that are more affected by room acoustics and cabinet placement, and at frequencies that the human ear are more sensitive to.
Remember, a transient of a given level will sound (subjectively) louder than a steady state signal of the same amplitude. And note that the transient ability of the midrange is greater at
400 Hz than the woofer is at 800Hz—thus the effect we just discussed.
Of course, the reverse is true. By crossing over the midrange-to-woofer one octave lower (400 Hz) takes the (dare I say) more transient sluggish woofer down into the bass region
which is more fluid in propagation and less projecting in sound quality, and is also in an area that the human ear is less sensitive. So, there is, effectively, only one driver producing
any significant amount of acoustical energy in the midrange band—the midrange driver.
Maybe a more illustrative way of explaining it is that with an 800 Hz crossover, there will be more acoustical energy (apparent and subjective power in the room) throughout the 400 to
800 Hz octave, since both drivers will be active, as the midrange still acts as a piston down below the 800 Hz. crossover ... albeit somewhat suppressed. And with a 400 Hz crossover,
the woofer—which really isn’t a very good midrange reproducer—is pretty silent in the 400-800Hz octave. The woofer does have a certain amount of intrinsic, upper end, auto-rolloff,
or acoustical rolloff, at 800 Hz., whereas the midrange is still quite a good performer down below 400 Hz-in piston mode. And again, due to the transient capability of the midrange over
the woofer, at these frequencies, the crossover has much greater control over rolling off the woofer than the midrange, which is very efficient with transients.
Note that it is at about 1.2 KHz where this woofer/midrange phenomena goes away, which may justify it for use in some smaller 2-way systems. More on that in the chapter on bookshelf

2. Phase Shift: Electrical and Acoustical

Technical Explanation:
Crossover designs are often compared and analyzed with resistive loads, from perfect signal sources, and under steady state conditions. All three of these test parameters have
nothing to do with the dynamics of reproducing audio program (signal) material—we do not buy an expensive audio system, just to take it home and listen to sine waves; we listen to
complex wave forms…called music.
Transient response, which defines the character, accuracy, and definition of reproduced material has a great subjective effect on apparent loudness—program level in the room.
When a transient is sent down the line to the speaker system, it first encounters the crossover network. In our example of the midrange driver, the crossover is highly reactive—both
inductive and capacitive. The transient may, or may not, have already been phase shifted by the preceding electronics, but once it encounters the massive values of reactive
components, it will surely be shifted in the time (phase) domain. But it doesn’t stop there. The driver, being a transducer that converts electrical energy to mechanical energy (a motor)
is inherently a phase shift converter. It takes time for the electromagnetic forces generated between the voice coil and magnetic field to convert the moving mass to motion. Add to that
the additional mass (inductive reactance) of the driver’s diaphragm, the suspension system (resistance), the rear air loading of the driver’s diaphragm (capacitive reactance) and all
the other consequential mechanical reactances and resistances incurred, and it is understandable that a perfect driver does not exist. However, we could make a perfect driver if it had
the properties of zero moving mass, infinite compliance, and was constructed of acoustically inert materials. But then we’d never be able to test it, since the atmosphere (air) is an
imperfect, and fluid, transmission medium and would introduce its own flavor of phase shifts.
A clear picture of these physics along with an understanding of transient spectral composition, helps the designer understand the effects of crossover frequency and apparent sound
pressure level (SPL). In our single woofer example above, note that the midrange passband is only about 1 1/2 octaves wide. That means that most, if not all of the midrange terminal
signal has been significantly shifted by the crossover filter ... at many frequencies up to 180 degrees—perfectly out of phase. Obviously a wider passband would reduce this condition
by placing the critical midrange frequencies farther from the filter skirts—but then the driver would be fed frequencies that it should not be asked to reproduce. Electrical phase shifting
within the crossover network is really a condition that cannot be remedied without electronic crossover technology

3. Fidelity, Distortion, Apparent Loudness, Transparency, and the elusive “third dimension”

Ask yourself a question: Why do two speakers that have very similar specifications sound so vastly different? How can one of those speakers sound “acceptable” and the other so
Speaker manufacturers who earnestly strive to develop top-end  products are all aware of test parameters and physical conditions that are seldom, if ever, published, and never
requested. A driver, or loudspeaker system, under development will (should) undergo a complete battery of tests and evaluations, for both performance and durability—most don’t.
Distortion, by definition, is a quality of change. Depending on the application and control of distortion, it may or may not be desirable. The air in your car’s tires allow for rolling
distortion, and that’s a good thing for a comfortable ride. The diving board over a swimming pool functions purely based on distortion, another good thing. But in the audio
reproduction realm it’s usually not accepted lovingly by the purists ...the faithful.  There are audio products designers that thrive on physical distortions of various forms and use them
to their advantage, but that’s for another chapter.
Let’s see what we seldom see in the hobby magazines and trade papers.
There are three basic forms of distortion that electromechanical designers must contend with: amplitude, frequency and phase. Amplitude distortion has to do with undesirable intensity
changes. Frequency distortion is the algebraic multiplying and dividing of fundamental notes. Phase distortion is the moving of an event (shift), or the stretching (expansion) or
condensing (compression) of time. All three conditions, whether in the intensity, frequency or time domain will add in algebraic fashion to create the subjective effect that we call
“coloration.” The third dimension, or “Z” dimension of ”staging” imaging is the elusive quality that is masked by excessive phase and IM distortions. If you can hear the “depth image” of
a stereo system, then you can be pretty sure that your total system is fairly low in these distortions. A direct comparison of a high-level crossover vs. a bi-amped system will make this
apparent. Likewise, transient response and damping characteristics are what gives the loudspeaker its “liveliness, or “openness.” If a speaker sounds like the sound is coming from
inside the box, then it probably has poor transient capability, and if it sounds dull and lifeless, then the damping qualities are probably not very good. Here’s a standard test that
engineers have used over the years: Play a known (to you), small jazz combo of acoustical (not electronic) instruments and listen to the bass drum and string bass. Are they separate
and distinct? Or is the woofer just flopping around in rhythm to the beat? Bass is bass, but what is it that makes up the bass—can you tell by listening? So this is basically why two
loudspeakers with similar “published” specifications can sound so vastly different. It would seem that no one ever offers specifications on IM, harmonic, and phase distortions.
In my 40-plus years as an audio products design engineer, it has never ceased to amaze me how audio manufacturers perpetuate the virtues of “flatness”—linearity—without even so
much as a mention of other physics characteristics. Over the years, amplifier producers have been forced, by public demand, to publish such numbers as intermodulation distortion,
harmonic distortion, damping factor, etc. But remember that these figures are gleaned, gathered and garnered on a test bench using sine waves as audio signals and resistors, not
loudspeakers, as loads. Seldom will you hear any discussions concerning “dynamic stability” or “transient reproduction.” Likewise, the loudspeaker industry suffers similar, if not worse,
negative virtues.

See graph and caption below.

              Typical 6dB/Octave Passive Crossover Response and Phase Shift Passband

Caption to graph:

Comparison of two midrange crossover curves. The plots assume resistive loads and do not take into account acoustical or mechanical reactances. Note the Linear Phase Bandwidth
plots. These lines define the circuit loop at the frequencies where reactive phase shift (from the crossover components) are minimal (approx. 10 degrees). For reference, the
capacitive phase shift currents can reach +90 degrees, and the inductive phase shift –90 degrees, at one octave or more, above and below the crossover frequencies where the
drivers are still very active—and can be heard. With complex program material, a total phase shift of 180 degrees is (theorhetically) possible. Since the phase shift bandwidth of the
example above is greater than the linear phase bandwidth, an electrical phase reversal would seem appropriate. This is especially true of the 800/2500 Hz condition as evidenced by
the graphs. Whether or not an electrical phase shift is indicated, is subject to much opinion and interpretation by engineers and listeners alike, since the tradeoff would be phase
distortion within the passband. The ultimate results, are based on the analysis of where in the passband the listener wants the most severe phase shift—or the least amount of phase
shift—at the center of the passband hump or at both skirts. Of course, bi-amping will eliminate most of the lower frequency phase shift, and tri-amping will eliminate virtually all of this
condition. That is to say that the curves would remain the same, but the Linear Phase Shift lines would extend along the entire graph, not the restricted band as indicated.
Note that the midrange, when crossed over at 800 and 2,500 Hz, is never allowed to operate in the non-phase shift domain – there is no flat section to the solid line curve.
A Few Words About Passive (High Level) Crossovers
In the early 1970s, when "phase coherency" and "time alignment" were (almost) religion among speaker manufacturers, marketing and sales organizations, and audiophiles alike, we
embarked on a very intensive and in-depth analysis of phase linearity ... Particularly in 3-way speaker systems. We examined the many papers given for the AES and ASA, among
others, and spent hundreds of hours in our own acoustical lab. Additionally, we joined in on several informal discussion sessions with other manufacturers at the various AES, IHF, and  
Consumer Electronics Shows. The definitive answer wasn't quick or easy in coming due to the trade-offs associated with the pros and cons of both options. We formulated our own
opinions, but before acting on them, we enlisted the "ears" of several (many) professional musicians ... some of iconic stature and highly respected in their business. After much
analysis, testing, and evaluation we made the decision to accept the phase shifts at the
center of the midrange band, rather than at both ends of the midrange band. We then sat back
and waited for the fireworks to begin. Oddly enough, there were amazingly few! This is surprising, since customers are usually very quick to express a complaint, but remain
conspicuously quiet when content. The feedback from our dealers, reps and end-users was almost unanimously complimentary. One Sunday morning I received a phone call from
Benny Goodman asking when I was going to come to his studio and "...
make the new repairs that I heard at the factory?"
This is not a "yes" or "no" or good or bad decision. It is a gray area of engineering that is associated with the subjectivity of how we listen, what we listen for, our personal tastes, our
ear-to-brain calibration from live vs. reproduced experiences (or lack thereof), and the intuitive thought process. The condition (and dilemma) of where to place the phase incoherency
is a trade off - neither is technically correct when applied to a passive crossover, but quite often, the intuitive thoughts of a semi-technical evaluator will weigh in favor of the in-phase
condition, only because "it seems to make sense." Oddly enough, Bozak Inc. was one of the last manufacturers to effect the midrange phase reversal. At that time, according to our
research of currently available 3-way speaker products, about 85% to 90% of the speaker industry had already made the "correction" changeover.