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1985-04-05
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.W:60
.L:60
.J:8
.H: ...Page $$$
.H:
Loudspeaker Crossovers
What They Should Do
and How to Get Them
To Do It
0. Abstract.
Crossover network technology has undergone considerable
change in the last 10 years. Since there are still a lot of
loudspeaker systems built with what amount to be old
fashioned crossovers, discussion of the "new" technology is
seems to be in order.
I. Tasks for the crossover network.
Crossover networks must do at least three things to be at
all effective. They are: route signals in different
frequency ranges to different drivers, maintain desirable
phase relationships between acoustical outputs of individual
drivers, and compensate for differing driver efficiencies.
If any of these requirements are not met, the over-all sound
quality of the resulting loudspeaker system is likely to be
severely compromised. Let's look at the requirements
individually:
Requirement 1. Route signals at in different frequency
ranges to different loudspeaker drivers.
Loudspeaker system quality is based on wide frequency
response range, smooth response, small size, low distortion,
good dynamic range, and low cost. To date, no single driver
system has been developed that has all these
characteristics. Systems composed of multiple drivers seem
to come closer to the ideal, but they introduce the need for
crossover networks to divide the input signal between
drivers operating in two or more frequency ranges.
The signal is divided between drivers operating in different
frequency ranges, to avoid wasting amplifier power and to
avoid feeding signals to drivers that may disrupt their
operation. If significant power in a range of frequencies is
absorbed by a driver that is not an efficient transducer in
that frequency range, then the power is wasted. If a driver
receives significant amounts of power in ranges where it has
poor power handling capacity, then the driver's operation
will be disrupted.
Requirement 2. Maintain desired phase relationships between
acoustical outputs of individual drivers.
There are two reasons to try to maintain desired phase
relationships between the acoustical output of the drivers:
one that is obvious, but sonically irrelevant; and one that
is not so obvious, and is important to sound quality.
An obvious reason for maintaining desired phase
relationships between the acoustic output of individual
drivers is to control the over-all phase response of the
loudspeaker system. Controlled listening tests have failed
to show any reason to be interested in system phase response
above 1 kHz. In addition, controlled tests that are
presented as being positive for the audibility of phase
response below 1 kHz relied on esoteric, non-musical
signals, and still did not develop results with 99 percent
confidence that they were not due to random guessing.
Therefore, over-all system phase response is at best
marginally related to listening quality.
A less-obvious reason for maintaining desired phase response
is to control system directivity through frequency ranges
where two or more drivers have significant acoustic output.
When there are two acoustical signals radiated from drivers
into a common space, but one acoustical signal has lagging
phase with respect to the other, the joint coverage pattern
will be tilted toward the lagging driver. This situation
causes dips in the on-axis frequency response vis-a-vis
power response.
It is therefore highly desirable to control the phase of the
acoustic output of the various drivers to be in phase
through the crossover regions. If two or more drivers have
significant acoustical output at some frequency, the
acoustic outputs should be, ideally, in phase. There are
three sources of phase differences between drivers, which
are the phase response of the drivers themselves, phase
differences due to the relative positioning of the drivers,
and phase differences due to the crossovers.
Requirement 3. Compensate for differing driver efficiencies.
It is not likely that drivers will have the same efficiency
unless they are designed for use with each other. Woofers
tend to be inefficient, while tweeters are relatively easy
to make efficient. Most systems include some prevision,
fixed, variable, or trimmable; for matching driver
efficiencies. Because woofers usually demand a low source
impedance, padding down the woofer to match the tweeter is
almost never done. The converse is common. In addition,
drivers tend to be a little non-uniform, and system
performance may be optimized by adjustment of the completed
system in the acoustical environment in which primary use
takes place.
B. Things that are nice to have done:
When building complex systems, it is very helpful if one or
more components in the system are able to accommodate the
peculiarities of other components. Crossovers may have the
potential to compensate for driver and/or enclosure
deficiencies, facilitate use of cost-effective amplifiers,
reduce "Up-front" design work, and reduce "Cut-and-try"
elsewhere in the system.
Accommodation 1: Compensate for driver and/or enclosure
deficiencies.
Many drivers have desirable characteristics such as good
power handling capacity and smooth response, but lack other
desirable characteristics such as flat frequency response.
Crossover designs usually assume ideal driver response.
However, it is often convenient to include equalization for
driver characteristics "In the same box" as the crossover.
A most common, but highly intractable enclosure fault is
positioning of of drivers in ways that create significant
phase shift. This situation is often described as: "mounting
drivers with non-coincident acoustic centers". Often, it is
difficult to position drivers ideally because doing so may
create obstructions in the radiation pattern of other
drivers in the system. Crossover designs usually assume
ideal positioning of the drivers, but it is often convenient
to include equalization for enclosure characteristics "In
the same box" as the crossover.
Accommodation 2: Facilitate use of cost-effective
amplifiers.
Power amplifier costs are often a non-linear function of
their power output. In addition, there is a "Barrier" of
sorts that makes amplifiers with power output much in excess
of 400 watts per channel into 8 ohms much less common.
Integrated circuits that would make power amplifiers more
economical are currently limited in power to the 20-30 watt
per channel range. Therefore, a crossover that permits use
of amplifiers whose power rating allows them to be more cost
effective can provide benefits that offset some of the
crossover's cost.
Individual loudspeaker drivers are not the easiest load for
amplifiers to drive. Unfortunately, some crossover designs
make the situation worse. In contrast, other designs help
minimize amplifier quality requirements. Therefore,
reducing power amplifier size and quality is a desirable,
and possible accommodation of the crossover network.
Accommodation 3: Reduce "Up-front" design work.
Loudspeaker system design requires knowledge of a wide range
of technologies, from the disciplines of both mechanical and
electrical engineering, including both static and dynamic
system analysis.
Crossovers, as components, can reduce the span of technology
required of the system designer, when they are pre-packaged
solutions. However, poorly designed components can create
more problems than they solve.
Accommodation 4: Reduce "Cut-and-try" elsewhere in the
system.
If a crossover design makes over-all system performance less
sensitive to parameters that are hard to control, then it
reduces the need for final "tweeking".
In addition, the crossover can include electrical adjustment
capabilities that provide the same function as mechanical
adjustments. For example, it is possible to electrically
adjust the location of acoustic centers, by providing small
amounts of time delay via all-pass filters.
II. Alternative crossover designs.
Historically there have been many alternative designs for
crossovers that have been selected from. In some cases, it
has been only recently that the full implications of certain
choices has been understood.
Alternative A: 6 dB/octave filters.
The most common, and simplest possible crossovers are the 6
dB/octave filters. In the case of a woofer with carefully
chosen voice coil inductance, and a piezoelectric tweeter,
this type of crossover may be achieved with no additional
electrical components.
Filters of this variety spread the range of simultaneous
operation of adjacent drivers over a wide range. In
addition, there is a 90 degree phase shift between the
electrical signal applied to the drivers at all frequencies.
When combined with an additional 90 degree or more phase
shift in the crossover region due to driver phase shift, a
situation is created where best performance is often
obtained when the drivers are wired out of phase.
When it is desired to obtain a 6 dB/octave filter using
passive crossover designs, care must be taken to ensure that
variations in driver voice coil impedance do not
significantly modify or totally wipe out the effect of the
electrical components in the crossover.
Alternative B: 12 dB/octave Butterworth filters.
12 dB Butterworth, or maximally-flat filters are the usual
next step up in sophistication. Sometimes 12 dB octave
low-end roll-offs can be obtained as inherent properties of
the drivers. Some horn-loaded, or sealed box designs with
their resonant frequency at the crossover frequency, and a Q
near 1.414, result in an upper driver crossover with this
characteristic. Similarly, by allowing the woofer voice coil
to decouple from the diaphragm with appropriate mechanical
Q, this characteristic is obtained in the low frequency side
of the system without additional electrical components.
Passive 12 dB octave designs will have twice as many
components as 6 dB crossovers, and are also significantly
affected by driver impedance characteristics. This is a nice
way of saying that some passive "12 dB" designs are
effectively "6dB" designs because they do not correct for
driver impedance characteristics.
The electrical outputs of the usual "Butterworth" 12
dB/octave crossovers are usually 180 degrees out-of phase.
There is often an additional 90 or more degrees of phase
shift due to the drivers. Thus there is a total of 270 to
360 degrees of phase shift between the acoustical outputs of
the drivers. The flattest frequency response is usually
obtained with the drivers wired in phase.
12 dB octave crossovers have reasonably narrow areas of
overlap of adjacent drivers. They are used with horn-loaded
tweeters to minimize distortion due to operation below the
flare cut-off frequency.
Alternative C. 18 dB/octave Butterworth filters.
Crossovers with higher slopes than 12 dB/octave are almost
always implemented actively. High slopes obtained with
these crossovers do a good job of minimizing both the region
of driver overlap and out-of band electrical input to the
drivers. The electrical inputs to the drivers are
approximately 270 degrees out-of phase. This is essentially
a throw-back to the 6 dB/octave case, in terms of phase.
When the drivers are connected out-of-phase, a degree of
phase linearity is obtained in the summed response, were it
not for the additional phase shift of the drivers.
Alternative D. All-pass designs:
All of the crossover designs described so far are minimum
phase. This means that the phase characteristics of the
summed response of high and low pass sections has a phase
response that is related to amplitude response by the
Hilbert transform. For those who are not totally conversant
with calculus this year, minimum phase means that the if you
equalize the frequency response to be perfectly flat at all
frequencies, the phase response will also be perfectly
equalized. Furthermore, the equalizer will be itself,
minimum phase.
Two points about minimum phase are important. First, drivers
that do not operate in diaphragm break-up mode are often
minimum phase, as are some drivers that do operate in
break-up modes. Loudspeakers with whizzer cones are almost
never minimum phase. Secondly, while common loudspeakers can
be thought of being minimum phase, systems of two or more
minimum phase loudspeakers are not often minimum phase
because it is difficult for two loudspeaker drivers to
perform as if they occupied the same space. Since the
drivers are displaced from each other, there are time delay
differences off-axis. Time delay is not a minimum phase
effect.
All-pass crossovers cannot be equalized to have both ideal
frequency and phase response in the summed response with
common minimum phase equalizers. This begs the question:
"Does anybody hear the difference." The answer is: "Probably
not." The most significant benefit of all-pass crossovers is
that in many cases. it is possible to get the acoustical
outputs of the lower and upper drivers to be in phase.
All-pass crossovers are readily constructed by cascading two
Butterworth filters.
1. 12 dB/Octave all pass crossovers are created by
cascading two 6 dB/octave filters in such a way that they
are electrically buffered from each other, and do not affect
each others response through loading. The electrical outputs
of the crossover are 180 degrees apart at all frequencies.
If the drivers are wired out of phase, they will be in
phase. As usual, driver phase response will affect the phase
of the acoustical outputs.
2. 24 dB/Octave all pass crossovers are created by
cascading two 12 dB octave filters in such a way that they
do not affect each other's response. The electrical outputs
of the crossover are 360 degrees at all frequencies, which
is very similar to being in-phase. In addition, the sharp
slopes minimize driver overlap, and avoid providing
significant out-of band inputs to the drivers. The cascade
of two 12 dB/octave filters can often be obtained using a
combination of driver roll-off characteristics, which often
have 12 dB/octave slopes, and a single 12 dB/octave
electrical filter.
Linkwitz of Hewlett-Packard described the desirable
mathematical properties of 24 dB/Octave crossovers in 1976.
His associate, Riley described their implementation in
common Sallen and Key type op-amp filters at the same time.
3. Phase compensation of 3-way and up all-pass
crossovers. Because of the residual phase shift of one
crossover point, phase compensation is required to preserve
desirable over-all phase characteristics of all-pass
crossovers operating with more than two bands. As a
practical matter, 3-way designs have marginal need for
compensation, but frequency response variations of from 1 to
10 dB, or more will be caused by leaving phase compensation
out of crossovers with from 4 or more bands.
Phase compensation also depends on how the crossover is laid
out. With three way crossovers the system can be built as
three filters: a high pass filter, a low pass filter, and a
band pass filter; or it can be composed of a low
pass-high-pass filter pair, which has one output further
divided by another filter pair. The latter is a "Tree"
configuration, and is preferable to minimize the need for
additional phase compensation.
With more bands, several different lay outs are possible.
D'Appolito pointed out that the ones that are shaped like
trees have fewer parts and are easier to phase compensate
than the ones that are laid out as a series of parallel band
pass filters.
As previously noted, some loudspeaker drivers have the same
response as 12 dB octave electrical filters. Therefore, with
some sacrifice in power-handling capacity, an acoustical 24
dB octave all-pass crossover can be obtained using a
combination of electrical and mechanical 12 dB/octave
filters From the standpoint of on-axis and off-axis
frequency response, this is ideal, and reduces the cost of
the crossover itself.
E. Delay-derived filters. One way to minimize the parts in
a crossover is to develop one filter characteristic by
subtracting the output of one filter from its input. The
elegance of this technique is upset by the fact that the
output of the crossover that is derived by subtraction has a
very gentle slope, often as gentle as 3 dB per octave.
This situation has been mathematically analyzed by Lipshitz
and Vanderkooy, who found that the gentle slope is due to a
time delay inherent in a minimum phase filter. For example,
a low pass filter with a corner frequency of 1 kHz has an
approximate time delay of approximately 1 millisecond at all
frequencies below 2 kHz. This makes it difficult to get
total cancellation at the output of the subtraction circuit.
One solution, totally obvious in retrospect, but requiring a
lot of thought moving forward in time, is to delay the
unfiltered path. Unfortunately, pure time delay is hard to
achieve at this time. An unexpected result is that some
forms of this filter have a linear phase characteristic in
their summed response. For example, a filter utilizing a
fifth-order Bessel filter, and appropriate time delay has
almost as good off-axis response as a 24 dB octave all-pass
design. The advantage is that the over-all summed electrical
response is linear phase.
There is some question whether this ideal mathematical
characteristic has audible significance. Of course,
implementing such a filter with good distortion
characteristics will cost hundreds instead of tens of
dollars per crossover point.
F. Driver Frequency response correction.
It is unlikely that anybody who does not actually
manufacture drivers would be able to develop a collection of
drivers with complementary response. Furthermore, doing so
might involve considerable sacrifice of power handling
capacity.
In general, there are two approaches to this problem. One is
to select drivers that are flat about an octave past the
crossover point, and accept the resultant minimal phase
shift. The other is to provide a minimum phase equalizer
that provides the desired response. Zaustinsky suggests the
use of selectively combined outputs of an state-variable
filter to transform the acoustic response of many drivers to
be one of the two required 12 dB/octave filters in a 24 dB
octave all pass (Linkwitz-Riley) design. One advantage of
this form of equalization is that it yields near-ideal
inter-driver phase response.
In some cases, bandpass filters with appropriately chosen
center frequency and Q can give useful results. The designer
need to be sensitive to the possibility that equalizing the
response to be flat over a limited range does not cause
excessive phase shift. Recall that equalizing drivers only
yields flat phase response when amplitude response is flat
at all frequencies. In practice, this means controlling
amplitude response for several octaves outside the bandpass.
III. Performance of alternatives:
Now that the choices are laid out, what are the trade offs?
The areas being considered here are frequency response on
and off axis, ease of design, power handling capacity, and
expense of implementation.
A. Passive versus Active crossovers. Active filters are
always the choice when price is no object. They allow the
designer to largely ignore driver impedance characteristics.
Active crossovers can be cost-effective in two cases. The
price performance of power amplifiers is non-linear. Two or
more small amplifiers that can be implemented by an
inexpensive integrated circuit are more cost-effective than
one amplifier built from discrete parts. The power ceiling
for inexpensive integrated circuits is around 30 watts per
channel at this time.
At the opposite end of the spectrum, amplifiers that exceed
the capacity of readily available discrete semiconductors
are very expensive. At this time, the technology of
high-power transistors is largely dictated by the most
common applications: high frequency power supplies for
computers and voice-coil drivers for high performance
computer disk drives. This puts an effective ceiling in the
range of 200 to 400 watts per channel. Higher powered
amplifiers exist, but they tend to be less cost effective.
Systems with power requirements outside this range are often
more cost effective when implemented using active crossovers
and multiple power amplifiers.
In addition, active crossovers minimize amplifier quality
requirements by reducing intermodulation distortion, and
decreasing the possibility of excessive reactive loading.
Finally, amplifier clipping in one frequency band can be
partially masked by clean output in another band.
B. Butterworth versus All-Pass crossovers. Whenever flat
response on and off axis is desired, All-pass crossovers are
the most desirable. Cost of crossover networks is more a
function of ultimate slope than tuning.
C. Delay-derived versus All-Pass.
As the cost of high quality time delay decreases,
delay-derived crossovers will be more practical for the
mathematically inclined perfectionist. For all intents and
purposes, time delay implies active crossover networks.
There may be no reliably detectable subjective advantage to
delay-derived crossovers when listening in most rooms using
most commercially recorded program material. Even if there
were a reliably detectable difference, preference may be
hard to establish.
D. Constant voltage versus Constant Power
E. Time delay alternatives:
Besides delay-derived crossovers, time delay is also useful
for repositioning the acoustic location of a loudspeaker
driver. Direct radiator tweeters tend to have the effective
source of their acoustical output ("Acoustic Center") close
to the mounting board. Cone woofers tend to have their
acoustic centers some distance back from the mounting board.
Stepping the tweeter back causes the woofer to block part of
the radiation of the tweeter, which can be minimized, but is
undesirable. An alternative, first suggested by Linkwitz, is
to use time delay to position the acoustic centers of the
woofer and tweeter in a plane parallel to the baffle board.
Significant amounts of time delay dictate the use of active
crossovers.
1. Digital Delay. The quality of digital delay can be
raised to almost any desired level by simply spending more
money. The majority of the cost lies in digitization of the
analog signal. This cost can be avoided by using digital
program material sources in digital form. Major problems
remaining are the high cost of multiple digital to analog
conversions and the need for a rather large number of ganged
level controls (1 for each loudspeaker).
2. CCD delay. The quality of CCD delay is slowly
improving, and may be almost good enough for top quality
applications, providing the delay is shorter than 20 or 30
milliseconds. Loudspeaker applications are usually for less
than 5 milliseconds. Cost is around $100 per frequency band.
3. Delay via all-pass filters. Bessel tuned all-pass
filters provide inexpensive high quality delay when the
product of highest frequency delayed accurately and time
delay is small. A single op-amp can provide a highly
accurate 10 microseconds of delay over the entire audio
range, or 1 millisecond of delay good to 500 Hz.
IV. Loudspeaker system construction.
Crossover networks by themselves are not very exciting to
listen to. It is only when they are used in conjunction with
loudspeaker drivers that they become interesting. While the
purpose of this paper is not to provide a complete guide to
loudspeaker design, a few comments on loudspeaker design
will be made. Loudspeaker systems are composed of
crossovers, transducers or loudspeaker drivers, and
enclosures. Evaluation techniques will also be touched on.
A. Driver selection. While crossovers can help a good
driver sound better, or at least allow it to develop its
potential, they cannot create quality where there is
none.
1. Direct radiators commonly having cone-shaped
diaphragms in units designed for use at the lower
frequencies, and dome shaped diaphragms for the high
frequencies, can have good performance and relatively
low cost.
Specifications or low frequency drivers that are
presented in terms of the well-known Thiel parameters
are about the specifications for direct radiators that
can be relied on because they are so easy to verify.
Of the Thiel parameters, Qt, or total system Q is
perhaps the most easily evaluated. Poor quality drivers
usually have high Qt's, on the order of 0.5 or above.
Good quality drivers usually have lower Qt's, on the
order of 0.25 to 0.35. It is a good idea to use a
computer program to design some trial enclosures, and
verify the suitability of the driver for the
application.
Thiel parameters for low frequency drivers tend to be
subject to sample-to-sample variations, and ideally are
measured individually, as a guide to tuning.
In general, specifications for mid and high frequency
direct radiator drivers are not overly reliable.
Measurements of driver response should be made with the
driver mounted as it will be in the final application,
particularly for midrange drivers.
2. Horn loaded drivers have been shunned by many picky
listeners for some time, but have never been out of
style in high quality public address systems and are
regaining favor for all applications. At this time it
is pretty well understood that the so-called "horn
resonance" and poor quality sound was the result of
using horns that were not designed for good power
response.
Constant directivity horns require equalization for
flat response, and can be quite large, but afford
unequalled control over the radiation pattern, and can
be cost effective when total system cost, including
power amplifiers, is considered.
B. Enclosure Designs. Enclosures can subtly affect sound
quality of loudspeaker systems. Obviously, the enclosure
should be of an appropriate geometry to ensure adequate
volume for the low frequency driver, and facilitate
orientation of the radiation patterns of the upper
drivers towards the listeners. Enclosures can subtly
effect the sound when they affect the directivity of the
drivers or have undesirable undamped resonances at
spurious frequencies.
1. Conventional free-standing enclosures are usually
built with a pressed wood core veneered with hardwood
or thermoplastic laminate. Wave guides may be
incorporated into the design of the front of the
enclosure to control directivity. The edges of the
enclosure are usually rounded to reduce diffraction,
though pleasing sound is sometimes obtained by
encouraging diffraction by placing the edges of the
drivers near the edges of the enclosure. Since the
drivers have decreasing dimensions, a "pyramid" shape
results.
2. Built-in loudspeakers allow avoiding disruption of
the listening room decor with large boxes. Some
subwoofers can be placed in the floor, ceiling, or wall
to utilize the structure of the building as their
enclosure. Higher range drivers are not often installed
this way because they are more critical of placement.
3. Esoteric enclosure designs include those made of
concrete, sand between concentric cardboard tubes, etc.
Good suppression of enclosure wall resonance can be
obtained in this way.
C. Evaluation techniques are important to any design
effort, especially those involving loudspeakers.
Obviously, the goal is subjectively perceived "Good
sound", but subjective perceptions have limited
reliability unless good experimental controls are used,
in which case they are also very time consuming. A rule
of thumb in carpentry is if you cut two boards to have
equal length by eye, you can always see the errors by
eye, while good quality measurements speed the process,
often yielding results that are perceived as being
essentially perfect. This is also true with loudspeaker
construction.
1. Microphones have always been a stumbling block to
loudspeaker construction, but recently miniature
electret capsules with outstanding response over the
entire range have come on the market for very low
prices, often on the order of a few dollars. There is
now no excuse for any loudspeaker constructor to not
have one or more good measurement microphone(s) in his
possession.
The reliability of acoustic measurements is enhanced by
using multiple microphones with separate rectification
for each microphone prior to summation into a single
measurement.
2. Ordinary audio oscillators are very inexpensive, and
can give remarkably good results as long as
measurements are not affected by standing waves in the
room. This is usually true above 500 Hz. Results may be
manually plotted when cost is an object, and time is
available.
3. Swept oscillators and chart recorders can give good
repeatable results at a much higher system cost than
using normal audio oscillators, but the results are
plotted automatically, and a wide range of tests can be
performed in a brief period of time.
4. Pink noise sources include relatively inexpensive
test sets, or even more inexpensive digital compact
disks, such as marketed by Denon. Standing waves are
less of a problem than when using audio oscillators,
but integrating results over a period of several
seconds is required to get reliable results below 200
Hz.
5. Coherent fractional octave sources have been
described by Linkwitz and others. Their major
advantages are: reduction in the amount of integration
time required for reliable results, and a relatively
pleasing sound.
6. Spectrum analyzers such as the ever-popular and
highly effective one third octave real time analyzer
are very effective, at a price. They often lack
fractional dB resolution on their LED displays, but can
be used with external CRT displays for greater
accuracy.
6. Computerized techniques include the highly effective
and expensive Time Energy Frequency (TEF) test set, at
one extreme, combinations of third octave filter banks
and personal computers in the other. A broad middle
ground is filled by dedicated and personal computer FFT
analyzers, where the trade off is low price versus fast
response and good resolution. As the cost of
computation and digital-to-analog conversion decreases,
all known and future audio test instruments will be
implemented using general purpose hardware and
sophisticated software.
V. Conclusions.
A. Electronic crossovers are desirable for many reasons.
These include: easy design, use of more cost-effective
amplifiers, greater flexibility in possibilities for
compensating for driver and enclosure characteristics,
and ease of final set-up.
B. Best price-performance in crossovers is obtained with
24 dB/octave acoustical all-pass. There is only one
alternative that has the possibility of "Better"
performance, the delay-derived design, and it is
prohibitively expensive and has benefits of marginal
audible significance at this time. There is a
possiblity that program material, driver, and
listening room characteristics along with
implementation cost cuts will change this situation
within a decade.
C. It is important to know actual driver characteristics.
Optimizing the performance of the combination of the
crossover and the drivers is the goal, and this goal
cannot be achieved by knowing only the characteristic
of the crossover. While useful woofer characteristics
can be determined from specification sheets, this is
not the general situation for midrange and tweeters.
D. Relatively sophisticated acoustic measurements are
possible at a reasonable cost. The major stumblig
block has been obtaining sophisticated, reliable
signal sources and microphones. Compact discs with
sophisticated test signals recorded on them are
becoming availible, and are quite reliable. Small,
inexpensive, electret microphones costing a few
dollars provide omnidrectional response that is flat
with one or two dB's from 20 Hz to 20 kHz. Small
general-purpose computers are capable of inexpensive
analysis of electrical signals. Their cost, and the
cost of analog-to-digital conversion will continue to
fall.