U.S. patent application number 15/390932 was filed with the patent office on 2017-04-20 for low frequency equalization for loudspeaker system.
The applicant listed for this patent is J. CRAIG OXFORD, D. MICHAEL SHIELDS. Invention is credited to J. CRAIG OXFORD, D. MICHAEL SHIELDS.
Application Number | 20170111019 15/390932 |
Document ID | / |
Family ID | 46327327 |
Filed Date | 2017-04-20 |
United States Patent
Application |
20170111019 |
Kind Code |
A1 |
OXFORD; J. CRAIG ; et
al. |
April 20, 2017 |
LOW FREQUENCY EQUALIZATION FOR LOUDSPEAKER SYSTEM
Abstract
A method of optimizing the low frequency audio response
emanating from a pair of low frequency transducers housed within a
cabinet. The low frequency transducers are electrically connected
to a power amplifier and source of audio content. The resonant
frequency (Fs) and amplitude (Q) are characterized as to the
high-pass pole of the low frequency transducers as they are mounted
within the cabinet. An equalizer is placed between the amplifier
and source of audio content for canceling the complex pole of the
low frequency transducers and for establishing a new complex pole
at a cut off frequency below which the sound generated by the low
frequency transducers will diminish.
Inventors: |
OXFORD; J. CRAIG;
(NASHVILLE, TN) ; SHIELDS; D. MICHAEL; (ST. PAUL,
MN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
OXFORD; J. CRAIG
SHIELDS; D. MICHAEL |
NASHVILLE
ST. PAUL |
TN
MN |
US
US |
|
|
Family ID: |
46327327 |
Appl. No.: |
15/390932 |
Filed: |
December 27, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11708406 |
Feb 20, 2007 |
8098849 |
|
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15390932 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04R 1/2873 20130101;
H04R 3/04 20130101; H04R 1/025 20130101; H04R 1/227 20130101; H03G
5/165 20130101; H04R 1/2803 20130101 |
International
Class: |
H03G 5/16 20060101
H03G005/16; H04R 3/04 20060101 H04R003/04; H04R 1/02 20060101
H04R001/02 |
Claims
1. A process for designing a speaker system, comprising: first
optimizing a low frequency transducer with respect to motor
strength, low mass, and high suspension stability; after optimizing
the transducer, selecting a speaker box size; after selecting the
speaker box size, choosing a lower frequency limit; after selecting
the speaker box size, installing the driver in the speaker box; and
measuring the Ftc, Qtc of the system.
2. The process of claim 1, further comprising the steps of:
installing an equalizer in the system; and setting equalizer
settings to optimize the low frequency transducer response.
Description
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/351,834, filed Jan. 17, 2012, which is a
continuation of U.S. patent application Ser. No. 11/708,406, filed
Feb. 20, 2007, now issued as U.S. Pat. No. 8,098,849, which is a
continuation-in-part application of U.S. patent application Ser.
No. 11/324,650, filed Jan. 3, 2006, and is entitled to those filing
dates for priority in whole or in part. The specifications,
figures, and complete disclosures of U.S. patent application Ser.
Nos. 13/351,834 and 11/708,406 and 11/324,650 are incorporated
herein in their entireties by specific reference for all
purposes.
FIELD OF INVENTION
[0002] This present invention involves a method of optimizing the
low frequency audio response emanating from a pair of low frequency
transducers housed within a cabinet. When the proper equalization
circuit is installed within the audio chain, the woofer portion of
a speaker system can be optimized to an extent not previously
achievable.
BACKGROUND OF THE INVENTION
[0003] Loudspeaker systems including those intended for residential
two channel audio or multi-channel theater systems intend to
embrace a substantial portion of the audio frequency range
discernable by a listener. An important part of this range are low
frequencies produced by relatively large loudspeaker transducers,
generally known as woofers.
[0004] As with the mid and high-frequency parts of the audible
range, it is known that the correct reproduction of musical pitch
and timbre is strongly related to the attack part of the sound and
less so to the decay part. The low frequencies are important in
this regard because in all of occidental music the harmony is built
upon the bass. If the reproduction of the bass frequencies has a
slow attack, the overall sound is perceived as having an uncertain
sense of pitch and a poor sense of rhythmic drive. It is thus of
very great importance to design woofer systems which correctly
render the attack part of the sound.
[0005] The correct rendering of the attack requires the ability for
the motor of the loudspeaker to quickly accelerate the diaphragm.
Since acceleration is proportional to force divided by mass it is
necessary that the woofer transducer has a light moving system and
a powerful motor. Conventionally designed woofer systems generally
embody the opposite of these requirements. This is because there is
a universal desire to make the woofer enclosure as small as
possible. As will be discussed below, the stiffness of the air in
the enclosure adversely modifies the characteristic of the woofer
transducer, making optimization difficult at best and often
impossible.
[0006] An excellent woofer system is shown schematically in FIG. 1.
Woofer system 10 is comprised of cabinet 11 housing low frequency
transducers 12 and 13. These low frequency transducers ideally
operate in phase with each other whereby diaphragms 14 and 15 face
each other being driven by motor assemblies 16 and 17. When low
frequency transducers 12 and 13 are mounted opposite to one another
as shown in FIG. 1, 10 large reaction forces associated with high
power woofers located in cabinet structure 11 need not rely on
mechanical grounding of the cabinet to the surrounding structures
upon which the cabinet is placed. In analyzing the low frequency
transducer model of FIG. 1, one can create an electrical equivalent
circuit (mobility analogy) of this assembly in free air. This is
shown 15 in FIG. 2A as a second-order resonant circuit with a
natural frequency determined by the stiffness of the suspension and
mass of the moving system. The amplitude (Q) of this resonance is
determined by the damping due to mechanical loss. The resonance can
be defined in terms of frequency and Q, and it constitutes a
complex high-pass pole in the response of the loudspeaker.
[0007] Notwithstanding the above discussion, the electrical
equivalent circuit shown in FIG. 2A does not tell the entire story.
In this regard, reference is made to FIG. 2B. In this regard, when
low frequency transducers 12 and 13 are placed within cabinet 11
which can be, for example, a sealed box, the stiffness of the air
in the box is added to the stiffness of the suspension of the low
frequency transducers and is shown as a parallel inductor. The
consequence of this is that both the resonant frequency and Q are
raised in value by approximately the square root of (1+(the
stiffness of the speaker divided by the stiffness of the air in the
box)). This can graphically be depicted by comparing FIGS. 2C and
2D.
[0008] A design goal of a woofer system is to maintain a low
resonant frequency. Traditionally, this was done by increasing the
moving mass (diaphragms 14 and IS), decreasing diaphragm stiffness
or both. Stiffness has traditionally been decreased by making
suspension components employed in such transducers more flexible or
"limp" or by making enclosure 11 larger. Again, moving mass can
only be increased by making diaphragms 14 and 15 heavier. However,
adopting any of these traditional expedients represent a
significant compromise as they tend to degrade performance of the
woofer system. Softer suspension parts are not reliable,
particularly if they are carrying a greater mass. Increased mass
further requires a corresponding increase in motor strength if the
ability to accelerate diaphragms 14 and 15 is to be maintained. A
larger motor translates directly to higher production costs and a
larger enclosure 11 may not be a suitable solution as cabinet size
is generally considered to be a design constraint on any
loudspeaker system. As a result, those engaged in loudspeaker
design generally simply choose appropriately sized low frequency
transducers, enclose them in an available volume and accept the
resulting response.
[0009] It is thus an object of the present invention to provide a
novel technique for dealing with the resonance of a low frequency
transducer system.
[0010] It is yet a further object of the present invention to
improve the operating range of a woofer system by providing an
electrical circuit as an equalizer within the audio chain.
[0011] These and further objects will be more readily apparent when
considering the following disclosure and appended claims.
SUMMARY OF INVENTION
[0012] The present invention involves a method of optimizing the
low frequency audio response emanating from a pair of low frequency
transducers housed within a cabinet, said low frequency transducers
being electrically connected to a power amplifier and source of
audio content, said method comprises characterizing the resonant
frequency (Fs) and amplitude (Q) of the high-pass pole of the low
frequency transducers as they are mounted within said cabinet,
placing an equalizer between said amplifier and source of audio
content. Said equalizer canceling the complex pole of the low
frequency transducers and establishing a new complex pole thus
establishing a new cut off point below which the low frequency
sound will diminish. The topology of the equalizer permits
independent variation of the parameters which facilitates dynamic
variation of said parameters to continuously adapt the equalizer in
order to prevent excessive excursion of the woofers.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIG. 1 is a side cut away view of a typical woofer cabinet
and enclosed low frequency transducers which can be employed in
benefiting from the present invention.
[0014] FIGS. 2A and 2B are electrical equivalent circuits of the
woofer assembly of FIG. 1 in free air (FIG. 2A) and in a sealed
cabinet (FIG. 2B).
[0015] FIGS. 2C and 2D correspond to FIGS. 2A and 2B, respectively,
showing a graphical equivalent of the relationship between the
output or response (dB) and frequency of woofer systems.
[0016] FIG. 3 is a block diagram of the equalizer system made the
subject of the present invention.
[0017] FIGS. 4A and 4B are schematic layouts and graphical
depictions of the equalizer system shown in FIG. 3.
[0018] FIG. 5 is a graphical depiction of the relationship between
woofer output (dB) and frequency showing the effect of the
equalizer system shown in FIGS. 3 and 4.
[0019] FIG. 6 is a block diagram of the equalizer with
voltage-controllable adjustment of the equalization frequency ratio
and control sidechain.
[0020] FIG. 7 is a schematic diagram of the variable equalizer.
[0021] FIG. 8 shows the effect of the variable adaptive
equalization.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0022] The present design approach or method of optimizing low
frequency transducer response in a loudspeaker system bears little
or no parallel to loudspeaker design methodology engaged in
previously. In the past, a designer would select what is believed
to be properly sized and dimensioned transducers placed in what is
hoped to be an appropriately sized cabinet fed by low frequencies
emanating from a power amplifier through an appropriate cross over
network. In practicing the present invention, however, a designer
could begin with a preconfigured woofer system and by inserting the
appropriate equalization circuit between the power amplifier and
the audio content source, this woofer system can be optimized.
[0023] All woofer systems have a natural resonance or preferred
natural frequency. In an electric circuit or an electric analogy to
a mechanical system, resonance occurs because of the exchange of
energy between the reactive elements, i.e., capacitance and
inductance, of the circuit. It is recognized that the resistive
elements of a circuit are dissipative, noting if there was no
resistance in a circuit (which is obviously a physical
impossibility), the resonant exchange of energy or oscillation
would persist indefinitely. As resistance is introduced into this
ideal model, the quality of the resonance or its amplitude (Q)
deteriorates. In the loudspeaker electrical analogy at hand,
capacitance corresponds to mass, inductance corresponds to
compliance and resistance corresponds to mechanical resistance.
Obviously, the opposite of Q is damping (d) so that d=1/Q. As such,
any single resonance can be characterized by its frequency and its
Q (or d), the mathematical description of a resonant system can be
described as follows:
S=jw+F
where
[0024] S=complex frequency variable
[0025] j=square root of (-1), the complex operator
[0026] w=2 pf, where f is in Hz=1/sqrt(mass.times.compliance)
[0027] F=phase angle
[0028] The notation of this equation denotes a real and an
imaginary axis for S. When a resonant circuit is expressed in S,
the roots of the equation in the numerator represent "zeros" in the
"S-plane" and the roots of the denominator represent "poles" in the
S-plane. In solving the transfer function for a system with both
poles and zeros noting that not all systems have both, if there are
identical coefficients for a pole and a zero, they cancel each
other. A complex pole in S is a resonance and can be described in
terms of F and Q.
[0029] It is recognized herein that any speaker, by itself, has a
fundamental resonant frequency (Fs) related to the mass of the
diaphragm or cone oscillating on the compliance of the transducer
suspension. The sharpness of this resonance is determined by the
friction losses in the parts and by the electromagnetic drag from
the motor which both drives and brakes the diaphragm.
[0030] It is further recognized that if one places a transducer in
a cabinet, the stiffness of whose air volume is significant,
generally characterized by a relatively small cabinet, the radian
frequency (w) will increase because compliance decreases. The
result is a new resonant frequency for the complete system, denoted
as Ftc, Qtc. It is a property of direct radiator loudspeakers that
below their resonant frequency, response diminishes. For a
closed-box system, the response falls asymptotically to 12
dB/octave below the resonance. As such, if the resonance has been
pushed up in frequency by a too-small box, the useful low frequency
response will be diminished.
[0031] These characteristics were previously discussed with regard
to FIGS. 2A and 2B and the corresponding FIGS. 2C and 20. As to
FIGS. 2A and 2C, the woofer or low frequency transducer in free air
shows that it is a second-order resonant circuit with a natural
frequency determined by the stiffness of the suspension and the
mass of the moving system. The amplitude of this resonance (Q) is
determined by damping due to mechanical losses and, as noted above,
is defined in terms of frequency and Q as it constitutes a complex
high-pass pole in the response of the loudspeaker. By contrast, as
noted in reference to FIGS. 2B and 20, the stiffness of the air in
the box is added to the stiffness of the suspension of the speaker
shown as a parallel inductor. The consequence of this is that both
the resonant frequency and its Q are raised in value by
approximately the square root of (1+(the stiffness of the speaker
divided by the stiffness of air in the box)). Designers in the past
have attempted to keep resonant frequency low by increasing moving
mass and decreasing stiffness of the transducer, or both. However,
as noted above, these design goals are difficult to achieve. By
contrast, the present invention optimizes the transducers enclosed
in an available volume by providing an equalizing circuit imposed
between the source of an audio signal and power amplifier used to
drive the lowest frequency transducers.
[0032] Although the equalizing circuit will be described in detail
hereinafter, broadly, it operate by (1) characterizing the enclosed
woofer system as to its resonant frequency (Fs) and Q of its
high-pass complex pole, (2) placing a matching complex zero in the
signal path to cancel the speaker characteristic and (3)
establishing a new complex pole at an arbitrarily chosen low
frequency which defines the new low frequency cut off of the woofer
system. This latter characteristic of the equalizing circuit is
necessary to prevent the woofer system from being overrun by large
signals below the intended operating range and may be made
dynamically variable to extend the dynamic range.
[0033] FIG. 3 provides a conceptual diagram of the equalizer of the
present invention. This is a two integrator state-variable filter
which is topologically well known in the art of filter design. The
conjugate equalizer shown in FIG. 3 is illustrated schematically in
FIG. 4. In the example of FIG. 4, resistor values are normalized to
10.0 Kw. For example, R11=Q.sub.p(F.sub.2/F.sub.p).times.10 Kw. The
radian frequency (w) equals 2 pf, so that, for example, given
C1=C2=110 nF and given F.sub.z=70 Hz, then R2=R3=22.74 Kw. The
functions are U1 and U5 are inverting summing amplifiers. U2 and U3
are integrators. U4 is a unity-gain inverting amplifier. As such,
Fz, Qz of the equalizer cancels the complex pole of the speaker
denoted as Ftc, Qtc. The combined response then remains flat down
to Fp, Qp which is the new cut off frequency for the complete
system. There are simpler circuits which will accomplish the
conjugate equalization, but the two-integrator state-variable
filter has the advantage that the four parameters of interest, Fz,
Qz, Fp and Qp, are independently adjustable. This allows an
improvement to be described below.
[0034] Graphically, the effect of the equalizer circuit is shown in
FIG. 5. It is noted that the equalizer response creates a new pole
while the response vs. frequency characterization of the speaker in
its cabinet shifts as depicted in FIG. 5.
[0035] Because the entire arrangement substitutes amplifier power
for moving mass (as a way of overcoming the increased stiffness),
it is important to recognize that the transducers must be
constructed so as to withstand high power inputs at low
frequencies. The rate of increase of response of the equalizer with
decreasing frequency is 12 dB/octave. Put another way, if the
equalization extends from 70 Hz downward to 20 Hz (typical values)
then the required amplifier power at 20 Hz will be 21.7 dB greater
than at 70 Hz (in a Bode straight-line approximation). This is a
power ratio of 148:1. This is not a problem because the previously
optimized woofers can have very high sensitivity. The elevated
sensitivity comes from the fact that the conversion efficiency is
proportional to the resonant frequency cubed, and inversely
proportional to the stiffness.
[0036] There is a further advantage to this arrangement. In a
conventional woofer system, the entire useful operating range is
above the fundamental resonance of the enclosed system and is
therefore mass-controlled. In a mass-controlled system, the
acoustic output lags the electrical input by 90 degrees. At long
wavelengths this is significant because 90 degrees at 50 Hz is
equivalent to a 5 foot distance, i.e., temporally the woofer is 5
feet more distant. In a conjugately-equalized system as the one
described, the behavior is effectively resistance-controlled over
most of the operating range. In the example cited above, the system
will be resistive from about 20 Hz to about 80 Hz which is the
entire operating range in many applications. In such a system, the
acoustic output is in-phase with the electrical input so no
additional delay is present.
[0037] The present invention represents a significantly powerful
technique because it turns the design process on its head. Usually
one would:
[0038] a. Choose the box size;
[0039] b. Choose a desired lower frequency limit;
[0040] c. Try to find (or design) a driver which will get you
there.
[0041] Usually, and especially for a small box and low cutoff
frequency, the driver has to have a loose suspension and a high
cutoff frequency, the driver has to have a loose suspension and a
high moving-mass. This is the only way the resonance can be held to
a low frequency. Unfortunately, this combination of attributes
leads directly to poor electroacoustic conversion efficiency and
poor acceleration, hence poor rendering of the attack of bass
sounds. These are the well-known deficiencies of so-called
"acoustic suspension" woofer systems. The tradeoffs for remedying
this in a conventional system are unyielding.
[0042] With the present invention, however, one would:
[0043] a. Optimize the driver with respect to motor strength, low
mass and high suspension stability;
[0044] b. Choose the box size;
[0045] c. Choose the lower frequency limit;
[0046] d. Measure the Ftc, Qtc of the speaker in the box; and
[0047] e. Set up the equalizer accordingly.
[0048] The use of equalization increases the power demand below Fz
compared to Fz and above. This is not the liability it might seem.
This is because the efficiency due to the high Ftc is substantially
increased so the starting point for looking at the power demand is
much lower. Given the statistics of low-frequency content in music
and movies, the average power required for a woofer system
employing the present invention is usually less than one for a
conventional one.
[0049] The methodology described above perfects the frequency
response of the woofers for small signals. It should be noted that
woofers are generally called upon to reproduce large signals as
there is often high acoustic power at low frequencies in music.
Regardless of the method used to achieve flat frequency response,
there is still the consideration that the required axial
displacement of the diaphragms of the woofers is inversely
proportional to the square of the frequency. For example, to
produce the same sound pressure at 25 Hz as is produced at 50 Hz,
the diaphragms of the woofers must travel four times as far.
Normally this leads to a situation where the woofers can reach
their excursion limits at very low frequencies. In the instant
invention the equalization is already present and it can be
conveniently modified on a dynamic basis to prevent said excessive
diaphragm excursion.
[0050] As noted above, the use of the 2 integrator state-variable
filter topology allows this control. What is required at high
amplitudes is to change the ratio of Fz/Fp independently of the
other three parameters, Fz, Qz and Qp. This can be accomplished by
introducing a multiplier circuit in the feedback path for the
frequency ratio and the pole damping as shown in FIGS. 6 and 7. The
equations for this implementation are as follows:
[0051] Assume the multiplier solves
(((+x)-(-x).times.(+y)-(-y))/10), i.e. the product of the
differential inputs divided by 10. The control coefficient is
(10/(+x)-(-x))=V.
V=(10/(+x)-(-x))=(Fz/Fp).sup.2
[0052] K=added damping coefficient
[0053] Qp-(KsqrtV)/(V+K)
[0054] The reason for the presence of K is that without it, V will
control the square of the frequency ratio, but will control Qp
linearly. This could be solved by adding another multiplier but
would be an unnecessarily complicated solution. Instead, adding a
fixed damping term, K will cause Qp to remain constant within about
10 percent. The practical consequence of this is less than 1 dB in
amplitude at the dynamically adjusted cutoff frequency and is not
audible in practice.
[0055] It remains to control V. For this purpose, the audio signal
is passed through a second order low-pass filter which has the same
frequency as Fp unmodified, (i.e., Fz/Fp is at the static maximum
value, see below) and the same Q as Qp. The output of this filter
varies with frequency the same as the diaphragm excursion of the
woofers, so it effectively is an analog of the diaphragm motion.
This voltage is then scaled and peak-detected above a predetermined
threshold and applied to the differential x input of the
multiplier. As the system attempts to overdrive the woofers, Fp
will be shifted upward just far enough to prevent frequencies below
it from causing excessive excursion. Because this process is
dynamic, and is only applied to the extent required to prevent the
overload there is almost no adverse audible effect.
[0056] It should be noted that the control law for Fp is dB/dB so
that the control sidechain can be arranged as either feed-forward
or feed-back. Many methods exist for peak-detection and detection
threshold setting and the details are left to one skilled in the
art of analog circuit design.
[0057] Thus, it should be understood that the embodiments and
examples described herein have been chosen and described in order
to best illustrate the principles of the invention and its
practical applications to thereby enable one of ordinary skill in
the art to best utilize the invention in various embodiments and
with various modifications as are suited for particular uses
contemplated. Even though specific embodiments of this invention
have been described, they are not to be taken as exhaustive. There
are several variations that will be apparent to those skilled in
the art.
EXAMPLE
[0058] The following assumptions are made in the present
example:
[0059] 1. The total box volume is 90 litres (3.18 cubic feet).
[0060] 2. Two woofers are mounted identically on opposite sides of
the box.
[0061] 3. The woofer nominal diameter is 300 mm (12'').
[0062] 4. The woofers are identical.
[0063] 5. The lower cutoff frequency is to be 20 Hz.
[0064] The driver is then optimized:
[0065] 1. A low moving mass is chosen consistent with adequate
structural strength in the diaphragm. A value of 45 grams is
reasonable based on experience.
[0066] 2. A mechanical compliance (Cm) is chosen which will give
good stability to the suspension of the diaphragm. A value of
4.59E-4 meters/Newton is reasonable based on experience. For a 12''
driver this equates to a compliance equivalent volume (Vas) equal
to Cm.times.r.sub.o.times.c.sup.2.times.Sd.sup.2, where r.sub.o is
the density of air, usually taken to be 1.18 kg/cubic meter, c is
the velocity of sound, usually taken to be 345.45 m/s, and Sd is
the surface area of the diaphragm, which for a 300 mm nominal
driver is about 0.045 square meters. Vas represents the volume of
air whose compressibility is equal to the mechanical compliance.
Vas in this case is equal to 131 litres.
[0067] 3. The mass and compliance chosen above will result in a
fundamental resonance frequency of 35 Hz.
[0068] 4. The total damping of the driver resonant system is
established by the motor strength expressed as the product of B,
flux density in the gap, and L, the length of voice-coil conductor
in the gap. Actually there are two sources of damping, the pure
mechanical losses of the moving system (Qm) and the force exerted
by the motor. In a well optimized driver, the motor damping
completely dominates. The motor damping alone is called Qe, the
electrical Q. It is established by the relationship
Qe=DCR/((B.times.L).sup.2.times.2 pFs.times.Cm). Since Cm and Fs
have already been determined, the Qe depends on DCR. the voice coil
resistance and B.times.L.
[0069] 5. Motor design in loudspeakers is superficially simple but
actually requires considerable experience, and/or the use of
assistive software which is commercially available. Those skilled
in the art will recognize that a motor with a B.times.L product of
about 20 Tesla meters and a OCR of 7 Ohms is quite feasible. These
values, along with the determinations made above, will yield
Qe=0.173.
[0070] 6. In the woofer system of the present example, the drivers
are connected electrically in parallel. The result is that the DCR
drops in half and B.times.L remains unchanged. However, total force
developed by the two motors is equal to B.times.L.times.I, where I
is the current through the voice coil. For a fixed applied voltage,
I doubles because DCR dropped in half. Therefore the total force is
double.
[0071] 7. To summarize the resulting driver parameters:
[0072] a. Nominal diameter=300 mm
[0073] b. DCR=7 Ohms, 3.5 Ohms for 2 drivers in parallel
[0074] c. B.times.L==20 Tesla meters
[0075] d. Fs=35 Hz
[0076] e. Qe=0.173, and assuming Qm=5, then
[0077] f. Qt=0.167. Qt is the parallel combination of Qe and
Qm.
[0078] g. Vas=262 litres for 2 drivers
[0079] There is now sufficient information to design the equalizer.
It is well known to those skilled in the art, that the parameters
of the drivers as modified by the enclosure is easily calculated.
The required computational inputs are:
[0080] 1. The box volume;
[0081] 2. The Vas of the intended drivers;
[0082] 3. The Qt of the intended drivers.
[0083] The compliance ratio, a (alpha) is equal to Vas/Vbox. In
this case, a=262/90=2.911. then, the term sqrt (a+1) is found equal
to 1.978 (2, for practical purposes).
[0084] This means that when the two optimized drivers are mounted
in the 90 litre box, or separately in 45 litre boxes as shown in
FIG. 1, the new values Ftc and Qtc will appear. These are the
modified values of the fundamental resonance due to the stiffness
of the air in the box. They are found by multiplying Fs and Qt by
1.978. Thus, Qtc=0.334 and Ftc=70 Hz.
[0085] Taken by themselves, these are unattractive parameters for a
complete system. The Ftc is too high and in this case the Qtc is
too low. The result will be deficient low frequency response.
[0086] Referring to the equalizer circuit of FIG. 4A, the design
objectives are met as follows:
[0087] 1. Qz is set equal to Qtc=0.334. Thus R8 is set for 3.34
Kw.
[0088] 2. Fz is set equal to Ftc=70 Hz. Thus, assuming C1 and C2
are arbitrarily chosen to be 100 nanoFarads (nF), then R2 and R3
must equal 22.74 Kw.
[0089] 3. The values indicated for R8, CI, C2, R2 and R3 cancel the
driver characteristic.
[0090] 4. The new low frequency pole is set according to the system
design objectives given. For a maximally flat response with a lower
limit of 20 Hz, Fpole=20 Hz and Qpole=0.71, a so-called Butterworth
alignment.
[0091] 5. Thus R6=(70/20).sup.2.times.10 Kw, and
R11=0.71(70/20).times.10 Kw=24.8 Kw.
[0092] 6. The total resulting boost between frequencies >>70
Hz and <20 Hz, in dB, will be equal to 40 log (70/20)=21.7 dB.
This corresponds to a power ratio of 147:1. It can be seen that
this approach requires significant power and the design details to
handle such power reliably. The means to do this will be well known
to those skilled in the art.
[0093] Referring to FIGS. 6 and 7, the reconfiguration for dynamic
adjustment of the Fz/Fp parameter is shown. For purposes of
illustration, consider a slightly different set of unequalized
woofer parameters and a slightly different design objective:
[0094] 1. Qz is set equal to Qtc=0.50. Thus R8 is set for 5.00
Kw.
[0095] 2. Fz is set equal to Ftc=60 Hz. Thus, assuming CI and C2
are arbitrarily chosen to be 100 nF, R2 and R3 must equal 26.5
Kw.
[0096] 3. The values indicated for R8, C1, C2, R2 and R3 cancel the
driver characteristic.
[0097] 4. The new low frequency pole is set according to the system
design objectives; in this case, Fpole=20 Hz and Qpole=1.
[0098] 5. Thus coefficient K is calculated as described earlier to
be about 4.5, thus R11=45 Kw.
[0099] 6. The equalization set voltage is adjusted for
Fz/Fp=60/20=3. This requires 1.11 Volt at the x(-) input of the
multiplier with respect to the x(+) input.
[0100] 7. The low-pass filter in the control chain is set the same
as the system objective; Fp=20 Hz, Qp=1.Thus, C3 and C4=795 nF and
R16=10 Kw.
[0101] The full-wave negative peak detector indicated in FIGS. 6
and 7 must perform the detection only after the input to it has
exceeded a certain threshold. This is related to the voice-coil
voltage at which the woofers reach their maximum allowable
excursion at Fp minimum (i.e. Fz/Fp maximum). This requires the
voltage gain of the power amplifier to be known. This amplifier is
not shown but is connected between the output of FIG. 7 and the
woofers. For example:
[0102] 1. Assume the maximum input voltage to the woofers, which
are connected in parallel so the voltage is the same on both of
them, is 40 Volts rms which is equal to 56.56 Volts peak.
[0103] 2. Assume the power amplifier voltage gain is 20. This means
that when the voltage at the output of FIG. 7 reaches 2V rms at Fp
minimum, the woofers will be at their mechanical limit.
[0104] 3. The low-pass filter, U7, has a gain of 2 in the passband,
so 2V rms at the output of FIG. 7 will cause 4V rms at the input to
the negative peak detector. The peak value of 4V rms is 5.656V
which is the threshold of operation. Signals larger than this will
cause Fp to rise, thus reducing the total boost and preventing
excessive excursion of the woofers. The low-pass filter, U7,
conditions the detector input according to the excursion vs
frequency characteristic of the woofers.
[0105] FIG. 8 shows the various relationships for the adaptive
embodiment of the equalizer.
[0106] 1. The voltage controlled filter characteristic describes
how the filter changes with changes in ((x(+)-x(-)), the
differential control input.
[0107] 2. The unequalized woofer characteristic is to be corrected
by the filter by setting Fz and Qz of the filter equal to Ftc and
Qtc of the woofer, respectively.
[0108] 3. The woofer diaphragm excursion vs frequency relationship
shows the inverse square relationship for constant sound
pressure.
[0109] 4. The dynamically equalized response shows that above the
threshold of detection, the reduction of FzlFp causes a reduction
in the output below the inflection point which eliminated excessive
excursion of the woofer diaphragms.
[0110] Thus, it should be understood that the embodiments and
examples described herein have been chosen and described in order
to best illustrate the principles of the invention and its
practical applications to thereby enable one of ordinary skill in
the art to best utilize the invention in various embodiments and
with various modifications as are suited for particular uses
contemplated. Even though specific embodiments of this invention
have been described, they are not to be taken as exhaustive. There
are several variations that will be apparent to those skilled in
the art.
* * * * *