Anonymous
2003-12-09 02:12:49 UTC
THE INFINITE BAFFLE SPEAKER
A brief introduction
Copyright (c) 2003 Andre Jute/Real McCoy Audio
There are two kinds of sealed enclosures, the infinite baffle and the air suspension speaker. This very basic introduction is about the infinite baffle, which uses a large enclosure in which the compliance of the air is greater than the compliance of the driver suspension.
The advantages of the infinite baffle over all other coned speaker enclosures, given that it is properly designed and built, include excellent transient response, good low frequency power handling, generally smaller box size, lower sensitivity to misaligned parameters than more complicated alignments, and straightforward ease of design and construction. Conversely, the price is lower sensitivity and higher low frequency cutoff.
The infinite baffle (and to a lesser extent the air suspension) enclosure, is the coned speaker enclosure of choice for the serious audiophile, next to true electrostatics and horns, because of its smooth handling of transients, and absence of one-note bass.
SUCK IT AND SEE?
Only if you are unimaginably rich. Speaker design is far more complicated and fraught with difficulties than amplifier design. The chances of stumbling on a good design by chance are infinitesimally small. Better to calculate twice and cut once.
All the infinite baffle enclosure calculations below use the famous Theile-Small parameters. These calculations also hold for air suspension systems, which are also sealed enclosures.
BOX SIZE
First choose a desired final total Q of the assembly at resonant frequency, Qtc, as the intended outcome for the design. Values of Qtc from 0.6 to 1.0 are theoretically possible, but values over 0.7 Qtc defeat the purpose as transient response degrades with increasing Qtc values. Commercial designs often increase the power handling of the speakers by choosing higher values of Qtc, and car audio designers go the whole hog, but that is not hi-fi. Higher values of Qtc than 0.7 rarely work except for true subwoofers with sub-20 cycle resonant frequency.
Calculate:
Qr = Qtc/Qts
Vr = Qr2-1
Vb = Vas/Vr
Fb = QrFs
F3 = Fb((1/Qtc2-2+((1/Qtc2-2)2+4)0.5)/2)0.5
Also dBpeak = 0
Except in the case where Qtc is larger than (1/2).5 when
dBpeak = 20log(Qtc2/(Qtc2-0.25)0.5)
where,
the Theile/Small parameters are:
Vas = Equivalent air compliance (liters)
Qts = total Q of the driver at its resonant frequency
Fs = resonant frequency of the driver (Hz)
and calculated data is:
Vb = net box volume (liters)
Fb = box resonant frequency (Hz)
F3 = -3dB frequency (Hz)
dBpeak = maximum peak or dip in system response
Net box volume is without dividers and braces, whose space must be added on to the value calculated above.
FREQUENCY RESPONSE
Calculate for each frequency of interest over the spectrum:
Fr = (F/Fb)2
dBmag = 10LOG(Fr2/((Fr-1)2+Fr/Qtc2))
where,
the Theile/Small parameters are:
Fb = resonance frequency of the system
Qtc = Final Q of the system at resonance
and calculated data is:
F = frequency (Hz)
dBmag = SPL 1W/1M at frequency F
POWER RESPONSE
To calculate power response of the bass driver/enclosure assembly, first make these intermediate calculations:
Sd = pi(Dia/100)2/4
Vd = SdXmax/1000
n0 = 9.6410(-10)Fs3Vas/Qes
SPL = 112 + 10LOG(n0)
K1 = (4pi3Ro/c)Fb4(Vd1.15)2
K2 = 112+10LOG(K1)
Amax = 1 except in the case where Qtc is larger than (1/2).5 when
Amax = Qtc2/(Qtc2-0.25)0.5
Par = K1/Amax2
Per = Par/n0
PeakSPL = SPL+10LOG(PEmax)
where,
the Theile/Small parameters are:
Vas = equivalent air compliance (liters)
Qes = electrical Q of driver at resonance
Fs = resonance frequency of driver (Hz)
PEmax = maximum input power of driver (W)
Fb = resonance frequency of the speaker (Hz)
Qtc = final Q of the system at resonance
Dia = effective diameter (cm), which is cone plus 0.333 of surround
Xmax = peak linear displacement of cone (mm)
and where,
pi = 3.14159265359
c = speed of sound in air (345 m/s)
Ro = density of air (1.18 kg/m3)
n0 = free-air efficiency
SPL = driver output @1W/1M
Par = maximum linear power output
Per = electrical input required to produce Par
PeakSPL = Thermally-limited SPL in passband
Now calculate for each frequency F,
Fr = (F/Fb)2
dBmag = 10LOG(Fr2/((Fr-1)2+Fr/Qtc2))
SPLd = K2+40log(F/Fb)
Pmax = K1((Fr-1)2+Fr/Qtc2))/n0
SPLt = dBmag+peakSPL
in which:
SPLd = displacement-limited SPL at F (dB)
Pmax = power required to produce SPLd at F (W)
SPLt = thermally-limited SPL at F (dB)
CAN AN IB ENCLOSURE BE SMALLER THAN THIS?
Yes, it can. If you plan to stuff the enclosure with longhair wool, calculate the volume of the enclosure as 0.75Vb. When it is built, continue to add stuffing until the resonance frequency of the assembly stops falling.
SHOULD AN IB ENCLOSURE BE SMALLER THAN THIS?
No, it shouldnt. The best results are achieved by building it fullsize and leaving it unstuffed, as is most often done in France, where audiophiles are particularly refined. A fullsize enclosure also leaves scope for a little judicious stuffing to finetune the enclosure.
CAN THE ENCLOSURE BE ANY SHAPE?
In theory, yes, but in practice non-standard shapes may require so much extra bracing for resonance-control that you may have to build a second set of enclosures to recover the volume lost to bracing. The standard tower shape has the advantage of a small footprint.
The best of the two proven low resonance tower formats is phi or (1+sqrt5)/2 or 1.618033988749895, where the internal measurements stand in the golden section ration of 0.618:1:1.618 to each other, and the bracing is similarly arranged for resonance cancellation. The other common ratio, for slack designers, is 0.8:1:1.25.
Multiple drivers can be arranged in the familiar dApolito configuration. The front baffle should be narrow, barely wider than the driver. This gets more important the higher the quality of the drivers. Tapering of the box is good, and some of the better commercial designs are tapered on all sides and thus appear to be pyramids with the sharp point lopped off.
The best shape for an infinite baffle is a sphere, which can be built out of dense foam or papier mache style from cold molded strips of ply.
Copyright (c) 2003 Andre Jute/Real McCoy Audio
A brief introduction
Copyright (c) 2003 Andre Jute/Real McCoy Audio
There are two kinds of sealed enclosures, the infinite baffle and the air suspension speaker. This very basic introduction is about the infinite baffle, which uses a large enclosure in which the compliance of the air is greater than the compliance of the driver suspension.
The advantages of the infinite baffle over all other coned speaker enclosures, given that it is properly designed and built, include excellent transient response, good low frequency power handling, generally smaller box size, lower sensitivity to misaligned parameters than more complicated alignments, and straightforward ease of design and construction. Conversely, the price is lower sensitivity and higher low frequency cutoff.
The infinite baffle (and to a lesser extent the air suspension) enclosure, is the coned speaker enclosure of choice for the serious audiophile, next to true electrostatics and horns, because of its smooth handling of transients, and absence of one-note bass.
SUCK IT AND SEE?
Only if you are unimaginably rich. Speaker design is far more complicated and fraught with difficulties than amplifier design. The chances of stumbling on a good design by chance are infinitesimally small. Better to calculate twice and cut once.
All the infinite baffle enclosure calculations below use the famous Theile-Small parameters. These calculations also hold for air suspension systems, which are also sealed enclosures.
BOX SIZE
First choose a desired final total Q of the assembly at resonant frequency, Qtc, as the intended outcome for the design. Values of Qtc from 0.6 to 1.0 are theoretically possible, but values over 0.7 Qtc defeat the purpose as transient response degrades with increasing Qtc values. Commercial designs often increase the power handling of the speakers by choosing higher values of Qtc, and car audio designers go the whole hog, but that is not hi-fi. Higher values of Qtc than 0.7 rarely work except for true subwoofers with sub-20 cycle resonant frequency.
Calculate:
Qr = Qtc/Qts
Vr = Qr2-1
Vb = Vas/Vr
Fb = QrFs
F3 = Fb((1/Qtc2-2+((1/Qtc2-2)2+4)0.5)/2)0.5
Also dBpeak = 0
Except in the case where Qtc is larger than (1/2).5 when
dBpeak = 20log(Qtc2/(Qtc2-0.25)0.5)
where,
the Theile/Small parameters are:
Vas = Equivalent air compliance (liters)
Qts = total Q of the driver at its resonant frequency
Fs = resonant frequency of the driver (Hz)
and calculated data is:
Vb = net box volume (liters)
Fb = box resonant frequency (Hz)
F3 = -3dB frequency (Hz)
dBpeak = maximum peak or dip in system response
Net box volume is without dividers and braces, whose space must be added on to the value calculated above.
FREQUENCY RESPONSE
Calculate for each frequency of interest over the spectrum:
Fr = (F/Fb)2
dBmag = 10LOG(Fr2/((Fr-1)2+Fr/Qtc2))
where,
the Theile/Small parameters are:
Fb = resonance frequency of the system
Qtc = Final Q of the system at resonance
and calculated data is:
F = frequency (Hz)
dBmag = SPL 1W/1M at frequency F
POWER RESPONSE
To calculate power response of the bass driver/enclosure assembly, first make these intermediate calculations:
Sd = pi(Dia/100)2/4
Vd = SdXmax/1000
n0 = 9.6410(-10)Fs3Vas/Qes
SPL = 112 + 10LOG(n0)
K1 = (4pi3Ro/c)Fb4(Vd1.15)2
K2 = 112+10LOG(K1)
Amax = 1 except in the case where Qtc is larger than (1/2).5 when
Amax = Qtc2/(Qtc2-0.25)0.5
Par = K1/Amax2
Per = Par/n0
PeakSPL = SPL+10LOG(PEmax)
where,
the Theile/Small parameters are:
Vas = equivalent air compliance (liters)
Qes = electrical Q of driver at resonance
Fs = resonance frequency of driver (Hz)
PEmax = maximum input power of driver (W)
Fb = resonance frequency of the speaker (Hz)
Qtc = final Q of the system at resonance
Dia = effective diameter (cm), which is cone plus 0.333 of surround
Xmax = peak linear displacement of cone (mm)
and where,
pi = 3.14159265359
c = speed of sound in air (345 m/s)
Ro = density of air (1.18 kg/m3)
n0 = free-air efficiency
SPL = driver output @1W/1M
Par = maximum linear power output
Per = electrical input required to produce Par
PeakSPL = Thermally-limited SPL in passband
Now calculate for each frequency F,
Fr = (F/Fb)2
dBmag = 10LOG(Fr2/((Fr-1)2+Fr/Qtc2))
SPLd = K2+40log(F/Fb)
Pmax = K1((Fr-1)2+Fr/Qtc2))/n0
SPLt = dBmag+peakSPL
in which:
SPLd = displacement-limited SPL at F (dB)
Pmax = power required to produce SPLd at F (W)
SPLt = thermally-limited SPL at F (dB)
CAN AN IB ENCLOSURE BE SMALLER THAN THIS?
Yes, it can. If you plan to stuff the enclosure with longhair wool, calculate the volume of the enclosure as 0.75Vb. When it is built, continue to add stuffing until the resonance frequency of the assembly stops falling.
SHOULD AN IB ENCLOSURE BE SMALLER THAN THIS?
No, it shouldnt. The best results are achieved by building it fullsize and leaving it unstuffed, as is most often done in France, where audiophiles are particularly refined. A fullsize enclosure also leaves scope for a little judicious stuffing to finetune the enclosure.
CAN THE ENCLOSURE BE ANY SHAPE?
In theory, yes, but in practice non-standard shapes may require so much extra bracing for resonance-control that you may have to build a second set of enclosures to recover the volume lost to bracing. The standard tower shape has the advantage of a small footprint.
The best of the two proven low resonance tower formats is phi or (1+sqrt5)/2 or 1.618033988749895, where the internal measurements stand in the golden section ration of 0.618:1:1.618 to each other, and the bracing is similarly arranged for resonance cancellation. The other common ratio, for slack designers, is 0.8:1:1.25.
Multiple drivers can be arranged in the familiar dApolito configuration. The front baffle should be narrow, barely wider than the driver. This gets more important the higher the quality of the drivers. Tapering of the box is good, and some of the better commercial designs are tapered on all sides and thus appear to be pyramids with the sharp point lopped off.
The best shape for an infinite baffle is a sphere, which can be built out of dense foam or papier mache style from cold molded strips of ply.
Copyright (c) 2003 Andre Jute/Real McCoy Audio