Note: Descriptions are shown in the official language in which they were submitted.
1 - 21 D 8 6 3 S PCr/US91/027~1
Improvement~ In zLnd Relating to Tran~mis~ioll Li~ Lou~lspeaXers
BACKGROUND OF THE INVENTION
1. Field of the Invention.
This invention relates to a method of and apparatus for
improving the performance of transmission line loudspeakers and
has particular applications in active noise control, high
fidelity audio, and sound reinforcement systems.
2. Discussion of the ~elevant Art.
The simplest form of a loudspeaker system is the direct
radiator. Such a loudspeaker radiates sound directly form the
enclosure aperture(s)--the driver diaphragm and, in the case of
vented-box syst~ms, a vent or port. There are no additional
devices through which the sound passes.
A transmission line loudspeaker adds an additional device,
such as a horn ~or impedance matching, through which some or
all o~ the sound passes. Prior forms of transmission line
systems may be divided into three classes. A type A
transmission line system consists of a closed-box direct
radiator loudspeaker with a transmission line added to the
driver aperture. All radiated sound passes through the
transmission line. A Type B or C system consists of a direct
radiator system with the transmission line coupled to the back
chamber of the enclosure. Both the Type B or Type C form
exhibit the fault that the transmission line presents an
acoustical short circuit to the back of the. driver at least at
some frequencies. This can cause serious dips in the system
response .
SUMMARY OF THE INVENTION
This invention relates to an improved form of the Type A
System in which the signals from both the drive aperture and
the port of a vented-box direct radiator system are combined to
drive the transmission line. The original form of the Type A
system prevents the back wave from the drive diaphragm from
interfering with the front wave by trapping the back wave in
the closed cavity behind the driver. The improved system
passes the back wave trough an acoustic phase inverter so that
it may be combined with the output ~rom the front side of the
W0~)2/19080 ~ ~ PCT/US91/02731
9 6
driver. This doubles the energy available to ~rive the
transmission line~ This improvement should not be confused
with hybrid systems which used a vented-box system with the
transmission line coupled to either the driver aperture or the
vent but not both.
The improved performance is roughly analogous to that seen
in a vented-box direct radiator system as compared to a closed-
box system. Either the efficiency or the bandwidth may be
increased; or the system size may be decreased; or a tradeoff
may be made among these possible benefits.
In one arrangement of the apparatus according to the
present invention one or more electrodynamic loudspeaker
drivers is installed in a vented-box direct radiator enclosure,
and a cover is added to the front of the enclosure. This cover
forms a front chamber into which both the driver and the vent
radiate sound. The sound passes through the front chamber and
into the transmission line~ For applications requiring high
2~ efficiency over a wide bandwidth the transmission line should
be a horn. However, a compact system mi-Jht use a short tube.
Such a tube is too short to exhibit transmission line
characteristics. It will act as lumped parameter acoustic mass
instead.
The transmission characteristics of the improved system
using a horn will be determined in great ~easure by the horn
and the acoustic load it presents to the ~ront chamber, but
will r in general, be high-pass in nature. The transmission
characteristics of the short tube system will be band-pass in
nature. the driver and the vented-box portion of the enclosure
will provide a 4-pole high-pass response, and the front chamber
and the outlet tube will provide a 2-pole low-pass response.
Anbther arrangement of the apparatus according to the
present invention is particularly useful for active noise
cancellation applications such as exhaust mufflers or duct
WO92/19080 2 1 ~ ~ 6 ~ ~ PC~/US9l/0273l
..
silencers. In this arrang~m~nt the pipe or duct through which
the noisy signal is flowing passes through the enclosure and
exists through the outlet tube. The end of the noisy pipe or
duct is aligned with the end of the loudspeaker and the two are
coaxial. Thus, the antinoise signal radiated by the
loudspeaXer during the active cancellation is coaxial with the
noise. Very good cancellation may be obtained at frequencies
with wavelenghts which are long compared to the size of the
outlet.
Another arrangement of the apparatus according to the
current invention which also has particular application in
active noise cancellation systems is similar to that described
immediately above. However, in this arrangmeent the pipe or
duct containing the noisy flow does not pass through the
loudspeaker. Instead, the loudspeaker outlet tube connects the
loudspeaker front chamber to the pipe as a tee fitting into the
pipeO In this case, the pipe need not end at the point where
the noise and antinoise are mixed. This arrangement is useful
for "in duct" cancellation.
The invention will now be further described by way of
examples, with reference to the accompanying drawings, in
which:
25BRIEF_DESCRIPTION OF THE DRAWINGS
FIGS. 1 and 3 are signal flow graphs of the improved
loudspeaker with a long transmission line and a ~hort outlet
tube,
FIGS. 2 and 4 are simplfied drawings of the invention, and
30FIGS. 5 to 9 show two ways ln which the invention may be
put to practical use in noise cancellation applications.
FIG. lO shows a gPneral form of a vented box bandpass
loudspeaker.
FIG. 11 shows a simplified acoustical analagous circuit.
35Description of the Preferred Embodiments
Consider first FIGS. 1 and 2. FIG. 2 shows an
electrodynamic loudspeaker driver 1 mounted in an enclosure 2
W092/1~08~ PCT/~S91/02731
2:~8~96
so that one side of the driver diaphragm radiates sound into
the fornt chamber of the enclosure 3. The sound form the other
side of the driver passes through the acoustic phase inverter
comprising the back chamber 4 and the inner vent 5 which
connects the front and back chambers. The total system o11tput
consists of the sum of the front wave and the phase corrected
back wave flowing through the front chamber and out via the
transmission line 6.
FIG. l shows the basic signal flow graph of the system
using an electroydnamic driver l. Electric potential Eg is
applied accross the driver voice coil which has a resistance RE
and a resulting current IVc flows. The electrodynamic coupling
Bl of the motor causes a driving force. The sum of this force
and the various reaction forces in the system gives in the
total force driving the diaphra~m FD. This force accelerates
the diaphrgam at a rate inversely proportional to the moving
mass MMS of the driver. The resulting acceleration of the
diaphragm aD is integrated once with respect to time ~the l/s
operation in the ~aPlace domain) to find the velocity of the
diaphragm uD and a second time to find the displacement o~ the
diaphragm XD. Now, moving the diaphragm results in some
reaction forces. As the diaphragm is displaced against the
mechancial springs in its suspension, an opposing force
inversely proportional to the mechanical compliance CMs of the
driver is added to the total force FD. Another opposing force
results from the motion through the mechanical losses RM~ f
the system and is equal to the product of RMS and UD. Also, as
the voice coil moves through the magnetic field of the motor a
back emf is generated which tends to oppose the driving
potential. This back emf, which is equal to the
electromagnetic coupling Bl times the diaphra~m velocity UD,
sums with the input potential Eg to give the voice coil
potential EVC.
As the diaphragm moves, the front side pushes against the
surrounding air and a flow into the front chamber 3 results.
This volume ~D is equal to the product of the diaphragam
velocity uD and its effective area ~D~ This volume velocity is
WO92/19080 21 Q ~ ~ ~ 6 PCT/US91/02731
one of the components of the total flow into the from chamber
UF. The conservation ~f matter requires that the flow into the
back chamber ~B across the boundary between it and the fro~t
chamber be equal to ~F but opposite in polarity. The volume
velocity UB presurizes the back chamber ~. The acoustic
pressure of the back chamber PB is equal to the lntegral of ~B
with respect to time divided by the acoustic compliance to the
back chamber CAB. This pressure exerts another reaction force
against the back of the diaphragm which is equal to the
pressure PB times the diaphragm area ~D. This another
component of FD.
For the purpose of an orderly description of the system,
assume that the inner vent 5 is blocked. This is equivalent to
the unimproved form of the transmission line loudspeaker. The
flow into the from chamber 3 pressurizes it. This component of
the front chamber acoustic pressure PF is equal to the inteyral
f ~F with respect to time divided by the acoustic compliance
of the front chamber CAF. The front chamber pressure drives
the flow through the transmision line 6 at a rate inversely
proportional to the i~put reactance X~ of the line. The
resistive part of the line impedance RAT causes a reaction
pressure which is also a component of PF~ X~T and RA~ are
frequency dependent line characteristics. The front chamber
pressure also causes a reaction force on the diaphragm equal to
PF times 8D. This is another component of FD.
Now, assume that the inner vent 5 is no longer blocked.
The pressure in the back chamber PB will drive a flow through
the inner vent with a volume velocity ~p which is equal to the
integral of the pressure PB with respect to time divided by the
acoustic mass of the vent ~AP. The volume velocity components
~D and ~p now add to form the total flow into the front chamber
which, in turn, drives the system output ~O.
In the arrangement of FIGS. 3 and 4, the analysis of the
system is similar, except that the line impedance is simplifed
because the short tube presents a l~mped parameter element. In
this case, the output flow ~O is equal to the front chamber
pressure PF i~tegrated with respect to time and divided by the
WO92/1908() ~ P~T/US91/027~1
acoustic mass of the outlet vent MAF. The opposing pressure
component f PF results from the flow losses in the outlet R~F.
Analysis of the signal flow graphs yields the approriate
design equations which allow the correct driver and enclosure
parameters to specify for a desired system.
FIGS. 5 to 8 show views of a practical loudspeaker system
using the present invention which has particular application in
active noise control systems. In this apparatus an additional
component, a flow tube 7 for the noisy flow (such as the
exhaust of an engine), has been added. Also, a drain tube 8
has been added between the front and back chamber so that water
or other liquids trapped in the back chamber may escape. If
the loudspeaker were used in an active noise cancellation
system on a vehicle and if the vehicle were driven through deep
water, the muffler could be flooded. The drain tube would
allow the trapped water to flow out of the back ~hamberO The
drain tube must be sized so that it acts as an acoustic mass
rather than an acoustic leak between the chambers. Its mass
must either be considered when adjusting the enclosure tuning
or be trivial compared to the inner vent 5 so that the effect
of the drain may be ignored.
FIG. 9 shows an apparatus using the present invention
which also has particular application for active noise control.
In this instance, the short tube 6 is formed by the area
between the heat shield plate ~ and the connection to the noisy
duct 8. A long, narrow tube 9 allows outsider air to enter the
enclosure. This tube, like the drain tube discussed above,
should be sized so that it has no adverse effect on the system
acoustic per~ormance. It may enter the enclosure through
either the front or back chamber. Air is forced through the
system because of the venturi-like dPtail lO in the noisy duct.
The flow through the duct over the "venturi" cause a low
pressure reyion which "draws" the outside air. This air may be
useful for cooling or removal of corrosive gases.
3 5 The analysis and derivation of the analog circuit of the
Vented ~ox ~andpass Loudspeaker is as follows: The sy~bol used
in Figures lO and ll and in the calculations ar~:
W092/19080 ~ i~ a86~6 Pcr/usgl/o273l l
in Flgures 10 and 11 and in the calculations are:
LIST OF SYMBOLS
CAB Acoustic compliance of Rear Box
CAp Acoustic compliance of Front Box
CAs Acoustic compliance of Driver (Loudspeaker VAS=POC2CAs)
MAp Acoustic mass of Front Port
MAS Acoustic mass of Driver
MAB Acoustic mass of Internal Port
RAS Acoustic Resistance of Driver
RE Electrical Resistance of Driver voice coil
SD Driver Diaphragm, M2
VB Volume of Rear Closed Box ~M3) (VB=POC2CAB)
Vp Volume of Front Box (M3) (Vp=POC2CAp)
Vd Peak displacement volume driver diaphragm (SDXM)
PO Mas densily of air (7.18 kg/m3)
C Speed of sound in air (345 m/sec)
Xm Peak linear displacement of driver diaphragm
Sp Area of the front port
SB Area of the internal port
B Magnetic flux density in driver airgap
l lenght of voice coil in the airgap of driver
UO Volume velocity at the front port
UAB Volume velocity at the internal port
UF Volume velocity inside the front box (UF=Us~UAB)
UB Volume velocity inside the rear box (UB=-UF)
US Volume velocity generated at the source
Pg Pressure generator (e~uivalent)
Eg Input voltage to the loudspeaker
Speaker Parameters
f5 (Ts= ~f ) Free Air Resonance frequency
QES Electro-Magnetic Q at f5
Qms Mechanical Q at fs
Qts Total Q at fSI QesQms
Qes+Qms
.
.~ .
WO92/19080 2 ~ PCT/US91/02731
G!8696 f~`
. .
Vas Volume of air having sam acoustic compliance as driver
suspension
Vd Peak displacement volume of diaphragm (=SDXM)
SD Effective diaphragm area
Xm Peak linear displacement of diaphragm
Referring now to Fig. lO, there is shown the general form
of the Vented Box Bandpass Loudspeaker (VBBP) configuration.,
Fig. ll shows the simplified acoustical analagous circuit of
the Vented Box Bandpass Loudspeaker (VBBP) configuration. The
terms Ro and Pg are determined by the following formulal:
R = ~L)2 p = Eg(BL)
RESD RSD
In the following circuit analysis, assumptions are made
tha`t there is a lossless enclosure (internal box resistance =
O and leakage resistance =~) and that the voice coil inductance
is small (LF%O)
The circuit analysis is as follows:
( ) g ¦ (Ro+RAS)+SMAS+ - ¦ Us~ F -~sMApUO
UF-U
(2) = sMAp-Uo
sCAp
(3) sMAgUAB+ - +sMAPUo~O
s,CAB
(4) From Equation (2) UF=(l+S2MApCAp)Uo Us+UAB=UF
(5) U5=UF-UAB
sM~ ~ sC~
WO ~2/19~0 PC~/US91/0:27~1 1
2 ~ 9 6;
.. . .
2 1 2
S MApCApMABCp~B+s (MABcAB+MApcAp~M~pcAB+l U
(6) Us= ' -- 1 o
S MABCAB
Substitute Equations ( 4 ) and ( 6 ) into the Equation ( 1 )
S2MAScAs + sCAS (Ro + RAS ~ 1
g ~ [ sCAS ¦ x
MApcAp~ABcAB + S (MABCAB + MApCAp -~ MApC.~B) + 1
2 O S MABCAB
(1 + S MAPCAP) + SMAp ~ Uo
sCAs
( 8 ) Pg ( S 3 CAsMABcAB ) = { S MASCASMP~PCAPMABCAB+
3 O s MAscAsMABcAB + S MAscAsMApcAp+s4MAscAsMApc~B
+s2MAscAs-~s5cAsRAtMApcApMABcAB~s CAsRAlMABcAB
+S CASRATMAPCAP+S CASRATMApCAB+SCASRAT
+S4MApCApMABCAB+S2(MABcAB+MApcAp+MApcAB)
1 S MABCAB+S CApMABCABMAp~S4CAsM~ABCAB}uo
45 ~9) Pg(S3CAsMABCAB)={S M~.SCAS~APCAP~ABCAB~
S5CP~SRATCAPMABCAB~ S (MAscAs~lABcAB+MAscA
Mp~scAscAB+~pcApMABcAB~MABcA~3M~7~ pcAp
+MARCA~APCA.~) +S CA,~RArr (MAPCAP~k5APCAR+
~' .
" ' ' ,
WO92/19080 ~1 ~ 8 ~ 9 6 PCT/~S91/0~73
)+s2(MAscAs+2MABcAg+MApcAp+MAp AB)
+SCASRAT+l )Uo
ASSUMPTIONS
10 (10) TS2=_= MASCAS
wS2
(11) TB2= _ = MABcAB.
WB
(12) Tp2= _ = MApCAp
20 Wp
(13) T 2= 1 = M C
25~ Wps
t14) TpB2= _ = MAPCAB
WPB
poC2 poC2
(15) RAT=Ro+RAS = WsVASQMS CASWsQts
1 Ts
~(16) CASRAT
WsQts Qts
(17) PO(S) = sMApUo
SYSTEM TRANSFER FUNCTION
sMAPUo Po ( s )
(18) G(s) = _ =
Pg Pg(s)
bs4
(19) G(s) =
S~ + a5S~ + a4S4 + a3S~ + a2S~ + alS + aO
when, TB2Tp2 1 B p s _ s
(20) a5= x
WsQts TS2TB2Tp2Ts2TR2Tp2QtS TsQtS Qts
.. . .
WO 92/1 9080 21~ 8 6 ~ 6 PCT/US91 /02731
11
5 (21) a4 T ~TB~Tp~ (Ts2TB2+Ts2Tp2-~TS2TpB2+~Tp2TB2+TB2Tp
= ~ + + P + + P = Wp2+WB2 +~_
W 2W 2
-~ 2Ws + ~ .
Wps
Ts ( p pB B ) l 1 TpB2
(22) A3=_ Ts~TB~Tp~ QtSTs l ~ TB~Tp7
Ws ¦ W 2+W~ Wp +W 2
(23) a2 ~- ~T .:! (Ts 2TB +Tp +TpB)
s B p
= (wB2wp2+2ws2wp2~ws2wB2+ 1~ ~
Ts l WsWB2Wp2
(24) al= x
Qts Ts TB2Tp Qts
( 2 5 ) aO = .~ - WS2WB2Wp2
Ts TB Tp
MAPCASMABCAB Tps TB Tps2 WS2Wp2
Ts TB Tp Ts~TB~Tp~ Ts~Tp~ Wps~
