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The present invention relates in general to headphoning and more
particularly concerns novel apparatus and techniques for reducing noise,
and producing a relatively uniform frequency response that does not vary
appreciably among users while reducing distortion. The invention achieves
these results with relatively compact headphones that may be worn
comfortably without excessive pressure on the head from forces urging the
cups against the head. The invention achieves noise reduction while
faithfully reproducing a music or speech signal.
A typical prior art approach for providing noise attenuation is to use a
headset having high mass, large internal volume and a spring support that
exerts heavy pressure upon the head. The high mass increases inertia which
resists acceleration and also contributes to the structural rigidity of
the headset walls. The heavy pressure effects a seal without air leaks to
increase low-frequency attenuation. The compliant air cavity of the
internal volume provides high-frequency roll-off. However, most of these
techniques increase the discomfort the user experiences.
Prior art active noise cancellation techniques include an approach
utilizing a microphone external to the headset for transducing external
noise. An electrical system then processes the transduced noise signal in
a manner similar to the attenuation produced by the headset upon the noise
sound signal to provide an oppositely phased signal to the headphone
driver for canceling the external noise. This approach is an open-loop
system that does not adapt to different users and may actually increase
the noise level inside the headset. Another approach uses a closed loop or
servomechanism system, such as described in report AB-A009 274 distributed
by the National Technical Information Service entitled A STUDY OF PROPOSED
EAR PROTECTION DEVICES FOR LOW FREQUENCY NOISE ATTENUATION by Patrick
Michael Dallosta dated April 1975. U.S. Pat. No. 3,009,991 discloses a
velocity-sensitive microphone closely adjacent to a loudspeaker diaphragm
in a feedback loop. U.S. Pat. No. 3,562,429 discloses motional feedback,
remote acoustical feedback and feedback around a headphone.
It is an important object of the invention to provide improved feedback
control.
According to the invention, in a feedback control system for providing a
controlled output signal in response to an input control signal having
components including amplifying means having an input and output for
amplifying a signal applied to the input and arranged in a closed loop
with feedback means for coupling the output to the input and the
amplifying means being characterized by open loop gain and phase margin
between the input and output when the feedback path is interrupted, the
improvement comprises means for establishing the open loop gain of the
amplifying means substantially uniform at a significant level over a
predetermined frequency range bounded substantially at at least one end by
a break frequency. The amplifying means includes means for establishing
the change in the open loop gain as a function of frequency outside the
predetermined frequency range in a region from the break frequency to a
critical frequency where the open loop gain is substantially unity with
magnitude of slope of the open loop gain greater than 6 decibels per
octave for a significant portion of this region while maintaining the
phase margin in the region sufficient to ensure stability, thereby
providing high gain over the predetermined frequency range while avoiding
oscillation and minimizing the error between the controlled output signal
and a desired controlled output signal designated by the input control
signal. Preferably the phase margin is at least .pi./6. Preferably the
means for establishing the change in frequency response includes means for
establishing this change in frequency response with the magnitude of slope
of the open loop gain being significantly greater than 6 decibels per
octave from the break frequency to a first frequency between the break
frequency and the critical frequency, less than 12 decibels per octave
from the first frequency to a second frequency separated from the first
frequency by the critical frequency and substantially zero decibels per
octave from the second frequency to a third frequency separated from the
critical frequency by the second frequency, the third frequency being
separated from the second frequency preferably by at least an octave.
Preferably the magnitude of slope between the break frequency and first
frequency is at least 12 decibels per octave and that between the first
and second frequencies being substantially 6 decibels per octave.
Numerous other features, objects and advantages of the invention will
become apparent from the following specification when read in connection
with the accompanying drawing in which:
FIG. 1 is a diagrammatical representation partially in section of a
headphone on the ear according to the invention through section 1--1 of
FIG. 1A showing a plan view seen from the ear;
FIG. 2 is a block diagram illustrating the logical arrangement of a servo
system according to the invention;
FIG. 3 is a graphical representation of measured noise reduction achieved
with the invention in comparison with the theoretical noise reduction
available;
FIG. 4 is a graphical representation showing open loop gain and closed loop
gain of the servo system plotted to a common frequency scale;
FIGS. 5A and 5B show a block diagram illustrating the logical arrangement
of a preferred embodiment of the invention;
FIGS. 6A and 6B show a schematic circuit diagram of electronic circuitry
implementing the block diagram of FIG. 5;
FIG. 7 is a block diagram illustrating the logical arrangement of a
preferred form of compressor;
FIG. 8 illustrates the compression characteristic of the compressor of FIG.
7;
FIGS. 9A and 9B show gain and phase characteristics for a normal
operational amplifier having a first order characteristic;
FIGS. 10A and 10B show modifications to the characteristics of FIGS. 9A and
9B, respectively, according to the invention; and
FIG. 11 is a modified band pass response according to the invention.
With reference now to the drawing and more particularly FIG. 1 thereof,
there is shown a diagrammatic representation of a headphone on an ear
according to the invention. A microphone 11 is positioned in cavity 12
essentially coaxial with headphone housing 13, driver 17 and driver
diaphragm 14, with cushion 15 sealing the region between outer ear 16 and
cushion support 21 of the headphone. Microphone 11 is close to the
entrance of ear canal 18 to insure that the amplitude of the pressure wave
at microphone 11 is substantially the same as that at the entrance to ear
canal 18. Cavity 12 is made as small as practical to help insure that the
pressure is essentially constant throughout the cavity. To this end
cushion 15 has high mechanical compliance, high flow resistance, high
density, and the axial cross sectional area is about the same as that of
diaphragm 14 and less than the axial annular cross sectional area of
cushion 15 around cavity 12. Headphone housing 13 is connected by friction
ball joint 22 to resilient headband 23, shown partially in FIG. 1, in
conventional manner.
A typical material for headphone cushion 15 is a slow recovery open cell
polyurethane foam. Cushion 15 presses against outer ear 16 over a
relatively large area to effect a good seal while distributing the force
required to maintain the good seal over a sufficiently large area so that
pressure on the ear is sufficiently low to avoid discomfort to the user.
Open cell high flow resistance material offers the mechanical advantages
of open cell material for conforming to the irregular shape of the ear
while providing the acoustical advantages of closed cell material in
significantly attenuating spectral components above a predetermined
frequency in the middle range of frequencies, such as 2 kHz. It also
maintains the pressure inside the cavity essentially uniform through this
frequency range. Fluid-filled cushions also have these properties. This
structural arrangement according to the invention may be contrasted with
typical prior art approaches using a circumaural seal that creates a large
cavity with high pressures on the head developed in response to the force
required to maintain the circumaural seal or open cell low flow resistance
cushions that negligibly attenuate low frequency signals. These prior art
cavities are characterized by a large pressure field divergence and
require greater diaphragm excursion to produce a given sound pressure
level than is required for the small cavity according to the invention.
Thus, the invention achieves better acoustical performance with a smaller
compact package that is more comfortable for the user.
Referring to FIG. 2, there is shown a block diagram illustrating the
logical arrangement of a system according to the invention. A signal
combiner 30 algebraically combines the signal desired to be reproduced by
the headphone on input terminal 24 with a feedback signal provided by
microphone preamplifier 35. Signal combiner 30 provides the combined
signal to the compressor 31 which limits the level of high level signals.
This in turn provides the compressed signal to compensator 32. The
compensation circuits 31 ensure that the open loop gain meets the Nyquist
stability criteria, so that the system will not oscillate when the loop is
closed. The system shown is duplicated once each for the left and right
ears.
Power amplifier 32 energizes headphone driver 17 to produce an acoustic
signal in cavity 12 that is combined with an outside noise signal that
enters cavity 12 from a region represented as acoustic input terminal 25
to produce a combined acoustic pressure signal in cavity 12 represented as
a circle 36 to provide a combined acoustic pressure signal applied to and
transduced by microphone 11. Microphone preamplifier 35 amplifies the
transduced signal and delivers it to signal combiner 30.
The compensation circuits 31A are designed so that the loop gain T(s) is
maximized over a region of 40-2000 Hz (open loop) as represented by curve
20 in FIG. 4. This loop gain is P(s)=(CBDEMA) where DM is the transfer
function of the electrical signal output of the microphone 11 referred to
the electrical input to driver 17, A, B, C, D, E and M being the transfer
characteristics of microphone preamplifier 35, power amplifier 32,
compressor circuits 31, compensation circuits 31A, driver 17 and
microphone 11, respectively. This loop gain is maximized subject to the
constraints that the phase margin and magnitude margin be high enough to
insure stability in differing conditions, including on the head of
different individuals and off the head.
The closed loop transfer function from electrical input to pressure output,
Po, at the entrance to the ear canal is:
P.sub.o /V.sub.I =T.sub.u =CBDE/(1+CBDEMA).
The magnitude of this closed loop transfer function as a function of
frequency corresponds to curve 21 shown in FIG. 4. The amount of active
noise reduction where P.sub.I corresponds to the acoustical noise input
is:
(P.sub.o /P.sub.I)=N.sub.R =1+CBDEMA=1+T(s).
Referring to FIG. 3, there is shown a graphical representation of the
actual noise reduction measured by a microphone simulating the eardrum by
curve 23 in comparison with the theoretical value obtained by measuring
the open loop gain plus 1 represented by curve 24.
Referring to FIGS. 5a and 5b, there is shown a block diagram illustrating
the logical arrangement of a preferred embodiment of the invention. It is
convenient to represent the system by six blocks designated by enclosed
numerals 1-6, respectively, and subdividing compensation block 2 into
three subblocks 2a, 2b and 2c, respectively, power amplifier block 3 into
subblocks 3a and 3b, respectively, and compressor block 5 into five
subblocks 5a, 5b, 5c, 5d and 5e, respectively. The portions of the
circuitry forming the blocks of FIGS. 5a and 5b have been indicated by
suitable broken-line boundaries in FIGS. 6a and 6b. Since those skilled in
the art will be able to practice the invention by building the circuit of
FIGS. 6a and 6b, the circuits will not be described in excessive detail.
It will be convenient to refer to FIGS. 5a, 5b, 6a and 6b in following the
discussion of this specific embodiment below.
The summer/multiplier 1 comprises summer 30 that receives the input audio
signal from input terminal 24 and the feedback signal provided by
amplifier 35. Summer 30 is implemented in FIG. 6b as an operational
amplifier connected in the normal inverting summer amplifier
configuration. A capacitor connected between the junction of a pair of
like input resistors and system ground shunts the high frequency signal
components to system ground. Half of analog switch U304 delivers the
remaining low frequency components to virtual ground at the input of
integrated circuit U102. A modulating signal on the MOD line from
compressor block 5 toggles the switches at a 50 kHz rate. Controlling the
length of time the switch is closed on each cycle effects multiplication.
For signals characterized by spectral components in a bandwidth much less
than 50 kHz the switch may be regarded as an impedance of magnitude
proportional to the duty cycle of the modulating signal waveform. In
normal operation the switch is closed most of the time. Upon detection by
compresser 5 of an exceptionally large input amplitude, the on duty cycle
is reduced, thereby attenuating low frequency spectral components of the
input signal.
A series connected resistor and capacitor delivers the high frequency
signal components directly to the input of U102 so as to be unaffected by
multiplier action.
The output of summer/multiplier block 1 is delivered to compensation block
2 comprising an active filter characterized by magnitude and phase
characteristics that insure stability of the feedback loop without
appreciably compromising the overall loop gain. Section 2c provides gain
with proper rolloff at high frequencies. Sections 2a and 2b compensate the
phase response of the loop gain at the low and high frequency crossover
points, respectively. The principles of this preferred form of
compensation are discussed below and facilitate high gain in a band of
frequencies including most voice spectral components while maintaining
stability that avoids oscillation.
Power amplifier block 3 receives the output signal from compensation block
2. Section 3b is a conventional noninverting amplifier with discrete
output current buffer. Section 3a comprises a simple diode limiter for
protecting the driver from being driven to a destructive level of power
dissipation. Light emitting diodes illuminate when limiting occurs.
Preferably, the input is A.C.-coupled to eliminate D.C. offsets from
previous stages.
The driver/microphone/ear system block 6 is not shown in FIGS. 6a and 6b.
Driver 17 receives the amplified signal from power amplifier block 3 to
produce an acoustical signal perceived by ear 16 and transduced by
microphone 11. Imperfect seal of cushion 15 causes a low frequency
rolloff. A complex structure of resonances at frequencies above a few
kilohertz also characterizes block 6. Furthermore, there is excess phase
shift caused by propogation delay from driver 17 to microphone 11 and the
distributed source nature of driver 17. Yet, the elements in the system
coact to compensate for these nonuniform characteristics and produce an
overall system closed-loop frequency response between input terminal 24
and ear canal 18 that is substantially uniform.
The microphone preamplifier block 4 receives the transduced signal from
microphone 11 and comprises a low noise operational amplifier connected
for noninverting gain. The amplifier and gain were selected to allow the
self-noise of the microphone to dominate, thereby minimizing the
contribution by the system electronics to the noise level at the ear 16. A
Zener diode provides the biasing voltage V.sub.cc for electret microphone
11. Amplifier 35 in summer/multiplier block 1 receives the preamplified
signal provided by microphone preamplifier 4.
Compressor block 5 monitors both the signal at input terminal 24 and the
feedback signal at the output of microphone preamplifier 4 to provide the
modulating signal on the MOD line for modulating the low frequency gain of
summer/multiplier block 1. Section 5a sums feedback and input signals in
both left and right channels. A low pass filter having a break frequency
typically at 400 Hz selectively transmits the combined signal for full
wave rectification. Section 5b averages the rectified signal with a fast
attack and slow decay time to provide an output signal proportional to the
low frequency spectral energy in both left and right loops. Section 5c
converts the latter signal to a proportional current with offset, the gain
and offset being controlled by potentiometers.
Section 5d receives the output current signal from section 5c for providing
the 50 kHz modulating signal on the MOD line. Integrated circuit U305 in
FIG. 6a comprises a 50 kHz clock pulse source that triggers integrated
circuit U306 to reset its output to ground every 20 microseconds. The
capacitor voltage at pin 2 of integrated circuit U306 then decreases
linearly at a rate proportional to the output current provided by section
5c until it reaches a threshold level to switch the output switches of
integrated circuit U306 high and reset the capacitor voltage at terminal 2
to the positive supply until triggered again. Since the analog switches in
summer/multiplier block 1 are closed for a ground potential on control
pins 1 and 8, the summer/multiplier gain for low frequencies is inversely
proportional to the level of the current provided by section 5c. Large
currents cause the capacitor potential on pin 2 of integrated circuit U306
to reach the threshold level faster, and the analog switches U304 are
correspondingly closed for a shorter period of time. Section 5e drives an
LED bar graph display which indicates the amount of compression. It is
sufficient to sense and act solely on low frequencies because low
frequency spectral components carry most of the energy of typical input
signals.
In summary the complete system may be considered as a servosystem with two
input signals. The first is the audio electrical signal to be reproduced.
The second is the ambient acoustic noise signal at the ear. The system
output is the acoustical signal produced at the ear. The feedback signal
is a voltage proportional to the instantaneous sound pressure at the
entrance to the ear canal. This sound pressure is a combination of the
sound provided by the driver and the ambient acoustic noise. The small
electret microphone 11 transduces this signal, preamplifier block 1
amplifies it, and summer/multiplier block 1 sums this feedback with the
input audio signal to provide an error signal representative of the
difference between the actual sound pressure at the ear and the desired
pressure, the latter being proportional to the input audio signal.
Compensation block 2 selectively transmits the spectral components of the
error signal to insure loop stability. Amplifier block 3 amplifies the
compensated signal and delivers the amplified compensated signal to the
driver 17 to produce a resultant sound pressure at the ear corresponding
to the desired audio input signal. Thus, over the range of frequencies for
which the feedback loop is active, the loop corrects for the spectral
coloration of the driver/microphone/ear system and cancels ambient noise.
The amount of correction is related to the magnitude of stable gain which
the loop can provide. Compressor block 5 coacts with the multiplier
portion of summer/multiplier block 1 to prevent an input audio or acoustic
signal from overdriving the loop into clipping.
Having described a preferred embodiment of the system, certain subsystems
and their features will be described. Compressor block 5 is embodied in
particularly advantageous form that reduces compression artifact and
avoids nonlinear oscillation. Prior art compressors typically may be
classified into basic types, n-to-1 and thresholding. An n-to-1 compressor
produces one dB change in output level for each ndB in input level. A
thresholding compressor typically is linear for input signal levels below
some threshold and assumes some n-to-1 compression ratio above this
threshold, the ratio sometimes being infinite above threshold level so as
to limit the average output level.
N-to-1 compressors are commonly used in compandors for compressing signals
for transmission through noisy communications channels or recording on
noisy media and then expanding the compressed signal after detection to
restore the signal to its original dynamic range with recording or
communications channel noise significantly attenuated after expansion. A
thresholding compressor is generally used in systems where the signal will
not later be expanded or uncompressed because, when properly designed,
they leave less of an undesirable artifact in the output signal than
n-to-1 compressors. A threshold compressor with an infinite compression
ratio above threshold is typically implemented with a feedback loop. If
the compressor gain and the compressor attack and decay time constants are
not carefully chosen, significant undesirable audible artifacts result,
particularly for input levels just above threshold, and the system may
oscillate, thereby producing unpleasant audible sounds.
The present invention incorporates an advance over the typical prior art
thresholding compressor with infinite compression ratio above threshold.
FIG. 7 is a block diagram illustrating the logical arrangement of the
system generally embodied in block 5. The system responds to an input
signal X on terminal 51 by providing a compressed signal Y on terminal 52.
The dividend input of divider 53 is connected to input terminal 51. Input
terminal 51 is also connected to the input of a full wave rectifier 54.
The output of full wave rectifier 54 is connected to the input of an
averaging low pass filter 55 characterized by a decay response time
constant that is much greater than the attack response time constant. The
output (X) of averaging low pass filter 55 is connected to the input of
amplifier 56 introducing a compressor gain K. Summer 57 receives a signal
K.sub.o on its other input to provide a divisor signal at the divisor
input of divider 53. Divider 53 provides a quotient signal x/a at the
input of output amplifier 58 that provides the compressed output signal Y.
It can be shown that for static signals, such as sine waves, the input to
output gain is Y/X=1/(K.sub.o +K(X)). FIG. 8 shows this compression
characteristic graphically. This characteristic is similar to the
characteristic of a thresholding compressor with infinite compression
ratio above threshold in that for small signals Y/X=1/K.sub.o =constant,
and for large signal Y/X=1/KX or Y=1/K. However, the compressor according
to the invention has at least two advantages over the prior art
thresholding compressor. It causes less audible compression artifact for
complex input signals, such as music, because the transition from no
compression to full compression is smoother. Furthermore, since there is
no feedback, it cannot go into nonlinear oscillation.
Turning now to preferred forms of compensation. It is known that if the
attenuation of gain A(.omega.) is known over the entire range of
frequencies, then the phase .PHI.(.omega.) for a minimum phase network is
uniquely determined; and similarly, if .PHI.(.omega.) is known over the
entire range of frequencies, then A(.omega.) is uniquely determined for a
"minimum-phase" function having no poles or zeros in the right half of the
s or p plane. This property is described in section 4.9 under the heading
ATTENUATION-PHASE RELATIONSHIPS FOR SERVO TRANSFER FUNCTIONS in Volume 25
of the M.I.T. RADIATION LABORATORY SERIES entitled "Theory of
Servomechanisms." This relationship was first reported in a paper by Y. W.
Lee in the Journal of Mathematics and Physics for June 1932 and is
discussed in Chapter XIV entitled "Relations between Real and Imaginary
Components of Network Functions" in NETWORK ANALYSIS AND FEEDBACK
AMPLIFIER DESIGN by Bode (D. VanNostrand Co., New York 1945). In section
4.8 of the aforesaid "Theory of Servomechanisms" the "attenuation-phase"
type of analysis is described as the most satisfactory approach to the
servo design problem and describes the criterion of phase margin at the
frequency of feedback cutoff as a good practical criterion of system
stability that should be at least 30.degree. and preferably 45.degree. or
more. For 6 db per octave attenuation beyond cutoff, this section explains
that the frequency where the gain A is one (log A=0) should be at least
21/2 octaves from the cutoff frequency to develop sufficient phase margin.
The purpose of establishing phase margin is to avoid a situation that
would support undesired oscillations, and also to eliminate peaking which
amplifies external noise. A disadvantage of establishing such an extensive
region between the frequency f.sub.c where the gain is 1 and the break
frequency is that the desirable effects of negative feedback for spectral
components within the frequency region is significantly reduced. The
present invention overcomes this disadvantage by combining networks in a
manner that provides high open loop gain in the frequency band of interest
while still maintaining stability to establish both attenuation or gain
characteristics and phase characteristics in such a manner that there is
adequate phase margin at the frequency f.sub.c of unity gain.
The present invention includes compensating means characterized by open
loop gain or attenuation frequency response characteristics with regions
of arbitrary slope at the pass band end or ends while establishing a
stable phase margin at the frequency f.sub.c where the gain falls to zero.
These principles will be better understood from the following example.
Referring to FIGS. 9A and 9B, there are shown graphical representations of
the gain or attenuation and phase characteristics for an operational
amplifier having a normally first order characteristic. The gain is
typically represented as uniform to the half-power or break frequency
.omega..sub.o and thereafter decreases linearly 6 db per octave. Referring
to FIGS. 10A and 10B there is shown a graphical representation of a
modification of the attenuation and phase characteristics shown in FIGS.
9A and 9B, respectively, applying the principles of the invention to
achieve more loop gain above f.sub.o while maintaining the phase margin
substantially the same. This is accomplished by adding the portion
indicated by broken lines with breakpoint at f.sub.1 beyond f.sub.o and
slope 12 db per octave to frequency f.sub.2 where the slope then resumes
the more gradual slope of 6 db per octave. The modified phase
characteristic represented by the broken line in FIG. 10B still has a
phase margin of substantially .pi./2.
Referring to FIG. 11, there is shown a modified bandpass response in which
the broken lines represent the modification of the gain or attenuation
over a more conventional approach having 6 db per octave slope on either
side of the transmission band. These compensation circuits have a slope
nearer the break frequency that is of greater magnitude than the slope in
the frequency range nearer the critical frequency f.sub.c where the gain
is unity while having adequate phase margin.
The compensation circuitry in block 2 of FIGS. 5 and 6 embodies these
principles. It can be seen that the loop compensation follows these
guidelines from the open loop gain curves. In FIG. 4, the slope just after
the break frequency (at 500 Hz) is 18 db/octave. The network in section 2a
has a zero at 80 Hz and pole at 92 Hz, with damping constants 0.56 and
1.1, respectively. The high frequency circuit in section 2b has a zero at
3.1 kHz and pole=7.3 kHz with damping constants 0.49 and 1, respectively.
The circuit and low pass filter in section 2c have zeroes at 1.6 kHz and
3.4 kHz and poles at 160 Hz, 320 Hz, 800 Hz and 34 kHz.
It is evident that those skilled in the art may now make numerous uses and
modifications of and departures from the specific embodiments described
herein without departing from the inventive concepts. Consequently, the
invention is to be construed as embracing each and every novel feature and
novel combination of features present in or possessed by the apparatus and
techniques herein disclosed and limited solely by the spirit and scope of
the appended claims.
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