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Maxim > Design
support > App notes
> Audio
Circuits > APP 4632

Feb 05, 2010

Keywords: phase delay, 3D stereo, transaural
crosstalk, speaker
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APPLICATION NOTE 4632

Phase delay enhances 3D audio

By:

Robert
Nicoletti, Applications Engineer

Abstract: This
article explains transaural crosstalk caused when two speakers
are placed close together and sounds intended for one ear
reach the other ear. The article shows how phase delay can be
used to produce a 3D effect to produce acoustical signals at
the two ears as the signals would occur in a normal listening
situation. The MAX9775 headphone amplifier is given as an
example device.

Attend
this brief webcast by Maxim on
TechOnline

A
similar article appeared on the Audio DesignLine,
August 2006.

Introduction
Stereophonic sound is usually achieved
only with a considerable amount of separation between the
speakers. However, many applications such as handheld
computers and cellular phones must mount their speakers close
together. For those designs, you can simulate stereo by
employing wave interference to cancel left-channel sounds in
the listener's right ear and right-channel sounds in the left
ear. Called transaural crosstalk cancellation, this technique
yields an apparent separation between speakers that is at
least four times greater than the actual separation.

Theory
To better understand this phenomenon, consider
how the ears and brain process information to determine the
location of a sound source.
The human ear is sensitive to what we call "audible" sound
waves in the approximate range 20Hz to 20kHz. As a sound wave
reaches the ear, it is shaped by the outer ear before reaching
the inner ear drum. This reshaping changes the wave's resonant
properties according to the direction from which it entered
the ear. The resulting spectrum allows the brain to determine
the direction from which the sound wave originated.

As
sound waves propagate towards a listener's head from a given
direction, any slight difference in arrival times at the left
and right ears also helps the listener to determine the
direction of the source. This time delay, known as ITD
(interaural time delay), operates with the ear's spectral
properties to determine the HRTF (head-related transfer
function)1 associated with each ear. The HRTF is a
mathematical transfer function that relates a specific sound
source to the ears of the listener. It accounts for the source
location in terms of distance to the listener's head, the
separation distance between the ears, and the sound
frequency.

The basic idea for simulating a 3D effect is
to produce acoustical signals at the two ears as the signals
would occur in a normal listening situation. This 3D effect is
accomplished by combining each source signal with the pair of
HRTFs corresponding to the direction of the
source.2

Multimedia 3D enhancement
Most stereo multimedia
products that offer 3D enhancement do not account for all the
directional information needed to create a fully 3-dimensional
sound. Those multimedia systems in most cases employ HRTFs
consisting of simple phase-delay circuits which produce a
widening effect on the perceived sound field. Thus, speakers
located closely together are perceived as being separated by a
greater distance.

When listening to sound from a
two-speaker source, the left-channel signal arrives at the
left ear before it arrives at the right ear, and the
right-channel signal arrives at the right ear before it
arrives at the left. The right ear, however, hears a little of
the left-channel sound, and the left ear hears a little of the
right-channel sound. That effect is called transaural acoustic
crosstalk (Figure 1).

Figure
1. Transaural acoustic crosstalk consists of some sound from
the right-hand stereo speaker reaching the left ear, and
vice-versa.

As the speakers are moved closer
together, these time delays diminish until sounds from the two
speakers appear to come from a single speaker. The resulting
crosstalk "tells" our brain that the sources are close
together. To simulate a greater separation between two closely
located audio sources, this crosstalk must be eliminated. By
adding a cancellation signal from each speaker to the other,
you can cancel the crosstalk for listeners directly in front
of the source. Again, this acoustic cancellation gives
listeners the impression of wider speaker
separation.3

Phase delay cancels crosstalk
The technique of
introducing a phase delay to each of the signals driving
multiple emitters is commonly used in radio-antenna arrays to
control their beamwidth and directivity. Whereas a single
antenna aligned along the
direction radiates equally in all directions along the x–y
plane, that spread of radiation can be limited to several
distinct lobes along the x–y plane by lining up several
transmitting antennas. For a given distance between the
antennas, the lobe width decreases with the number of antennas
and with the frequency of the radio waves. For example, a
five-element array with zero phase difference between the
elements (i.e., all antennas emitting the same signal)
produces the typical radiation pattern of Figure
2.

Figure
2. A five-element antenna array with zero phase differences
between the elements produces this radiation pattern. The
antennas are located at the origin and spaced at
half-wavelength intervals along the x-axis.

Besides
changing the lobe width, you can rotate the main lobe in the
x–y plane by delaying the signal to each successive element in
the array by a constant phase angle α
(Figure 3). The array's radiation pattern is then
proportional to an array factor F(u):

Where N is the number of antennas in the array;

is the radiation wave number; d is the separation between
antennas; and Ψ is the angle with the positive
x-axis.4

Figure
3. These radiation patterns are produced by a five-element
antenna array in which the phase difference between elements
is π/2 (a), and 2π/3 (b).

Application to sound
Because sound waves also obey the
superposition principle, you can apply these results to the
creation of a speaker array which directs the sound from one
stereo channel to one ear and the sound from the other channel
to the other ear (Figure 4).

Figure
4. In this block diagram of an audio-speaker array for stereo
sound, the two buffer amplifiers each add α° of phase delay.

Because each
HRTF is specific to the relationship between a given sound
source and the listener, we must make some assumptions in
deriving the HRTF that cancels transaural acoustic crosstalk
for a specific application.

Assuming that the speakers
are mounted on a handheld device, the parameter d should be no
greater than 7cm. Next, assuming a 20cm head width and a
distance of 50cm between the ears and the device, the angles
ΨL and ΨR (measured from the positive x
axis to the listener's left and right ears, respectively)
should be 78.5° and 101.5°. For the condition of no signal on
the left and a nonzero signal on the right, the optimal phase
difference is one that maximizes sound amplitude in the
vicinity of the right ear (Figure 5).

Figure
5. For a signal applied only to the right channel in Figure 4,
the ratio of sound amplitudes at the right and left ears is
maximum when α = 90°, f = 6.1kHz, and
d = 7cm.

Looking back at equation 1, F(u) for a
two-element array has a maximum when u = 0 and a minimum when
u = π. For a nonzero signal on the
right channel, therefore:

Thus, the optimal phase difference is -90°. Using
the relationship :

This result is fortunate, because 6.1kHz lies
close to the peak of sensitivity for the frequency response of
our ears. The constant phase difference causes a performance
degradation as the signal departs from this optimal frequency.
Nonetheless, the constant-phase technique has been found
superior to techniques that feature other phase-frequency
relationships, such as linear
phase versus frequency.

Circuit design
Networks that produce a constant phase
shift (i.e., a phase difference) find considerable application
in radio electronics, and techniques for their design have
existed since the 1950s. The basic topology consists of two
cascades of first-order allpass stages (Figure 6),
which produce a nonconstant phase shift with respect to their
common input. Over a specified frequency range, however, they
maintain an approximately constant phase shift relative to
each other.

Figure
6. A basic first-order allpass circuit.

Passive
implementations are available, but the most commonly used
first-order section is an active circuit (Figure 7). It
presents a phase-shift filter with ft = 10kHz for
the linear signal (the proper input channel), and an
ft of 1kHz for the quadrature
signal (the other input). The goal is a 90° phase shift
between the linear and quadrature signals over the audio bandwidth
of 1kHz to 10kHz.

Figure
7. Among cascaded, first-order, active allpass circuits, this
one is most commonly used.

The cascaded,
first-order, allpass circuit of Figure 8 achieves a
phase difference between the L and Q outputs of close to 90°
throughout the frequency range of 1kHz to 10kHz. The 1kHz to
10kHz range is acceptable, because most of the speakers in
portable audio devices are too small to support full-spectrum
audio. Typically, they offer very little response below
300Hz.

Figure
8. This response of the Figure 7 circuit shows a reasonable
approximation to the desired 90° phase difference over the
range 1kHz to 10kHz.

To improve the 3D effect, you
can add more stages in cascade and then align them
appropriately to widen the frequency range over which the
circuit maintains a 90° phase shift. The two-stage cascade
shown, however, is a good tradeoff among circuit complexity,
power consumption, and performance. Audio ICs such as the MAX9775 incorporate
a phase-delay circuit and audio amplifier that simulate a
wider perceived sound field with a single
chip.

References
Bedrosian,
S.D., "Normalized design of 90° phase-shift networks.,
IRE Transactions on Circuit Theory, (June 1960), pp.
128–136.

Albersheim, W.J., Shirley, F.R.,
"Computation methods for broad-band 90° phase-difference
methods," IEEE Transactions on Circuit Theory, 16, (2)
(May 1969), pp.
189–196.

Endnotes
1Sibbald,
Alastair, An Introduction to Sound and Hearing,
Sensaura LTD., 2000.

2Casey, Michael,
Gardener, William G., Basu, Sumit, Vision Steered
Beam-Forming and Transaural Rendering for the Artificial Life
Interactive Video Environment, MIT Media Laboratory,
Cambridge MA, 1995.

3Gardner, William G,
3D Audio Acoustic Environment Modeling, Wave Art Inc.,
99 Massachusetts Ave., Suite 7, Arlington, MA. March 15,
1999.

4Kong, J. A, Electromagnetic Wave
Theory, Second Ed., John Wiley & Sons, Inc., New York,
1990. pp. 243–269.

Related parts

MAX9775

2 x 1.5W, Stereo Class
D Audio Subsystem with DirectDrive Headphone
Amplifier

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Download,
PDF format (147kB)
APP 4632: Feb 05, 2010

AN4632, AN 4632, APP4632,
Appnote4632, Appnote 4632

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