Download The Use of Optocouplers in Measuring Loudspeaker Cone

Alps
Adria
Acoustics
Association
3rd Congress of the Alps Adria Acoustics Association
27–28 September 2007, Graz – Austria
THE USE OF OPTOCOUPLERS IN MEASURING
LOUDSPEAKER CONE DISPLACEMENT
Milan Uskoković, M.Sc.E.E.
Radio 101, Zagreb, Croatia
E-mail: [email protected]
Abstract
The article presents a method for measuring loudspeaker cone displacement employing a photo-interrupter. The photointerrupter is set to work in the linear regime, such that any movement of the barrier between the transmitting diode
and the receiving photo transistor results in a change in the collector current of the photo transistor. The barrier is
fitted to the loudspeaker cone so that the change in the collector current is proportional to the movement detected. In
order to achieve better linearity, temperature stability and S/N ratio, two photo-interrupters forming a differential
connection are used. The paper ends with an example of the practical implementation and experimental measurement
results of the proposed sensing methodology.
Key words: photo-interrupter, cone displacement, frequency response, noise.
1. INTRODUCTION
There are several methods for measuring loudspeaker
cone movement. One of them, and the most popular, is
the method with laser beam movement detectors.
Although this method yields accurate and error-free
results, it requires very expensive measuring equipment
and is largely restricted to laboratory settings. Simpler,
less costly and more practicable measuring solutions rely
on the use of capacitive, inductive or optical sensors that
can measure cone movement as a proportional change in
the capacity, inductivity or intensity of light that is emitted
from the light-emitting source to the light-receiving
element. However, these methods require that additional
measuring elements be mounted on the loudspeaker cone
(such as electrical contacts, light transmitters, electrically
conductive coatings, etc.), which may affect mechanical
properties of the cone itself, degrade overall speaker
performance to a certain extent and ultimately
compromise measurement accuracy.
The purpose of this article is to provide an overview and
analysis of a method for measuring cone displacement that
would be both practicable and economical and have only a
minimal or negligible effect on loudspeaker properties.
The method proposed in this paper is based on the use of
optocouplers or, more precisely, photo-interrupters.
2. PHOTO-INTERRUPTERS
1.1. Background
The structural block diagram and the schematic of a
typical photo-interrupter design are shown in Figure 1.
The interrupter consists of a light-emitting diode that
emits light (LED) and a photo-transistor that detects said
light. The value of the photo-transistor collector current
depends on the amount of light emitted by the LED and
the percent of the photo-transistor area obscured by the
barrier that prevents the passage of light emitted by the
LED. In order to make the measurement system robust to
the conditions that cause interference, both the LED and
the photo-transistor are made to operate in the infrared
region of the electromagnetic spectrum.
Fig.2 Interrupter transfer function
1.2.2 The effect of temperature on electrical properties
Fig.1 Structural and functional diagrams of
a photo-interrupter design
1.2. Electrical properties of photo-interrupters
1.2.1 Transfer function
Interrupters are usually used to detect and count the
movement of some barrier between the transmitting diode
and the receiving photo-transistor, where the linear part of
the transfer curve needs to be as small and as steep as
possible in order to avoid counting errors. If interrupters
are to be used as movement sensors, however, the
opposite is required: the transfer function
Ic=f(d)
The internal operating temperature of a loudspeaker may
vary greatly, depending on the amount of acoustic power
being emitted by the loudspeaker and its efficiency. At the
specific position where this photo-interrupter is placed,
we can expect a relative temperature change of
approximately 80 degrees Celsius, which is an important
design issue that must not be overlooked.
(1)
where
Ic is the collector current, and
d is the percentage of the photo-transistor area shadowed
by the barrier,
should be as linear as possible in the widest working
range. The linearity of the transfer function will have a
direct effect on the linearity of the movement sensor and
measurement accuracy. Also, the wider the range, the
better the signal-noise ratio.
Figure 2 shows the transfer function of the photointerrupter used in this paper. It can be observed that the
transfer function is linear for 20 to 80 percent of the
shadowed area, providing a linear output over the range of
about 0.5mm.
Fig.3 LE diode forward voltage vs. temperature
characteristic
Figure 3 illustrates the effect of temperature on the LE
diode forward voltage whereas Figure 4 shows the
dependence of the photo-transistor collector current on
ambient temperature.
electronic device. Its value depends on the temperature of
the electronic device and the bandwidth conveyed. The
Johnson noise can be calculated using the following
formula:
I j = 4kTB / Rsh
(3)
where
Ij= Johnson noise (A)
k = Boltzmann's constant (1.38 x 10-23 joules/K)
T = absolute temperature (K)
B = noise bandwidth (Hz)
Rsh = photodiode shunt resistance (Ω).
Apart from the above-mentioned types of noise sources,
which are generated from within the emitting and
receiving elements of the photo-interrupter itself, noise
and interference can also be caused by outside light
sources or by reflection against the wall of the coil
assembly, as well as by the power supply of the lightemitting diode and photo-transistor.
Because the value of the decoded useful signal is not
constant but rather depends on the power emitted by the
loudspeaker, and it decreases as the frequency rises, it is
of utmost importance to keep noise at a minimum.
Fig.4 Collector current vs. temperature characteristic
The above figures clearly indicate that both the power
emitted by the LED and the collector current of the phototransistor vary in response to ambient temperature
changes, which may lead to measurement errors and
deviation of the sensor operating point from the optimum.
1.2.3 Noise
Before going further into the subject, we shall look briefly
into the main sources of noise in photo-interrupters.
The main sources of noise in photo-interrupters are
thermal noise (or Johnson noise), shot noise and flicker
noise (1/f or contact noise). These noise sources are
independent of each other and the total noise current is the
root of the sum of the square of each of these noise
sources:
2
2
In = I j + Is + I f
2
(2)
where
In = total noise current (A),
IJ = thermal or Johnson noise current (A),
IS = shot noise current (A),
IF = flicker noise current (A).
The Johnson noise is dominant. It is a form of white noise
generated by the random motion of electrons in an
1.2.4 Response time
Another parameter of great importance in sensor design is
the response time of the photo-interrupter. It determines
the highest frequency of loudspeaker cone displacement
and the maximum decodable slew rate ratio. To be useful
for the purposes of the design discussed in this paper, the
photo-interrupter must be able to detect electrical signals
in the frequency range up to 200Hz, with a slew rate of
0.1V/µS. Figure 5 shows the response time of the photointerrupter for the square wave signal. It can be seen that
the rise time is dependent on the collector current and that
the required slew rate ratio of 0.1V/µS can be easily
achieved.
Fig.6 Barrier design
The angle of the slit aperture (or wedge) k is determined
by the coefficient of the reduction of the relative
movement of the barrier, using the following equation:
k=arc tan(d/xmax)
(4)
where
d = linear movement of the photo-interrupter, and
xmax= maximum cone displacement.
Fig.5 Output signal rise time characteristic
2. Design of the optical movement sensor
As noted earlier in the text, the amount of cone
displacement depends on the power emitted by the
loudspeaker and the frequency of the signal emitted.
Loudspeaker manufacturers generally publish data on the
peak cone displacement, xmax, for a given loudspeaker,
which means that the maximum amount of cone
movement that can be detected by the sensor is already
known. This xmax value is usually in the range of 5 to
15mm so, for simplicity, in our further analysis we shall
take the arithmetic mean of these values (i.e. xmax =
10mm) as our estimate of the average xmax value.
On the other hand, the amount of cone displacement drops
as the frequency increases, in accordance with the below
formula:
x( peak ) =
Pn
4 ρ 0π 2 f 2 a 2
(5)
where
Pn= pressure,
ρ0 = density of air,
f = frequency,
a = cone radius.
Figure 7 illustrates the relationship between cone
displacement and frequency of the loudspeaker at 1W.
Figure 2 shows that the photo-interrupter has a linear
characteristic for a maximum barrier movement of 0.5mm
whereas the value of cone xmax is 10mm. This means that
the barrier should be shaped so that for xmax=10mm the
amount of its relative movement is 0.5mm. The shape of
the barrier by which this is achieved takes the form of a
wedge-shaped slit shown in Figure 6.
Fig.7 Cone displacement vs. frequency characteristic
As can be seen, a decrease in the amount of cone
displacement that is caused by frequency rise will
decrease the value of the output signal of the sensor and
reduce the S/N ratio. To keep noise at a minimum, two
photo-interrupters forming a differential connection are
used. This will enable us to reduce the impact of
temperature changes on measurement accuracy to the
lowest degree possible, assuming that the physical
properties and temperature of the photo-interrupters are
equal.
The barrier has the shape shown in Figure 6. The shape is
first printed with a laser printer on a piece of transparent
foil and then glued with binding glue to the inner surface
of the coil former. The barrier is extremely light (it weighs
less than 0.1g) so it does not affect any of the woofer
parameters.
The differential amplifier is implemented as shown in
Figure 10.
3. Implementation of the optical movement sensor
The experiment described here uses a woofer driver with a
diameter of 160mm. The photo-interrupters are mounted
onto the pole piece just below the driver's dust cap and the
connection wires are inserted through an opening in the
center of the pole piece. The barrier is a piece of printed
foil with two wedge-shaped slits on it, and it is glued to
the coil former on the inside of the driver. The details of
the test assembly are shown in Figures 8 and 9.
Fig.10 Differential amplifier schematic
Fig.8 Sensor placement I
The signal from the emitter resistors R1 and R2 of the
respective photo-transistors is amplified using the
inverting amplifiers IC1A and IC1B. Resistors R6 and R7
are used to adjust the amplification of the inverting
amplifiers in the circuit so that both sensors produce equal
output signals for the same amount of cone displacement.
Potentiometers R8 and R9 are used to null out any DC
offset at the output of the amplifier. Signals from the
output of the amplifier are passed to the differential
amplifier IC2, at the output of which differential voltage is
generated in proportion to the amount of cone
displacement. The gain of the differential amplifier is
adjusted so as to give the transfer ratio of 0.5V/1mm of
the amount of cone displacement.
For lack of more accurate methods, the linearity of the
sensors was roughly checked with a micrometer to
produce the transfer characteristic shown in Figure 11.
Fig.9 Sensor placement II
4. CONCLUSION
Fig.11 Sensor transfer characteristic
Figure 11 indicates that the linearity of the sensor in the
cone displacement range of ±4.5mm is fully satisfactory.
In addition, a measurement microphone was used to
measure the waveform and THD of the sound pressure
produced by the loudspeaker at a frequency of f=100Hz so
that a comparison could be made with the results from the
sensor. The characteristics of the resulting waveforms are
basically the same, both with comparable THD of about
1%.
The frequency response of the driver was also measured
both by the microphone and the sensor, with the results
shown in Figure 12.
Fig.12 Measured frequency responses
The red line on the chart indicates the output signal from
the sensor. It can be seen that the amount of cone
displacement decreases at a slope of 12dB/octave above
frequencies exceeding 40Hz. The green line on the chart
shows the sound pressure level measured by the
microphone while the blue line plots the level of noise at
the output of the sensor (when the cone is not excited).
The resulting S/N ratio is approximately 40dB for
frequencies up to 100Hz while at the frequency of about
1kHz the ratio measures 0dB.
The type of sensor described in this paper can have
practical application in measuring loudspeaker cone
displacement within a limited frequency range not
exceeding 2-3 octaves. In the specific example presented
here, the sensor has been used effectively in the frequency
range from 0Hz to 200Hz. At frequencies above f=200Hz,
however, sensor noise becomes an issue. To suppress the
noise and ensure good temperature stability of the sensing
unit, two photo-interrupters in a differential connection
have been used, together with the accompanying
electronic circuitry. The linearity of the sensor achieved
by this design is very good, particularly for large cone
displacements and low frequencies (basically all the way
down to 0Hz), suggesting that this type of sensor may be
efficiently employed in servo control of low-frequency
drivers. In practice, such an application would also require
the use of differentiators or integrators, depending on
which signal is used as a reference (the one from the
sensor or the signal from the output amplifier). The effect
of the physical implementation of the barrier on the cone
of the loudspeaker is not evident as the TS parameters of
the loudspeaker have remained unchanged.
With additional photo-interrupters for decoding the
resting position of the cone, this sensor has the potential
of a successful application in driver and power amplifier
overload protection circuits as well (e.g. circuits that
guard against abnormal or excessive cone excursion, DC
offset and so on).
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