Download 2-D Optical Position Sensor

FEATURE
ARTICLE
Roger Johnson &
Chris Lentz
2-D Optical Position
Sensor
p
Surprisingly, it isn’t
too difficult or expensive to build a twodimensional optical
position measurement system. In this
article, Roger and
Chris show you how
to do it. All you need
is a PIC, LCD, and
some analog gadgets
to get moving on the
perfect PSD project.
Circuit Cellar, the Magazine for Computer Applications. Reprinted
by permission. For subscription information, call (860) 875-2199, or
www.circuitcellar.com. Entire contents copyright ©2001 Circuit
Cellar Inc. All rights reserved.
www.circuitcellar.com
osition sensitive
detectors (PSD)
have been around in
various forms for over
30 years, working quietly in the background of CD/DVD focus and tracking
controls, heat-seeking missile guidance
systems, and metrology instruments
such as range sensors and 3-D laser
trackers. Basically, the PSD gives the
analog coordinates of a spot of light on
its surface. We’ve designed many optical measurement systems that involve
lasers, complex lens designs, sophisticated electronics, computers, and
motion control. The PSD is a small
but important part of these systems.
We were wondering if there was a
project that would emphasize PSD technology without the added complexity of
other systems. Hardware and on-line
stores now sell high-quality laser tools
for $40 and up. The basic tool is a laser
pointer that’s integrated with a bubble
level (i.e., a laser level). This laser beam
is projected parallel to the base of the
level and establishes a datum; it transfers the line of sight that’s established
by the beam with the aid of a position
detector. In addition, a laser level can
create lines/planes that are plumb and
perpendicular to the level planes, which
is ideal for construction purposes.
CIRCUIT CELLAR®
The majority of these tools don’t
offer an accurate way to determine the
center of the laser beam, so most people just use their eyes. This method is
adequate for a good number of construction purposes; however, there
are many situations in which more
accuracy is required. Some of the
detectors included with these tools
can measure the position of the laser
beam to about one thirty-second of an
inch, but there aren’t any high-accuracy sensors to determine the exact
location of the laser beam. It dawned
on us that such a system would be the
perfect PSD project.
In this article, we’ll describe the
operation of a unique optical sensor
and its incorporation into a practical
two-dimensional position measurement system. The sensor is a lateraleffect photodiode, which is a special
member of the family of optical PSDs.
Our system consists of a microprocessor, LCD, some analog electronics, a typical medium-area PSD,
and a four-channel, 12-bit A/D converter. The result is an instrument
that has a position resolution of onefortieth the diameter of a strand of
human hair. We’ll describe how PSDs
operate, explain how they’re used, and
present you with a specific application. Note that we teamed a PSD
with a PIC16F873 microprocessor to
produce an instrument that gives the
2-D coordinates of a laser beam on its
active surface with a resolution of
0.0001″, an accuracy of 0.001″, and a
measurement range of ±0.2″. With
this sensor and a laser level, you can
measure the straightness, flatness,
angle, centration, and parallelism of
virtually any surface.
To persuade those of you who want
such an instrument, our set of PCBs
and the PSD are offered at cost. The
rest of the project requires inexpensive
electronics. You may download the
code and board files for the project
from the Circuit Cellar ftp site.
LATERAL-EFFECT PHOTODIODE
The lateral-effect photodiode is a
2-D PSD that generates photocurrents proportional to the position and
intensity of the centroid of light on
the active area. Two-dimensional
Issue 152 March 2003
1
PSDs have sensing areas ranging
from less than 0.05″ in diameter to
more than 1 square inch.
There are three basic types of PSDs:
duolateral, tetralateral, and pincushion tetralateral. For additional information about these PSDs, visit the
Hamamatsu web site. In addition,
there are several other useful sources
on the ’Net. Use PSD as a keyword
and try your own search!
electrode pair is inversely proportional to the distance between the
incident spot of light and electrodes.
But, this PSD’s complex structure
also makes it the most expensive.
TETRALATERAL TYPE
The PSD shown in Figure 2a has a
single resistive layer and four electrodes on the front surface of a photodiode and a fifth lead that provides a
bias. The signal photocurrent is divided into four parts that are used to generate the position signal; because of
this, it has only half the theoretical
resolution of a duolateral type.
The equivalent circuit in Figure 2b
shows how the four signals interact
with each another on one surface. This
PSD also has distortion that’s greater
on the perimeter. Nevertheless, it’s
less expensive, features a simple bias
scheme, smaller dark current, and
faster response time than a duolateral type. Its position formulas are different than the duolateral type’s formulas, too.
DUOLATERAL TYPE
The duolateral PSD shown in
Figure 1a consists of N-type silicon substrate with two resistive layers separated by a PN junction. The front side has
an ion-implanted P-type resistive layer
with ohmic contacts on two sides. The
backside has an ion-implanted N-type
resistive layer with two contacts at
opposite ends placed orthogonally to
the contacts on the front side. (On a
single-axis PSD, the electrodes are
placed at opposite ends of one P-type
resistive layer.) The equivalent circuit
shows how each position signal is
divided into two parts by the two
resistive layers (see Figure 1b).
Because the position signal is
divided only into two parts, the duolateral PSD has the highest positiondetecting ability of all the sensor
types. The resistivity of the ionimplanted layers is extremely uniform, so the photocurrent for each
PINCUSHION TYPE
The PSD shown in Figure 3a is an
improved version of the basic tetralateral type. It gets its name from the
surface contacts that have a large
radius rather than straight sides.
Viewed from above, the four contacts
look like a pincushion. This subtle
X
X’
b)
a)
RP
X
Y
P
D
CJ
RSH
X'
Y'
RP
Y'
Y
Figure 1a—The duolateral 2-D PSD has a resistive layer on both sides of a substrate that acts as a PN junction.
This type of PSD is the most accurate, has the highest resolution, and is the most expensive—the two resistive layers being the main reason. This type of PSD has only four leads; biasing it is more complicated than the other
types of PSDs. b—The interelectrode shunt resistance, RSH , affects frequency response; usually it’s in the neighborhood of 5 to 20 kΩ. In addition, the larger the PSD’s area, the larger the junction capacitance (CJ ) and the
slower the frequency response.
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Issue 152
March 2003
CIRCUIT CELLAR®
change greatly improves the extent of
the high-linearity region over the
tetralateral type while still retaining
simple signal processing and biasing.
The position equations are the same
as the ones for the plain tetralateral
type. Finally, the equivalent circuit in
Figure 3b shows how the surface electrodes are placed at the four corners
instead of the four sides.
The PSD will operate at a low frequency in this application. The shunt
and positioning resistance and the
junction capacitance give a definite
limit on how fast they can respond to
modulated light. Generally, larger
devices are slower than smaller ones;
applied bias voltage increases speed,
but does so at the expense of dark current. Typical upper-frequency limits
are well in excess of 20 MHz. And, if
signal-integration schemes are used,
PSDs can respond to 100-ps pulses.
The position resolution of a PSD is
the minimum detectable displacement of a spot of light on the detector’s surface; it is dependent on
detector area, light intensity, bandwidth, and temperature. This application will use a low bandwidth, relatively high intensity, and low noise
to give good resolution.
Position nonlinearity is defined as the
geometric position error divided by the
detector length; it is measured within
80% of the detector length. In addition,
position nonlinearity is typically better
than 0.05% for a single-axis PSD,
approximately 0.3% for a duolateral
type, 1% for a pincushion PSD, and 2 to
3% for a tetralateral type of PSD.
It should be emphasized that the PSD
is not an imaging sensor. Unlike a CCD
sensor, the PSD cannot detect any
structure of the pattern of light falling
on it. Instead, it senses only where the
centroid, or center of “mass,” of the
light pattern is falling on it. By design,
this is usually a laser beam or small
point of light imaged by a lens; it’s not
a limitation. Alternatively, if the PSD
is flooded in light except for a small
dark spot or stripe, it can detect the
position of that feature. PSDs are
easy to interface—requiring only a
few op-amps to produce signals—so
it’s no wonder this sensor is used in
a variety of applications.
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a)
b)
X
Y
X
Y
Rp
X'
Y'
X'
Y'
P
viewed at an angle different
from that of the laser axis,
the imaged spot of light
walks back and forth across a
detector as the distance to
the surface changes.
The position equations for a tetralateral/pincushion PSD are depicted in
Figures 4e and f. Note that x and y are
the photocurrents flowing from the
PSD’s terminals. The denominator
term is proportional to the total incident power. Handily, because the position value requires the sum term, the
PSD can easily sense optical power.
The instantaneous power is displayed
with x and y position data.
RSH
D C
J
POSITION EQUATIONS
Bias
Bias
When light falls on the
PSD, the photocurrent collected by an electrode is
inversely proportional to the
distance between the incident
position and the electrode.
Several of the equations in
Figure 4 relate the photocurrents I1 and I2 collected by the electrodes with position along the detector,
where L is the active length of the PSD
and I0 is the total photocurrent.
In Figures 4a and b, you see the equations of a 1-D PSD for the two photocurrents with respect to the center of
the detector. For these two equations, L
is the active length of the PSD, x is the
position of the centroid of the light
falling on its surface, and I0 is proportional to the incident power. Figure 5
illustrates the coordinates used in
describing the terms; the dot indicates
the centroid of a light spot.
The difference of the two photocurrents is proportional to the position
and intensity of the centroid of light
striking the detector. As you can see
in Figure 4c, dividing the difference of
the photocurrents by their sum cancels the I0 term and yields a normalized position value that’s independent
of incident optical power. Note that n
is a dimensionless position value that
ranges from –1 to 1 (i.e., –1 ≤ n ≤ 1).
You can solve for x with the equation in Figure 4d.
Figure 2a and b—The 2-D tetralateral type of PSD has a single
resistive layer on only one surface. The bias electrode is a dedicated lead on the rear of the substrate; it makes biasing simple. A higher reverse bias causes a reduction in the junction capacitance and
higher frequency response, but also causes higher dark current.
This type of PSD has the worst accuracy—typically a 3 to 6% position error near the perimeter of the device.
TYPICAL APPLICATIONS
As continuous position sensors,
PSDs are unparalleled. Compared with
discrete element detectors, such as the
charge-coupled device (CCD) sensor,
the PSD features nanometer positioning resolution, sub-microsecond
response times, simple interface circuits, and high reliability.
Optical alignment, involving a laser
beam that’s used as a reference line, is
the most common application for a
PSD. The PSD is mounted on the
system being tested (e.g., the wobbling of a shaft, the straightness of
machine tool axis, or an aircraft fuselage that’s being assembled).
PSDs are also used in more lethal
applications. In heatseeking missile
systems, a PSD that’s sensitive to IR
radiation is located at the focal point of
a lens that’s mounted behind a cleardomed window on the front of the missile. After the missile is launched, the
outputs of the PSD drive the missile’s
fin actuators to keep the IR energy centered on the PSD all the way to the target (i.e., the jet exhaust of an aircraft).
The scanning laser level is a more
down-to-earth application. In this
instance, remote optical targets that
contain a 1-D PSD pick up a spinning, level laser beam. These systems
are used for pouring concrete and
installing ceiling tiles in addition to
laying pavement.
Note that PSDs are also used in
non-contact distance sensors, which
incorporate optical triangulation to
measure the range to a target surface.
The sensor actively projects a laser
spot onto a surface. When the spot is
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b)
a)
CIRCUITRY
If you decide to build this system,
the layout is important for the detector pre-amps and ADC. A ground
plane-type board is recommended.
We decided to design a PCB because
it makes development much easier (see
Figure 6). To limit noise pickup, the distance between the PSD and pre-amps
should be no more than 1″ (see Figure 7).
The four-channel 12-bit ADC should be
well bypassed and located near the gainstage amps. Our circuit was laid out on
two PCBs. We used a small pre-amp
module for the pincushion 10 mm ×
10 mm Hamamatsu S5991-01 lateraleffect photodiode and the larger one for
the rest of the circuitry.
Power comes from the two AA alkaline batteries that we mounted underneath the main board. The batteries
drive an efficient charge-pump regulator
and voltage inverter for operating the
rail-to-rail op-amps. We recommend
Linear Technology LT1490s.
All of the op-amps use 0.1% precision resistors (these tolerances must be
used for measurement accuracy); the
rest of the component tolerances are
standard. For biasing this PSD, R9 is
omitted, and R8 is 100 Ω. The design
of this instrument assumes a laser
Y
X
RP
Sensitive surface
X'
Y'
P
D
CJ
Bias
Figure 3a and b—The 2-D pincushion type of PSD is really a tetralateral type that uses shaped electrodes to
increase its linearity near the perimeter. It has the same simple biasing requirements as the tetralateral PSD, but
only suffers from positioning errors of approximately 1%.
CIRCUIT CELLAR®
Issue 152 March 2003
3
POWER DATA
a)
=
b)
=
–
g)
The power of the incident beam is
proportional to the aforementioned
sum signal, S = X1 + X2 + Y1 + Y2. The
optical power (in milliwatts) is obtained
via the equations in Figures 4h and i,
where S is in A/D counts, G is the
gain of the second stage, and R is
the responsivity of the PSD in amps
per watt. Rf is the value of pre-amp
feedback resistors.
h)
c)
i)
d)
e)
j)
f)
k)
n–1
n–1
FIRMWARE
n–1
n–1
Figure 4—Study these equations carefully. In addition to the position equations a through f, we’ve included the
equations for the following: g—the feedback resistor; h and i—the optical power; and j and k—the algorithm
for the low-pass filter.
pointer of less than 5 mW of power
(most operate in the 2- to 3-mW
range) and a PSD wavelength responsivity of 0.40 A/W.
The first-stage pre-amp gain must
be set so that a 5-mW pointer can’t
saturate it. Also, this type of PSD
divides the total photocurrent seen
by each lead by four. Finally, the
rail-to-rail pre-amps will saturate
when the output reaches 5 V. The
feedback resistor value is determined
by the equation depicted in Figure 4g.
Therefore, the pre-amp gain resistors
should be no larger than 10 kΩ. You
must allow for ambient light, which
will force Rf to be smaller. Four
0.1%-tolerance, 2.4-kΩ resistors were
finally selected.
The second gain stages U7 and U8
invert the negative output from the
pre-amps and offer a means to
change the overall gain if a lowerpower pointer is to be used. Note
that the PSD used here will become
nonlinear if the power density on its
surface exceeds 3 W/cm2. The typical
2- to 3-mW laser level has a beam
diameter of roughly 3 mm and a
power density 70 times less than this
limit. Saturation will occur when
milliwatt power levels are focused to
small spots on the PSD surface.
The outputs of the second stages
go through 10-Hz, anti-aliasing, lowpass filters and are input to a
Microchip MCP3204 four-channel,
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Issue 152
March 2003
12-bit analog-to-digital converter.
Tactile push buttons serve to initiate
the nulling functions and to change
display modes. A MAX232 sends
position data to an external device.
Finally, a 2 × 16 LCD that’s addressed
in nibble format and based on the
Hitachi HD44780 controller is used
as the display.
SIGNAL PROCESSING
The four photocurrents are turned
into voltages by the pre-amps and
then converted into 12-bit values.
Remembering that the normalized position value (n) always ranges from –1 to
1, the problem is how to convert it to
dimensional units. So, the first question
to ask is: what resolution is desired?
Our goal for this instrument was
0.0001″ resolution (2.5 µm). Because
the measurement range from the center of the PSD is L/2, 5 mm or
0.1968″, multiply the normalized position value by 1968—the largest position that can be sensed in units of
tens of thousandths of an inch.
Now, we’ll recap. To display data
with 0.0001″ resolution, the PSD signals are processed by: obtaining X1, X2,
Y1, and Y2 from the 12-bit ADC and
bounds check for high and low; calculating the numerators in Figures 4e
and f; multiplying the numerators by
1968; dividing both results by the sum
signal (i.e., S = X1 + X2 + Y1 + Y2); and
discarding the remainder.
CIRCUIT CELLAR®
The firmware for this project was
written in C using a CCS compiler.
The main task is interrupt driven
from Timer0 and continually acquires
data from the four-channel ADC,
solves the position equations, and
then displays the data. The Mode and
Null push buttons are polled to determine if the operator has pressed them.
There are additional points that
must be emphasized. The low-pass
filter on the outputs of all four gain
stages won’t completely remove the
strong 120-Hz optical noise signal
created by room lights. We also
wanted the PSD to be able to produce
good results without the use of an
optical filter. The firmware implements a first-order infinite impulse
response (IIR) low-pass filter. The
algorithm for this type of low-pass
filter is given in Figure 4j. Note that
Cn is the current filter output, and
Cn–1 is the previous filter output. Rn
is the current input to the filter, and
Rn–1 is the previous input to the filter.
Finally, f is the 3-dB breakpoint frequency of the filter in hertz, and T is
the sample period in seconds.
For this filter, the sample period
was 10 ms, and the 3-dB breakpoint
was 5 Hz. Thus, the algorithm
becomes a simple one with two coefficients (see Figure 4k). The actual
code fragment is:
filter = ((signed int32)
olddata * coefs.a) +
(((signedint32) newdata +
(signedint32) lastsample) *
coefs.b); olddata = (signed
long int) (filter >> 15);
The two coefficients were multiplied
by 32,768 before being multiplied by
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L
I1
I2
X
I2 – I1
2X
=
L
I2 + I1
Sensitive surface
Figure 5—Take a look at the coordinates we’ve used
to describe the terms. Note the dot that indicates the
centroid of a light spot.
the delayed terms. Then, the result
was shifted to the right by 15. This
software filter effectively reduces the
induced optical noise to low levels.
Even under extremely intense lighting,
the displayed position is rock steady.
NULL AND MODE
The process is continuously grabbing the four ADC values. You can
pick one of two ways to display this
data. Position Display mode shows X
and Y displacement in inches, as
well as laser power. Voltage Display
mode shows the raw voltages in millivolts of the four ADC values.
Pressing the Mode switch toggles
between these two displays.
Because the PSD is sensitive to the
centroid of the light pattern on it, any
light other than the laser will cause
errors. A voltage-nulling process solves
the problem. This stores the background values of the four signals without the laser on the PSD. Subsequent
position calculations first subtract
these stored values. The voltage-nulling
process is initiated at power-up, or at
any other time, by pressing the Null
button in Voltage Display mode.
There is also a position-nulling (i.e.,
zeroing) process that forces the current
laser position to be 0.0000 in X and Y.
This is handy for observing small
changes from a starting point. To initiate the process, press the Null button
in Position Display mode.
The power in the laser beam is displayed on the right-hand side of the
upper line of the LCD. If the bounds
checking done during the ADC acquisition process indicates values that are
too high (i.e., 0FFF from any A/D conversion result) or too low (i.e., less
than 0.05 mW), then the right side of
the lower line will display “DETSAT”
or “LOWSUM.” This means that the
detector is saturated or the sum signal is too low.
The RS-232 serial port transmits
data at the same rate as it is written
to the LCD screen. The format in
Position mode is: <X data>, <Y data>
Figure 6—The 2-D optical position sensor uses two op-amps in each leg of the PSD. The first stage is located near the PSD, and the voltage generated is negative with
respect to ground. The second stage is located on the main board. It inverts the signal from the pre-amp stage back to a positive voltage for the 12-bit ADC.
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CIRCUIT CELLAR®
Issue 152 March 2003
5
carriage return line feed. The
format in Voltage mode is: <X1
data>, <X2 data>, <Y1 data>,
<Y2 data> carriage return line
feed. With no parity and 1 stop
bit, the data rate is 9600 bps.
nate indicates a deviation
from flatness.
For precise applications,
the detector is placed in a
mount (see Photo 1). We performed some accuracy tests
on the system and found it
to be within 1% over the
LINEARITY
entire measurement range.
This pincushion PSD will
The PSD was securely fixed
show some nonlinearity near
to a precision translation
the perimeter. The conversion
stage and moved in increequations assume the PSD is
ments. At 0.1000″ the dislinear over its entire range.
play indicated 0.0993″,
The on-board EEPROM can
Photo 1—A laser level and the 2-D optical position sensor measure the flatness
which
wasn’t bad at all! The
store correction coefficients
of a surface. Note the four-digit resolution. The main board is only a little larger
stages were positioned with
and use them to extend the
than the LCD. The PSD connected to the system is located in the mount with a
micrometers that have
linear range all the way to the filter. The Hamamatsu PSD is shown in the foreground on the pre-amp PCB.
0.0005″ resolution; therefore,
edges. Doing so, however,
this result is consistent with our
requires the scanning of the detector
MORE APPLICATIONS
ability to accurately position the
in precise steps over its entire surface
A typical application, precisely
stages by hand.
area and recording all of the errors.
measuring the flatness of a surface,
Probably the most common appliThis entails precision translation
is depicted in Photo 1. The source is
cation is to simply mount the PSD
stages and is beyond the scope of this
a low-cost torpedo laser level. First,
to monitor the relative movement
project. If you’re interested in doing
the laser level is placed on the surbetween the laser beam and PSD.
this, mapping in 0.020″ increments
face and turned on. The PSD is
This setup can measure the moveand storing a gain and offset factor
brought next to the level and zeroed.
ment of a mirror, the bending and
applied to measurements in each
When the PSD is scanned along the
twisting of a structure caused by
increment segment works well.
surface, any change in the Y ordi-
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Issue 152
March 2003
CIRCUIT CELLAR®
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loads or thermal upsets, and so on.
If the PSD is moved along a single
surface, a surface and edge, or is
mounted on a moving mechanism,
all of the position data should lie in a
straight line. If it is not, then the
extent of deviation from a straight
line should be measured by analyzing
the data. This technique is performed
to measure the straightness of travel
for machine tools, the straightness of
shafts, and so on.
The PSD usually has to sit in a
mount that is suitable for the job at
hand. The precision mount that you
can see in Photo 1 is used for measuring the straightness and flatness of
surfaces and edges.
LOOKING FORWARD
The purpose of this article was to
present you with a 2-D optical sensor
that you can use with standard laser
tools and pointers. In addition to the
advantage of being inexpensive, the
sensor has a resolution of 0.0001″
and an accuracy of better than 1%.
At some point in the near future, we
would like to linearize the PSD even
further. To achieve this, we plan on
mapping the entire surface of the sensor and storing correction coefficients
in the EEPROM. Furthermore, we will
probably vary the sample rate, perform
different types of signal averaging,
and make the electrical center of the
mounted PSD coincident with its
mechanical center by using a two-step
calibration technique.
If you were to use other 2-D sensors, all that would change is the preamp resistors (for use with different
optical power) and the position equations. In addition, note that silicon
PSDs can measure position at near-IR
wavelengths, and InGaAs PSDs are
available in telecom wavelengths
(i.e., 1300 through 1500 nm).
As you know, there are other options
if you’re interested in this type of opti-
cal measurement system but don’t want
to invest the time required to make a
board. For instance, you can purchase
the unpopulated, two-board PCB along
with the Hamamatsu PSD for $175. I
Roger Johnson is a physicist and senior electro-optical engineer working
in the Seattle area. He earned degrees
from The University of Washington
and The University of Illinois at
Champaign-Urbana, and has been
designing precision, non-contact, optical measurement systems for 17 years.
His interests include miniature optical systems, precision motion control, and instrument design. You may
reach him at [email protected].
Chris Lentz is a Washington-based
senior electronics designer. For the
past 17 years, Chris has been developing hardware and software for electro-optic and electro-mechanical systems. His interests include miniature
sensors, tinkering, and supporting science teachers by designing and
demonstrating electronic instruments
for students. You may reach Chris at
[email protected].
PROJECT FILES
To download the code, go to
ftp.circuitcellar.com/pub/Circuit_
Cellar/2003/152/.
SOURCES
PCB Set with S5991-01 PSD
Aculux
(425) 378-0567
www.aculux.com
PSDs
Hamamatsu Corp.
(908) 231-0960
www.usa.hamamatsu.com
LT1490 Op-amps
Linear Technology Corp.
(408) 432-1900
www.linear.com
Figure 7—The first and second stages must use micropower rail-to-rail op-amps (LT1490s are used here). A programming port is located at J3 for downloading and flashing the PIC16C873 processor. The gain resistors in the
second stages R12 through R19 and those in the pre-amp stages should be 0.1%-tolerance types to achieve the
better than 1% accuracy that’s possible with the PSD.
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CIRCUIT CELLAR®
PIC16F873 Microcontroller
Microchip Technology, Inc.
(480) 786-7200
www.microchip.com
Issue 152 March 2003
7