This page was generated using an imperfect translator. Text may be poorly positioned and mathematics will be barely readable. Illustrations will not show at all. If possible, view the PostScript or PDF versions of these notes.
09-1 Displacement and Proximity *
* 09-1
Displacement transducers measure the location of an object.
Proximity transducers determine when an object is near.
Criteria Used in Selection of Transducer
- How much force can transducer exert on object?
Requirement can be as low as zero when the object is small or cannot be
touched.
- What is the range of positions to be measured?
- How fast will the object be moving?
- What accuracy is required?
09-1 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-1
09-2 Types of Displacement Transducers *
* 09-2
Potentiometer.
Object moves tap on a variable resistor.
Linear Variable Differential Transformer (LVDT).
Object moves core of three-winding inductor.
Capacitive Transducers.
Object is either one plate of a capacitor, or moves the capacitor's
dielectric.
Coded.
Object moves surface covered with code marks. A transducer reads
the code marks.
There are many other ways to measure position : : :
: : :these will not be covered individually : : :
: : :but may be explained as part of problems.
09-2 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-2
09-3 Potentiometers *
* 09-3
Symbol:
Construction and Operation:
Resistive material formed into either a strip or coil.
An external object, through a mechanical linkage, moves the tap.
Tap slides along resistive material.
Tap and both ends of resistive material connected to leads.
Miscellaneous Facts:
These are built for instrumentation purposes.
(Unlike the volume control on a radio.)
Multiple-turn potentiometers can be made precise.
(Percent calibration error less than 1%.)
09-3 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-3
09-4 *
* 09-4
Desirable Characteristics
- Easy to read output.
- Linear response. Other responses also possible.
- Inexpensive.
Undesirable Characteristics
- Adds friction to motion of object.
- Can wear out.
- Limited precision.
- Can only measure relatively large displacements.
09-4 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-4
09-5 Capacitive Displacement Transducers *
* 09-5
Symbol: no special symbol used.
Two types discussed: moving plate and moving dielectric.
Construction and Principle of Moving Plate Type:
One plate of capacitor mounted to a fixed surface.
The other plate mounted to the object.
Capacitance changes with position of object.
Possible ways of mounting and moving plates:
- Plates move normal to plane of plates.
- Plates move parallel to plane of plates.
- Plates, shaped like pie slices, rotate.
Construction and Principle of Moving Dielectric Type:
Both plates of capacitor mounted to a fixed surface.
The dielectric mounted to an object.
Capacitance changes with position of object.
Possible ways of moving dielectric:
- Dielectric slides.
- Dielectric is a fluid that flows in and out of the capacitor.
09-5 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-5
09-6 *
* 09-6
Model Function
This varies for each type.
Moving-Plate Type
If the area of the plates is large compared to the distance between
them
and one plate moves normal to its plane:
Ht1 (x) = C m___x, x > 0 m.
Moving-Dielectric Type
Ht1 (x) = C0 (1 + Kx),
where K is a constant determined by the transducer construction.
There are many variations on capacitive sensors, so there are many model
functions.
Derivation and use of model functions for capacitive sensors is beyond the
scope of the course.
09-6 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-6
09-7 *
* 09-7
Typical Conditioning Circuits
Oscillator
Capacitive transducer may be part of an LC pair in an oscillator.
Capacitance measured by counting frequency.
Bridge
Capacitive transducers can be placed in a bridge.
(In the same way as resistive transducers.)
AC voltage placed across bridge : : :
: : :instead of DC, as with resistive transducers.
Bridge voltage is amplified, rectified, then measured.
Analysis of these circuits is beyond the scope of this course.
09-7 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-7
09-8 *
* 09-8
Desirable Characteristics
- No physical contact with object. (Moving dielectric type.)
- No wear with motion.
- Can measure small displacements.
(Including the position of a diaphragm in some microphones.)
Undesirable Characteristics
- Can only measure small displacements.
- Conditioning circuits might be more troublesome.
09-8 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-8
09-9 Linear Variable Differential Transformer (LVDT) *
* 09-9
Symbol:
Construction:
A three-winding transformer with a movable core.
Primary winding runs length of transformer.
Each secondary covers one half of transformer.
Secondaries are connected to oppose each other.
Object is connected to core.
09-9 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsli*
*09. 09-9
09-10 *
* 09-10
Principle of Operation
When core is centered : : :
: : :voltage at two secondaries are equal.
Because they are connected in opposition : : :
: : :voltages cancel : : :
: : :and so output is zero.
When core is off center : : :
: : :voltage at one secondary : : :
: : :is higher than at other.
Output voltage is linearly related to core position.
09-10 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-10
09-11 *
* 09-11
Model Function
Ht1 (x; t) = Kxvp (t), : : :
: : :where K is a constant, vp (t) is the voltage at the primary winding,
and t is time.
Note, if x is negative then phase of output is reversed.
In Typical LVDTs:
The primary voltage can range from 1 to 10 V.
Frequency from 50 Hz to 25 kHz can be used for primary winding.
Desirable Characteristics
- Low wear.
- High speed, can measure vibrations.
- Can measure small displacements, < 0:1 nm .
(Precision determined by conditioning circuit.)
- Low repeatability error.
Undesirable Characteristics
- Complex conditioning circuit needed.
- Expensive.
09-11 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-11
09-12 Coded Displacement Transducers (CDT) *
* 09-12
These can be either:
- Relative.
Transducer indicates change in position, not actual position.
- Absolute.
Transducer indicates actual position.
They can measure:
- Linear displacement.
Position along a line.
- Angular displacement.
Angular position.
A generic CDT will be described, then the various types.
09-12 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-12
09-13 Coded Displacement Transducers_General Description *
* 09-13
Physical Construction:
A strip or disk of some material, such as plastic, is mounted on object or
on something linked to the object.
Strip or disk has marks in one or more tracks or rings.
Transducers, which can read the marks, are mounted in a fixed position.
A variety of transducers can be used to measure the marks.
Output of transducers is converted into a digital form.
Symbols di will denote the digital form of the transducer output.
The strip or disk is usually in a sealed package, to keep dirt out.
CDTs differ in the number of tracks and how the marks are placed.
09-13 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-13
09-14 Relative One-Way Angular Coded Displacement Transducers *
* 09-14
Use: measurement of angle in systems limited to one-way rotation.
Marking
Two rings are used, position and index.
There are many marks on the position ring, regularly spaced.
Call signal from position ring dp .
There is a single mark on the index ring.
Call signal from the index ring di.
09-14 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-14
09-15 *
* 09-15
Conditioning
A counter is used.
Output dp increments the counter, and di resets the counter.
Further processing may be done to get the output in the desired form, for
example radians.
Model Function
This includes both___ the CDT and the counter.
Ht1 (x) = ____x____2ssNrad, where N is the number of position-ring marks.
Note that the output is incorrect : : :
: : :from power-on : : :
: : :until the sensing of the index mark.
09-15 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-15
09-16 Example of Relative One-Way Angular CDT *
* 09-16
Design a system to convert process variable x 2 [0 rad ; 2ss rad ], the
rotation angle of wheel, to a floating point quantity, H (x) = x= rad ,
to be written in variable theta. The wheel will rotate in only one
direction. The precision must be at least 0:001 rad .
Solution
Use a relative one-way angular CDT.
Link the CDT disk to the wheel : : :
: : :so that one turn of the wheel results in one turn of the CDT.
(It would also have been possible to put the marks directly on the wheel,
but this might have been less convenient.)
Need at least 6284 marks.
Assume an N = 10; 000-mark CDT is available.
Then a dlog 2 N e = dlog 2 10000e = 14-bit counter is needed.
Using these, Ht1 (x) = ____x____2ss1rad0000.
Need Hf(Ht1 (x)) = H(x).
Let r = Ht1 (x) = ____x____2ssNrad; solving, x = 2ss_rad__Nr.
Then Hf(r) = H 2ss_rad__Nr = 2ss_Nr.
_______________________________________
__theta_=_r_*_0.000628319;______________
09-16 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-16
09-17 Relative Two-Way Coded Displacement Transducers *
* 09-17
Use: measurement of angle or linear displacement in systems in
which displacement will frequently be equal to some value (e.g., 0).
Marking
Description is for linear CDT; angular CDT is similar.
Three tracks are used, position, direction, and index.
Call the signal from the position track dp , direction track dd , and index
track di.
There are many marks on the position and direction tracks, regularly
spaced.
Position and direction tracks partially overlap.
When dp makes a 0 to 1 transition, dd gives the direction of travel.
There is a single mark on the index track.
09-17 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-17
09-18 *
* 09-18
Conditioning
An up/down counter is used.
Output dp clocks the counter and dd determines the direction of count.
As in the one-way CDT, di resets the counter.
Further processing may be done to get the output in the desired form, for
example radians.
09-18 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-18
09-19 Absolute Binary-Coded Displacement Transducers *
* 09-19
Use: measurement of linear or angular position.
Marking
For an n-bit precision device, n + 1 tracks or rings are used.
One track is called the clock track, the others are called position tracks.
There are 2n clock marks, spaced regularly.
Call signal from clock track dOE and the signal from the i'th position track
di.
Let - be the largest distance (in the direction of displacement) between
transducers. (In an ideal system, - = 0).
Marks are positioned so that at position x - ,
if there is a transition in dOE then there is no transition in any di.
As one might expect, the di give the position in binary.
09-19 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-19
09-20 *
* 09-20
Conditioning
An n-bit register is used.
The di connect to the register's data inputs.
The register is clocked with dOE.
09-20 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-20
09-21 *
* 09-21
Purpose of Clock Marks
Consider a system in which there were no clock marks.
Output would be conditioned transducer signals, di, rather than register
output.
Only n tracks would be needed for 2n distinct positions.
This won't work. Consider a change from position 7 to 8:
Before: d = 01112 . After: d = 10002 .
Either all mark-reading transducers change at the same instant,
or d 2 f0000; 0001; 0010; 0011; 0100; 0101; 0110; 1001; 1010; 1011; 1100;
1101; 1110; 1111g in the moments between.
09-21 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-21
09-22 *
* 09-22
Why Binary?
Other (not 100% serious) possibilities:
- Binary-coded decimal.
- Seven-segment display. Output can be fed to seven-segment displays.
- ASCII numerals. (E.g., 123). Read the number into a computer with-
out ever having to do a binary conversion.
- ASCII words. (E.g., One hundred twenty three.). It can be done, but
who would buy it?
The cost of a CBT is proportional to the number of tracks.
Binary is good because the minimum number of tracks are used, plus_one.___
09-22 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-22
09-23 Absolute Gray-Coded Displacement Transducers *
* 09-23
Use: measurement of linear or angular position.
Marking
For an n-bit precision device, n tracks or rings are used.
All tracks are called position tracks.
Call signal from the i'th position track di.
As one might expect, the di give the position in gray code.
Gray Code Properties
Gray-coded number: sequence of zeros and ones (like binary).
Let a be a nonnegative integer.
Gray-code for a differs from gray-code for a + 1 in exactly one digit.
Therefore, with gray code, only 1 transducer's output will change at a
time_no races.
09-23 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-23
09-24 *
* 09-24
Gray Code Definition
Gray code is defined for non-negative integers.
Let B 2 [0; 2n ). (That is, B is any number from 0 to 2n 1.)
Let bi be digit i in B's binary representation, for i 2 [0; n).
(The least-significant digit is b0 .)
Symbol gi is digit i in B's gray-code representation if
gn1 = bn1 and gi = bi+1 bi, for i 2 [0; n 1).
Symbol bi is digit i in B's binary representation if
bn1 = gn1 and bi = bi+1 gi, for i 2 [0; n 1).
09-24 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-24
09-25 *
* 09-25
Gray Code Examples
Four Bits
7 (decimal) = 0111 (binary) = 0100 (gray)
8 (decimal) = 1000 (binary) = 1100 (gray)
Five Bits
11 (decimal) = 01011 (binary) = 01110 (gray)
12 (decimal) = 01100 (binary) = 01010 (gray)
13 (decimal) = 01101 (binary) = 01011 (gray)
14 (decimal) = 01110 (binary) = 01001 (gray)
Twenty Bits
123,456 (decimal)
=0001 1110 0010 0100 0000 (binary)
=0001 0001 0011 0110 0000 (gray).
09-25 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-25
09-26 Gray- and Binary-Coded Displacement Transducers *
* 09-26
Four-Bit Binary and Gray:
Eight-Bit Binary:
Nine-Bit Gray:
09-26 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-26
09-27 Coded Displacement Transducers Characteristics *
* 09-27
Desirable Characteristics
- Linear (or any other response needed).
- Accurate and precise.
Strip or disk can have 65536 or more marks per track or ring.
- Low wear.
- Simple conditioning circuit.
Undesirable Characteristics
- Contact with object required, or object must have marks.
Form of Marks
Ink on a ceramic or glass substrate.
Holes in some material. (Read optically or mechanically.)
Current-conducting ink on an insulating substrate.
09-27 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-27
09-28 Proximity Transducers *
* 09-28
Detect when an object is near.
Types of Transducers
- Reed switch.
Switch closed by magnet on object.
- Hall effect.
Magnetic field from object induces a potential : : :
: : :on a block of semiconductor.
- Magnetic reluctance.
An object passes through a magnetic field: : :
: : :inducing a voltage in a coil.
Plus many more, not covered.
No conditioning circuits will be given for the proximity transducers.
09-28 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-28
09-29 Reed Switch *
* 09-29
Construction and Operation:
Small glass tube with two switch contacts.
Magnet pulls switch contacts closed.
As with all switches, it does not go from open to closed neatly. (When
closing, it might go from open to closed many times before settling into a
closed state.)
Conditioning Circuit
Output might have to be "debounced" (low-pass filtered).
Desirable Characteristic
- Cheap.
Undesirable Characteristics
- Low speed.
- Limited life.
09-29 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-29
09-30 Hall-Effect Proximity Sensor *
* 09-30
Construction
and Operation
Consists of a block of semiconductor material. There is no PN junction.
The object detected must produce a magnetic field.
If it's not naturally magnetic and you can't glue a magnet to it, you
can't use a hall-effect transducer.
Consider the three axes normal to the block's faces.
A constant current is passed along one axis.
The transducer is positioned so that the magnetic field from the object is
parallel to a second axis.
And, voila, a potential is induced on the faces normal to the third axis.
Contacts on these faces connect to leads.
The output of the transducer is the voltage.
09-30 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-30
09-31 Magnetic Reluctance Transducer *
* 09-31
Construction and Operation
Consists of a coil of wire wrapped around a c-shaped magnetic core.
Magnetic field lines pass through gap in core.
Object passes through the gap.
This changes the strength of the magnetic field which: : :
induces a voltage in the coil ends.
Voltage is proportional to rate_of_change_____ of field strength.
09-31 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-31
09-32 Other Proximity Transducers *
* 09-32
Many ways of building these.
Type depends upon what is being detected and where it is being
detected.
Broken light beam.
Radiated heat.
Sound.
..
.
09-32 EE 4770 Lecture Transparency. Formatted 13:17, 10 February 1999 from lsl*
*i09. 09-32
| David M. Koppelman - koppel@ee.lsu.edu | Modified 10 Feb 1999 13:18 (19:18 UTC) |