capacitive angle transducer _cat

8/12/2019 Capacitive Angle Transducer _CAT

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Author: Jeremy Leach Email: [email protected] June 2006

IntroductionThis article describes an experimental PICAXE-

based transducer that detects angular displacement ofa shaft. It relies on the variation in capacitance

between 'plates' of aluminium foil, therefore the name

"Capacitive Angle Transducer" or CAT !Commercial transducers are available that rely on

variation in capacitance and there are a number of

techniques used, often with considerable complexity(Capacitive Angular Displacement Transducers).

This project is a relatively basic idea compared to

commercial versions, but proves that a basic, cheap

transducer giving 32-Sector resolution seems

possible.

It has proved fascinating to make working capacitors

out of household materials, and there is much moreexperimentation that can be done. This project also

demonstrates the power and versatility of the

PICAXE08M chip.

ACKNOWLEDGEMENTS

PICAXE is a trademark of RevolutionEducation Ltd.

PICAXE Forum http://www.rev-ed.co.uk/picaxe/forum/

IN THIS ARTICLE

2 Basic Principles

3 Details of the CAT

3 Measuring Capacitance

5 Real Capacitance Graphs

5 Algorithm to read the Graphs

7 Conclusion

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Figure 1 : Ideal Graph

0 90 180 270 360Degrees

Capacitance

Figure 2 : The Base

Figure 3: The Disc

Basic principles

A variable Air Capacitor

An 'Air capacitor' consists of two conducting 'plates'

a small distance apart. The 'dielectric' is air and thecapacitance is represented by this general formula:

C = A/D + C0

Where:

= Relative-permittivity of the dielectric.

A = area of overlap of the plates.

D = distance between the plates.

C0 = a constant for the 'stray' capacitancebetween the plates and other conductors.

By having plates that rotate, it's possible to make a

variable capacitor, where the capacitance varies

depending on the overlap between the plates. Radio

sets have typically used variable air capacitors, which

have two sets of interleaved plates or 'vanes'.

This is the basic principle behind the CAT. It

measures the capacitance between plates, and

'knowing' the relationship between overlap andangular displacement, calculates and outputs anglevalues.

Unambiguous output

The transducer must generate a unique output for

each unit of angular displacement. A bit of thought

shows that, whatever the shapes of the plates, it's not

possible to have a unique capacitance value for each

angle. In general there will be at least two positions

of the shaft that give the same capacitance value.

One way of getting round this problem would be to

know the starting angle and for the transducer to

'deduce' the most likely angle out of the two or more

choices. This is entirely feasible, although it relies on

the shaft position being sampled rapidly compared tothe rotation speed.

Dynamic duo

My solution uses two variable capacitors. This does

allow a unique transducer output per angular unit.

Figure 1 shows an ideal output of capacitor valuesagainst angular displacement. Each angle has a

unique combination of capacitance values. Thegraphs for each capacitor are out of phase by 90

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Figure 4 : Shaft Contact

degrees. The straight-line segments would berelatively easy to implement in code.

This output is also useful for 'auto-scaling', which is

discussed later.

Details of the CATThe title picture shows the prototype unit. A disc is

attached to a copper shaft and rotates over a 'base'. I

stuck a computer-generated pattern on the disc

showing sectors to approximately 5.625 degrees.

Figure 2 shows the base, with three separate sectors

of aluminium foil, but actually only two adjacentsectors being used. The foil is glued to the MDF base

using contact-adhesive, which seems to work well

and produces a very flat foil surface.Figure 3 shows the disc, which rotates above the

base. I made the disc out of the lid of a CD holder.

The plastic is very brittle to cut but is nice and flat.

The copper shaft is literally a piece of thick copper

wire, carefully rolled until straight. The shaft rests ina hollow on a small piece of metal sheet, shown in

Figure 4. The shaft is electrically connected to thedisc by a thin wire on top of the disc.

For best operation it's critical to get the disc as close

as possible to the base in order to achieve themaximum fluctuation in capacitance. It's alsoimportant to avoid any tilt in the disc. I managed to

get a pretty consistent gap of around 1 to 2 mm.

Measuring capacitanceThere are two sectors on the base each of 90 degrees,

and a single 180 sector on the rotating disc. This

arrangement gives two independent variable

capacitors.

Figure 5 shows the CAT circuit, with C1 and C2

being the variable air capacitors. Figure 7 shows the

circuit constructed on Strip-board. Figure 8 and

Figure 9 show the Strip-board layout.

The PICAXE generates a 250KHz signal on Output

2, which is fed into the variable capacitors via the

copper shaft. Each variable capacitor has an

associated resistor (C1 and R4; C2 and R7). Each R-

C pair is therefore a high-pass filter.

The output from each filter feeds into a unity gainbuffer in the LM358N dual Op-amp, and then to a

low-pass RC pair which extracts a DC voltage

corresponding to the amplitude of the AC voltage

from the filter. This DC voltage feeds into aPICAXE ADC input. The PICAXE reads the ADC

values, and translates them to angular displacement

information that is output serially via Output 0.

The frequency of the driving signal and the values ofR4 and R7 have been chosen carefully. A simple

PICAXE program was written that generated a range

of frequencies and captured ADC values while thevariable capacitor C1 was fixed at it's maximum

overlap and R4 = 47K. The response curve is shown

in Figure 6. Note that the PICAXE can only generate

a selection of frequencies, which are shown as steps

in the graph. I've added a smooth trend-line to the

graph.

From this graph the ADC value reaches it's

maximum value when the driving frequency is

around 230KHz. If the driving frequency is fixed at

this value, then variation in capacitance will give a

good variation in ADC values.

250KHz is the nearest value that can be generated bythe PICAXE, so this is the frequency I've used.

R4 and R7 should ideally be metal film to minimise

the effect of temperature. 50ppm per degree is a

quoted figure. The Op-amps have high inputimpedance and low output impedance with unity

gain, and so are not expected to show anytemperature-related effects.

The values of R5 and R6 aren't too critical becausethey effectively just determine the responsiveness of

the smoothing capacitors C4 and C5 to changes inDC level. I chose tantalum capacitors for C4 and C5



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Figure 5 : CAT Circuit

0V

O0/Serout

I/O1

I/O2

+ V

Serin

I/O4

I3 PICAXE

08M

IC1C3

0.1uF

+

22K

R2

10k

R1

Download

4K7

R3

R7(Me

tal

Film

)

47K

+ 5V

GND

250KHz Signal

C4

1uF

+R4(Me

tal

Film

)

47K

+ V

Out B

InB -

InB+

Out A

InA -

InA+

- V LM

358N

IC2R5

10K

C1

C2

R6

10K

C5

1uF

+

D1

(Shottky)

Figure 6 : Frequency response of R-C combination

Frequency Response

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200 220 240 260

F KHz

ADC

Value

C1ADC

Poly. (C1ADC)



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Figure 7 : Strip-boarded circuit

Figure 8 : Strip-board topside

GND

I/O1I/O4

SOutSIn

I/O2I3

Vcc

IC8

PicAxe08M

R34K7

R2

22K

R1

10K

21

3

J1

C3

ST1

1

2

C5+

R7

47K

A+ B-

OB

V-

V+OA

B +

A-

IC5

LM358N

R6

10K

R5

10K

C4

+R4

47K

GND

I/O1I/O4

SOutSIn

I/O2I3

Vcc

IC8

PicAxe08M

R34K7

R2

22K

R1

10K

21

3

J1

C3

ST1

1

2

C5+

R7

47K

A+ B-

OB

V-

V+OA

B +

A-

IC5

LM358N

R6

10K

R5

10K

C4

+R4

47K

GND

I/O1I/O4

SOutSIn

I/O2I3

Vcc

IC8

PicAxe08M

R34K7

R2

22K

R1

10K

21

3

J1

C3

ST1

1

2

C5+

R7

47K

A+ B-

OB

V-

V+OA

B +

A-

IC5

LM358N

R6

10K

R5

10K

C4

+R4

47K

Figure 9 : Strip-board underside

GND

I/O1I/O4

SOutSIn

I/O2I3

Vcc

IC8

PicAxe08M

R3

4K7

R2

22K

R1

10K

21

3

J1

C3

ST1

1

2

C5

+

R7

47K

A+ B-

OB

V-

V+OA

B +

A-

IC5

LM358N

R6

10K

R5

10K

C4+

R4

47K

GND

I/O1I/O4

SOutSIn

I/O2I3

Vcc

IC8

PicAxe08M

R3

4K7

R2

22K

R1

10K

21

3

J1

C3

ST1

1

2

C5

+

R7

47K

A+ B-

OB

V-

V+OA

B +

A-

IC5

LM358N

R6

10K

R5

10K

C4+

R4

47K

because this type has low leakage current.

Normal temperature variation is not likely to affect

the capacitance of the variable capacitors

significantly. The expansion of the copper shaft etc

should not be too great, and if it was then the shaft

could be shortened. The aluminium in the disc andbase shouldn't expand or contract much at all.

Overall I believe that temperature effects are

therefore minimised. However a significant factor totry to take account of is the variation in capacitance

with humidity. This is discussed later.

Real capacitance GraphsFigure 10 shows graphs of the ADC values recorded

for one rotation of the disc. The values weresurprisingly stable at the time of reading them,

fluctuating by only +/- 1 digit. A clear difference

between these graphs and the 'Ideal' of Figure 1 is the

sloping top sections. My explanation for this is that

there is probably a slight tilt to my shaft - but I can'tsee it easily!

The lack of 'flat tops' is a pity, but nevertheless these

are useable graphs, which demonstrate unique pairs

of values for each angle of rotation.

Another feature of the graphs is the generalsmoothness, which is possibly due to effects at the

edges of the foil plates.

Also, the values fall to zero, or almost zero, when

there is no overlap of foil. This is a good thing and

shows that stray capacitance in the foil, connecting

wires and strip-board tracks is very low. Which

means that the capacitance equation is more like:

C = A/D

This means that changes in the permittivity of the airdue to fluctuations in humidity are likely to increase

the capacitance values in a linear fashion.

Algorithm to read the GraphsThe full code listing is given at the end of this article.

The basic job of the PICAXE software is to take the

pair of ADC values and translate them into angular

displacement. However in addition to this, the

software must also allow for tolerance in the

readings, and fluctuation of the readings due tohumidity changes.

There are a number of methods that could be used to



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Figure 10 : ADC values vs Angle

ADC Value vs Angle

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

0 45 90 135 180 225 270 315 360

Angle in Degrees

ADC

Value

C1

C2

achieve this, and I've experimented with a few.

However the programming space on a PICAXE08M

is limited, so whatever method is used has to be

simple and effective.

Translation

I've stored the graphs in 64 bytes of EEPROM as

sequential pairs of readings. When a new pair of

values is obtained, the values are compared to thoseon the graph until a matching 'scenario' is found.

What this means in detail is that the reading relating

to Capacitor1 lies between a pair of data-points on

the C1 graph, and the reading relating to Capacitor2lies between the associated pair of data-points on the

C2 graph.

Tolerance

Because there is slight fluctuation in ADC readingsfor a fixed shaft position, a tolerance value is

employed, which allows values to be 'matched' that

fall slightly outside the data-point ranges.

The tolerance value starts small. The graph data is

scanned. If the end of the graph is reached and no

matching scenario has been found, then the graph

data is scanned again with a slightly increased

tolerance.

This process will repeat a number of times until amatch is found, or the tolerance reaches a maximum

value, at which point an error value (Sector = 32) is

generated.

Auto Scaling

Humidity is likely to change the capacitance in alinear fashion. This will affect the range of ADC

values obtained when the disc is rotated. The ADC

values are not a direct measure of capacitance and

the relationship between how the ADC values

change with capacitance is complex. However as a

fairly good approximation, I've assumed that the

ADC Value graphs scale in a linear way as Humiditychanges. To do anything more complicated is not

easy with the limited code-space available!

The code detects the special condition where theADC values are equal (or nearly equal) then

compares this value to the same point on the internal

-graphs, and calculates a 'gain' value to apply to the



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Figure 11 : Flowchart

ADC Values equal

(special condition)?

Initialise

Adjust Gain

Calculate Normalised

ADC Values

Loop

Yes

No

Find Matching

Scenario from

internal Graphs

Output Sector

Sector = 32 (Error)

Tolerance =

MinimumTolerance

Increment

Tolerance

Tolerance

Maximum

Value?

No Match

No

Yes

Match

Read ADC Values

ADC values. There are two shaft positions where thespecial condition is met, but only the one with the

higher ADC values is used, in order to get best

granularity of the gain value.

The gain 'normalises' the range of ADC values to

match those of the internal graphs. The gain isadjusted automatically whenever the shaft is in the

correct position. (In the ideal graph, the auto-scaling

could occur over a whole 90 degree range).

Whether this solution to address humidity variation

really works well is difficult to say as I've only testedthe CAT over a few days, and the automatic

adjustment in gain has been small.

The gain value is held as 'GainNumerator' and

'GainDenominator' bytes in code. This is an effective

way of performing an accurate multiplication usinginteger arithmetic.

CAT Output

The CAT outputs values via a Seroutcommand. At

present I read the output via the 'Terminal' program

in the PICAXE Programming Editor. However in a

real application, the output pin could be connected to

other PICAXE chips etc.

The CAT outputs a 'Sector' number from 0 to 31

(which avoids using a Word value for 'Angle'). Alsothe gain numerator and denominator value, to

indicate when re-scaling has occurred.

An outline software flow is shown in Figure 11.

ConclusionThis project should be classed 'proof of concept'. It

demonstrates that it's possible to build working

variable air capacitors out of basic household

materials, and it's possible to make a working

transducer with a simple circuit, relying on the powerand versatility of the PICAXE08M chip. It also hints

at further possibilities using home-made capacitors.

The likely accuracy of this transducer is admittedly a

bit questionable. I haven't put it through any thorough

testing, but it seems to work well to 32-sector

resolution.

There are limitations in the design that would need to

be considered if it was used for any serious

application. For instance, the copper shaft simplyrests on a metal 'dent' contact, which is not fantastic.I've used a small piece of aluminium for this contact

and think I've already experienced some oxidation

problems at the point of contact.

It's also not clear how this transducer could be used

in real-life. A key feature is low shaft-friction with

no mechanical contact with any gears etc.

Optical solutions also have this advantage, although

to make your own optical encoder to 32-sector

accuracy might need multiple sensors and perhaps be

harder to achieve.

v



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PICAXE Code'***************************************'* *'* CAPACITIVE ANGLE TRANSDUCER (CAT) *'* Version:1 *'* Author:Jeremy Leach 2006 *

'* *'***************************************

'**********************'**** LOOKUP TABLE ****'**********************

'NOTE: Data is stored in the Lookup Table in a sequence of 32 pairs of'Cap2Value>.'The first pair in the table is for Angle = 0 degrees,'the last pair for Angle = 348.75 degrees (11.25 degrees * 31).

Eeprom0,(169,9,164,19,159,29,152,44,146,59,141,76,136,93,127,118,118,143,94,142,70,142,50,138,31,135,20,131,10,128,5,122,0,116,0,98,0,81,0,65,0,49,0,36,1,24,3,17,5,10,18,8,32,6,58,5,85,4,111,4,137,4,153,6)

'**************************'**** GLOBAL VARIABLES ****'**************************'Word0 (b0 and b1) SymbolCap1ADCValueLSB = b0 Symbol Cap2ADCValueLSB = b1'Word1 (b2 and b3) Symbol TempValue = b2'Word2 (b4 and b5) Symbol CheckValue = b4 Symbol Tolerance = b5'Word3 (b6 and b7) Symbol SectorIndex = b6 Symbol IsBetween = b7'Word4 (b8 and b9) Symbol GainW = w4 Symbol GainNumerator = b8 Symbol GainDenominator = b9'Word5 (b10 and b11) Symbol Address1 = b10 Symbol Address2 = b11'Word6 (b12 and b13) Symbol Value1 = b12 Symbol Value2 = b13

'*******************'**** CONSTANTS ****'*******************'Pin assignmentsSymbol Cap1InputPin = 1Symbol Cap2InputPin = 4Symbol PWMOutPin = 2Symbol ResultOutPin = 0

'Character constants



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Symbol COM = 44 'commaSymbol RET = 13 'carriage returnSymbol LFEED = 10'line feed

'Other constantsSymbol MaxSectorIndex=31Symbol LookUpTableEndAddress=63Symbol Yes = 1

Symbol No = 0Symbol C1C2HighCrossover = 125Symbol ErrorSector = 32Symbol MinimumTolerance = 2Symbol MaximumTolerance = 10Symbol DifferenceThreshold = 3Symbol DoubledDifferenceThreshold = 6

'***********************'**** RAM POINTERS *****'***********************

'*********************'**** INITIALISE *****'*********************

PwmoutPWMOutPin,3,8'Sets a 250KHz signal with 50:50 DutyGainW= 257 'Set Gain Numerator and Denominator both to 1.Pause 1000 'To let the smoothing capacitors charge

'************'*** MAIN ***'************

GetAndTransmitSector:

'READ THE ADC VALUES 'Although ReadADC10 is used, only the lower byte 'is relevant as the ADC values do not exceed 255. Readadc10 Cap1InputPin,Cap1ADCValueLSB Readadc10 Cap2InputPin,Cap2ADCValueLSB

'CHECK FOR 'HIGH CROSSOVER' SCENARIO TempValue=Cap1ADCValueLSB-Cap2ADCValueLSB+DifferenceThreshold IfTempValue > DoubledDifferenceThreshold Or Cap1ADCValueLSB < 40 ThenGATS_2

'ADJUST GAIN GainNumerator = C1C2HighCrossover GainDenominator = Cap1ADCValueLSB

'NORMALISE THE ADC VALUES GATS_2: Cap1ADCValueLSB=Cap1ADCValueLSB * GainNumerator / GainDenominator Cap2ADCValueLSB=Cap2ADCValueLSB * GainNumerator / GainDenominator

'FIND SECTOR 'Scan the Lookup table for a scenario that fits the normailised ADC 'values and return the associated SectorIndex. 'If a Scenario can't be found then set SectorIndex = ErrorSector Tolerance=MinimumTolerance-1

FS_1:

Tolerance=Tolerance + 1 ForSectorIndex = 0 ToMaxSectorIndex



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'Check if Cap1ADCValue is between the indexed Cap1 data points from the 'Lookup Table.

CheckValue=Cap1ADCValueLSB Address1 =SectorIndex * 2 GosubCheckIfBetween If IsBetween = No ThenFS_2

'Check if Cap2ADCValue is between the indexed Cap2 data points from the 'Lookup Table.

CheckValue=Cap2ADCValueLSB Address1 =Address1 + 1 'Note Address1 is not corrupted by CheckIfBetween. GosubCheckIfBetween If IsBetween = Yes ThenGATS_3

FS_2: Next

'Try relaxing the tolerance IfTolerance


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Value1=Value1/240Xor1*Value1 Value2=Value2/240Xor1*Value2

'Check if the CheckValue is between Value1 and Value2. CIB_2: IsBetween=No

IfCheckValue =Value1ThenCIB_5

IfCheckValue >Value1ThenCIB_3 IfCheckValue >= Value2ThenCIB_5 Return

CIB_3: IfCheckValue < Value2 Then CIB_5 Return

CIB_5: IsBetween = Yes Return

capacitive angle transducer _cat

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