PROJECTS MICROCONTROLLERS
Brim Full
Capacitive liquid-level
measurement
Wolfgang Rudolph (Germany), Rudolf Pretzenbacher (Austria), and Burkhard Kainka (Germany)
Electronics enthusiasts are sometimes a breed apart. Most people simply look at a bottle
when they want to know how full it is, but we want to measure it.
Of course, it doesn t have to be We re sure that our readers can
Measuring methods
a bottle. Situations that involve come up with many other situa-
measuring the level of a liquid tions where the liquid-level sen- A wide variety of measuring meth-
stir the creative juices and fos- sor described here can be put ods are used. Many lavatory cis-
ter true acts of genius, and there to good use. However, let s first terns have a float valve that first
are countless applications for liq- consider the question of how to reduces the inflow of water when
uid-level sensors, ranging from measure a liquid level accurately the float rises to a certain level
rain barrels to heating-oil tanks. and reliably. and finally stops it completely. In
40 elektor - 5/2009
After all, we re used to working with
capacitors. However, it s not as sim-
+5V
Table 1
ple as it seems at first glance. We have
R1 R4
Inductor specifications
to do a bit of maths first. This article
(vertical package
is based on a capacitive liquid-level
with moderate rated current) R3
sensor built by Rudolf Pretzenbacher,
100k
which uses a simple but remarkably
Manufacturer: Fastron;
stable oscillator for the sensor circuit
type number 09 P-103 J-50
IC1
C1
and an AVR microcontroller for the sig- 5
8
2
Dimensions: Ø 9.5 mm, height 14 mm, fout
nal processing. His liquid-level gauge 6
7
10
LM311
lead pitch 5 mm
provided the inspiration for this ATM18 16V 3
R5
L1
4
article, and it delivers truly astound-
Inductance: 10.0 mH (at 20 kHz)
1
10mH
ing results. This setup can be used to
Self-resonant frequency (SRF): 0.41 MHz
measure capacitances in the range of
R2
Rated DC current: 90 mA
nanofarads (nF) to femtofarads (fF). In
C2
case you ve forgotten, a femtofarad is
Resistance: 35.0 ©
10
GND
10 15 F or a thousandth of a picofarad.
16V
Tolerance: Ä…5 %
How can such high sensitivity be
080707 - 16
achieved? The answer is that the
Q (min): 70
 sense capacitor in the liquid is one
of the frequency-determining com-
Figure 1. Schematic diagram of the oscillator used for
ponents of a resonant loop, which in
capacitance measurement.
this case, the float is not only the sen- turn is part of an oscillator circuit. If an
sor but also the actuator, which con- object to be measured is brought in the
trols the valve via a lever mechanism. vicinity of the capacitor, the resonant
Although this is a very reliable prin- frequency of the loop changes. The can be seen very nicely on an oscillo-
ciple, it can t be used to measure the more the capacitance of the capacitor scope. The damping results from the
liquid level. The same principle was is increased by the object, the lower resistive losses in the wire and the
used in the past (and is sometimes the resulting frequency. The task of magnetic losses in the core. A resonant
still used) to measure the fuel level in the microcontroller on the Elektor loop with an inductance of 10 mH and a
petrol tanks of cars. In this case, the ATM18 board is to measure the fre- capacitance of 6300 pF has a resonant
float moves the wiper of a potentiom- quency and then calculate the value frequency of 20 kHz, and the inductive
eter instead of actuating a valve. This of the capacitance from the measured and capacitive impedance are both
variable resistance forms part of a volt- frequency and the known value of the 1260 ©. The ratio of this impedance to
age divider that drives a milliammeter, inductance. the DC resistance (35 ©) yields a theo-
which indicates how full the tank is. In This sounds quite simple, but there are retical Q factor of 36, which means that
some cases, the accuracy of this gauge still a few details to be sorted out. the resonant impedance of the circuit
leaves a lot to be desired. is 45 k© (1260 © × 36). The Q factor
Nowadays a wide variety of modern and the resonant impedance increase
Oscillator
measuring methods are used in many as the capacitance is reduced and the
different situations. They include The oscillator circuit can affect the res- frequency rises. For a high Q factor,
hydrostatic and differential pressure onant loop due to its own capacitance we have to aim for a high L/C ratio. At
measurement, conductivity measure- or as a result of excessively strong around 3000 pF and 30 kHz, the calcu-
ment, light absorption measurement, coupling. To keep this effect as small lated value of the Q factor is approxi-
transit time measurement using ultra- as possible, the resonant loop should mately 70. The core losses increase at
sound, distance measurement using have a high quality factor (Q) and the very high frequencies, which causes
microwaves, and even transit time excitation level should be kept low. It the Q factor to drop. However, the
measurement using radar pulses. is also important to choose a suitable oscillator circuit has an even larger
From an electronic perspective, capaci- inductor. effect, since a resonant loop with a
tive measurement is also interesting. In this case, we decided on a fixed high resonant impedance is especially
This method involves measuring the inductor made by Fastron. This induc- sensitive to external influences.
change in the capacitance between tor (type number 09 P-103 J-50; avail- Figure 1 shows the oscillator circuit
two electrodes. If these electrodes are able from Reichelt and other sources) used here, which is built around an
located in a container with a liquid has an inductance of 10 mH, a DC LM311 comparator. It compares the
that covers them more or less depend- resistance of 35 ©, and a self-resonant input voltage with a reference voltage
ing on its level, the capacitance of this frequency of 410 kHz. This means that and converts the sinusoidal signal
 capacitor changes accordingly. The it has a remarkably low stray capac- from the resonant loop into a square-
capacitance depends on the dielectric itance of 15 pF. In addition, it has a wave signal at its output. This signal
constant of the liquid, and it increases specified Q factor of 70 (max.). Its char- excites the resonant loop via a feed-
as the level of the liquid rises. acteristics are listed in Table 1. back resistor. A voltage divider at the
The higher the Q factor of a resonant non-inverting input of the comparator
loop, the lower its damping. A Q fac- provides a voltage equal to half the
Capacitive sensing
tor of 70 means that the amplitude of supply voltage. The inverting input is
You ve probably guessed that this is a  free (damped) oscillation is reduced fed by a comparison voltage obtained
the method we intend to use here. by a factor of e after 70 cycles, which by integrating the output voltage. As a
5/2009 - elektor 41
1k8
100k
47k
C sensor
100k
PROJECTS MICROCONTROLLERS
result, the operating point of the oscil- com AVR series (Elektor Decem-
lator is set automatically, and it starts ber 2008). The counter input is T1
Listing 1
reliably and produces a symmetric (PD5), and the frequency in hertz can
Capacitance measurement
square wave at the output. be obtained directly with a gate period
With regard to the effect of the oscil- of 1 second. It is sent directly to the PC
Config Timer0 = Timer ,
lator circuit on the resonant loop, the at 9600 baud, without any correction
Prescale = 64
main consideration is the resistor val- or window dressing. All that s left is
Config Timer1 = Counter ,
ues. The voltage divider formed by to convert the frequency into capaci-
Edge = Falling , Prescale
the two 100-k© resistors loads and tance. We use a single-precision vari-
= 1
thus damps the resonant loop with an able for this. The conversion formula
On Ovf0 Tim0_isr
On Ovf1 Tim1_isr effective value of 50 k©. There is also must be broken down into individual
Enable Timer0
the resistance of the negative feed- operations in Bascom. Here you have
Enable Timer1
back resistor (100 k©) divided by the to ensure that the intermediate values
effective voltage gain. As a result, sta- do not become too large or too small,
Do
ble oscillation is possible with sensor since this would degrade the accuracy.
Ticks = 0
capacitance values of up to 100,000 pF This means that the sequence of the
Enable Interrupts
(or more). The open-circuit frequency operations is somewhat important. The
Waitms 1100
is approximately 350 kHz, which yields 10 mH of the inductor is expressed as
Disable Interrupts
an effective capacitance of around a factor of 10,000,000. The underlying
Lcdpos = 2 : Lcdline = 1 :
Lcd_pos 20 pF. The inductor accounts for 15 pF
Lcdtext =  Freq = 
of this, while the input capacitance of
Lcdtext = Lcdtext +
the LM311 and the stray circuit capaci-
Body capacitance
Str(freq)
tance add another 5 pF.
Lcdtext = Lcdtext +  Hz
If you use an oscilloscope to view the
If you move your hand close to the oscil-

signal on the inductor, you will see an lator (Figures 1 and 2), you will see the
Lcd_text
measured capacitance change by a few
amplitude of approximately 1 V at the
Print Freq;
femtofarads, even if no sensor cable is con-
highest frequency and a somewhat
Print  Hz
nected. We measured the following approx-
distorted sinusoidal waveform. This
C = Freq / 10000000
imate results at various distances between
C = 1 / C means that the excitation level could
the board and our hand:
C = C * C
be reduced even further. However,
C = C / 39.48 5 cm 0.005 pF
with increasing sensor capacitance
If Pinb.0 = 0 Then C0 = C
the amplitude decreases noticeably
4 cm 0.009 pF
C = C - C0
and the signal becomes more sinusoi-
3 cm 0.020 pF
Print Fusing(c ,  #.### );
dal. The oscillator still works at 100 nF,
Print  pF
2 cm 0.040 pF
with a frequency of 4.9 kHz and a sig-
Lcdpos = 2 : Lcdline = 2 :
nal amplitude of 0.1 V. It stops operat- 1 cm 0.100 pF
Lcd_pos
ing suddenly somewhere above this
Lcdtext =  Cap =
This is interesting from a physics perspec-
Lcdtext = Lcdtext + figure.
tive. The phenomenon of body capacitance
Fusing(c ,  #.### )
The next issue to be considered is
is both familiar and notorious among radio
Text = Fusing(c ,  #.### )
frequency stability. The fact that the hobbyists. If a DIY receiver is not adequate-
Lcdtext = Text
ly screened, it is often possible to detune
circuit only contributes 5 pF to the
Lcdtext = Lcdtext +  pF
it slightly by moving your hand toward it.
capacitance of the resonant loop is in

Some people make handy use of this effect
itself favourable. This leaves us with
Lcd_text
for fine tuning when receiving SSB signals.
the difficult question of the tempera-
Waitms 10
Musicians who use Theremin instruments
ture dependence of the inductance.
Loop
also take advantage of body capacitance.
The only way to answer this question
is to perform experiments. To make a
Tim0_isr: long story short, we can say that the
 1000 µs
stability of the prototype version built
Timer0 = 6
on stripboard in the Elektor labs (Fig- reason for this is to arrive at a value in
Ticks = Ticks + 1
ure 2) is sufficient to achieve a sensi- picofarads at the end. If comparative
If Ticks = 1 Then
tivity of 0.001 pF, or in other words 1 fF measurements indicate that the actual
Timer1 = 0
(1 femtofarad  what an uncommon value of the inductor is slightly differ-
Highword = 0
term!). Incidentally, frequency meas- ent, such as 1% higher or lower, this is
End If
urement is not the limiting factor. At the place to make the correction. The
If Ticks = 1001 Then
350 kHz and 20 pF, a change of 1 Hz inductor has a rated tolerance of 5%,
Lowword = Timer1
Freq = Highword * 65536 corresponds to a capacitance change of which means that the capacitance can
Freq = Freq + Lowword
only around 0.1 fF. However, the effec- be measured with a potential error of
Ticks = 0
tive constancy is somewhat lower. approximately 5%.
End If
The open-circuit capacitance C0 is
Return
around 20 pF. Of course, the exact value
Frequency measurement
depends on several factors, including
Tim1_isr:
Now we come to familiar ground. Fre- component tolerances, PCB construc-
Highword = Highword + 1
quency measurement was already tion, and perhaps even the type of sol-
Return
described in instalment 4 of the Bas- der that is used, since the dielectric
42 elektor - 5/2009
constant of solder flux can have an approximately 20 ºC (to around 30 ºC),
effect on the order of a few femtofar- the measured capacitance increased
ads. The only solution to this is to per- by approximately 0.15 pF. This means
form a zero-point calibration. that if your objective is to measure the
Nothing could be easier: when the user value of an unknown capacitor, the
presses a button connected to port B0, temperature is scarcely important.
the current zero-point capacitance C0 However, if you actually want to meas-
is measured and stored. This is any- ure capacitance with an accuracy of a
how necessary, because if you use a few femtofarads, you must first allow
cable to connect the sensor it can eas- the oscillator to stabilise for a few min-
ily contribute another 10 pF. Conse- utes and then make a zero-offset read-
quently, we measure and store the zero ing. The measured value changes by
offset before making the actual meas- less than 5 fF over the course of sev-
urement, and this way we obtain the eral minutes.
Figure 2. Prototype version of the oscillator, built on a piece of
best possible accuracy
perforated circuit board.
The measured values are output in two
Capacitance measurement
different ways: via the serial interface
and on the familiar LCD with its two- People who play around with RF cir-
wire interface. At first this was a bit cuits almost always have something
to measure, such as a variable capaci-
tor. Before a true radio hobbyist tosses
an old radio in the bin, he at least sal-
Their hand movements alter the frequency
vages the variable capacitor, since
of an oscillator and thus change the audio
frequency in a smooth, continuous manner. they are not so easy to come by nowa-
days. Naturally, you have to measure
You can try this for yourself with this oscilla-
the salvaged part to know what you
tor. Connect a copper-plated board in Eu-
actually have. If it has a range of 8 pF
rocard format (100× 160 mm) to act as the
sense electrode. This adds approximately to 520 pF, it s brilliant.
17 pF to the capacitance of the resonant
You can also measure unknown SMD
loop, and the frequency drops to around
capacitors, variable-capacitance
260 kHz. This is in the long-wave radio
diodes, the input capacitances of FETs
band, and you can pick up the signal on
or valves, and cable capacitances. You
a radio. With a bit of luck, you can find a
can even determine the length of a
long-wave broadcast signal that interferes
cable by measuring its capacitance.
with the oscillator signal to produce a beat
For example, suppose you have a par-
frequency. Then you can start making mu-
tially used roll of coax cable and you
sic, assuming you have the knack.
want to feed it down a disused chim-
All the neighbourhood cats will probably
ney. Before you start, it s a good idea
run for cover, but that shouldn t stop you
to know whether it s long enough
from trying out the effect and learning to
L
to reach the bottom. We ve all heard
understand it, even if you ll never compete
enough stories about cursing men on
with Theremin virtuoso Lydia Kavina, a
great-niece of the inventor of the Theremin. high roofs.
The most effective variation in capacitance,
This question is easily answered with
around 0.1 pF, occurs at a distance of
our capacitance meter. The capaci-
around 5 cm due to the relatively large size
tance per metre is stated on the data
h
of the sense electrode.
sheet. For example, popular 50-© RG58
cable has a capacitance of 100 pF/m.
If you don t have a data sheet, you
can simply measure the capacitance
too much for the LCD routine, which of a known length, such as 1 metre, to
didn t want to cooperate with the determine the number of picofarads per
timer interrupts. The problem was metre. Once you know this value, you
found to arise from passing variables can easily calculate the cable length
to the subroutines, and it was cured from the measured cable capacitance
by declaring all variable as global. In (cable capacitance divided by capaci-
addition, the timing was improved to tance per metre yields cable length in
make data transfer even more reliable metres). The fact that the cable also
(see Listing 1). has an inductance doesn t matter,
Now the program displays the current since the measuring frequency is much
080707 - 11
frequency and the capacitance. This less than the quarter-wavelength fre-
enables us to make some experimental quency. For example, at 100 kHz the
measurements of temperature stability. wavelength is 3 km.
Figure 3. The liquid-level sensor is a tube with an insulated
For example, you can warm the induc- inner electrode that forms a cylindrical capacitor. Here L is
tor with your hand and observe the the length of the active portion of the tube (wrapped with
Liquid level measurement
aluminium foil) and h is the height of the water in the tube.
change. With a temperature increase of
5/2009 - elektor 43
PROJECTS MICROCONTROLLERS
were sealed watertight (Figure 3). The
od2 conductor of the hookup wire must be
Table 2
fully insulated (galvanically isolated)
od1
Sensor tube data (for Figure 6)
from the space inside the tube. Then
Ci
id2
we wrapped the length of the tube
Standpipe outside diameter: 12 mm
id1
between the two stubs with aluminium
Cx
Standpipe inside diameter: 8.5 mm
foil applied as uniformly as possible
and attached a bare connecting lead
Standpipe length: 300 mm
Co
to the aluminium foil (held in place by
Inner electrode
electrician s tape). The bare lead and
conductor diameter: 0.4 mm
the end of the hookup wire protruding
from the tube form the terminals of our Inner electrode
sense capacitor. outside diameter: 0.6 mm
Standpipe tube dielectric constant: 3.0
A cylindrical capacitor is a rotation-
Inner electrode dielectric constant: 2.3
ally symmetric form, so its capaci-
tance can be calculated rather accu-
Electrolyte dielectric constant: 83
rately by using the following formula
if the length is much greater than the
diameter:
080707 - 12 determined by the series connection of
2 0 r l
the individual capacitors (Figure 4). If
c

od we divide the cylindrical capacitor into
Figure 4. The concentric capacitors of the sensor tube structure. LN
a portion filled with water or another

id
liquid (CW) and a portion filled with air
µ0 = dielectric constant of vacuum and (CA), the total capacitance of the tube
air (8.854 × 10 12 As/Vm) is CT = CW + CA (parallel connection),
µr = relative dielectric constant (mate- with the portion filled with water hav-
CiL CxL CaL
rial constant) ing a length h and the portion filled
L = cylinder length with air having a length L  h. The
od = diameter of the outer electrode equivalent circuit of this arrangement
(here od2) is shown in Figure 5.
CiW CxW CaW
id = diameter of the inner electrode The relative dielectric constant (µr)
(here id1) of air is 1.0, while the relative dielec-
tric constant of water depends on the
080707 - 13
If we combine the constants and con- temperature and ranges from 55 to 88
vert metres to millimetres, we obtain (approximately 83 at 10 °C). The die-
Figure 5. The equivalent circuit of the sensor tube.
the following formula: lectric constant of transparent plastic
is around 3.0 (polystyrene and poly-
0.0556 r carbonate) or 3.2 (acrylic), and the
c l pF/mm
To make our liquid-level sensor, we fit- dielectric constant of wire insulation

od
LN
ted a small Plexiglas (polycarbonate) is around 2.3 (polyethylene) or 4 to 5

id
tube with two connection stubs. (polyvinyl chloride).
A length of polyethylene-insulated If a cylindrical capacitor consists of This is excellent for our intended meas-
hookup wire was stretched through several concentric layers, each layer uring applications because it means
the tube and centred as well as pos- forms a separate capacitor (here Co, Cx, that there will be a rather large differ-
sible, and then both ends of the tube and Ci). The total capacitance is then ence between the values of the capaci-
tance Cx in air and in water.
The capacitances in the air-filled por-
tion of the tube are:
350
300

0.0556 2.3 l h
CiA
250

id2
LN

200 id1
150

0.0556 1 l h
Cxl
100

od1
LN

50

id2
0
0.000 10.000 20.000 30.000 40.000 50.000 60.000

0.0556 3 l h
capacitance [pF] 080707 - 14
CoA

od2
LN


od1
Figure 6. The capacitance increases linearly with the liquid level.
44 elektor - 5/2009
fluid level [mm]
oscillator
od1
+5V
Cx
fout
id2
Ci
id1
GND
Cx
LCD 20 x 4
DATA
CLK
+5V
GND
080707 - 15
water
Figure 7. Wiring diagram of the Elektor ATM18 board for the liquid-level gauge.
080707 - 17
stainless steel tube
while the capacitances in the water- between the total capacitance and the
filled portion are: water level, you will discover that it
is fully linear if you use a fixed dielec-
Figure 8. Simplified sensor construction using a stainless-steel
tric constant for water. Figure 6 shows
or copper outer tube and an insulated brass tube as the inner
0.0556 2.3 h
the capacitance as a function of liquid
CiW
electrode.

id2
level for a standpipe sensor with the
LN
dimensions given in Table 2.
id1
Now we can use our standpipe sense
capacitor and an inductor with a more height of the water in the standpipe.
0.0556 83 h
CxW
or less known value to form a resonant We first measure the capacitance Cmin

od1
LN
loop, measure the resonant frequency, with the standpipe empty (h = 0) and

id2
and use the well-known resonant-loop the maximum capacitance Cmax with
formula the standpipe full (h = L), after which
0.0556 3 h
we can use the straight-line formula to
CoW

od2
1
calculate the height:
LN
f 0

od1

2 L C
L Cmeasured Cmin
h
If you use a spreadsheet program to to calculate the capacitance of the
Cmax Cmin
calculate and plot the relationship standpipe and thus determine the
Here the mechanical accuracy of the
construction and the accuracy of the
Y = Cap * K
reference inductor do not matter, and
Listing 2
Y = Y + D
the absolute accuracy of the frequency
Yfix = Y
Calibration and calculation of the
measurement, the presence of para-
End Sub
liquid level
sitic capacitances, and the dielec-
Hmin = 0.0 tric constants of the materials used
 Calibrate Minimum Value
Hmax = 300.0
to construct the sensor are equally
Sub Calibmin
Getminmax
irrelevant.
Print  Minimum Calibration
If Cmax <= Cmin Then
The oscillator module (Figure 2)
Bitwait Pind.7 , Set
Cmin = 7.0
should be located as close to the sen-
Cmin = Cap
Cmax = 52.0
sor as possible in order to minimise the
Print  Cmin ; Cfix ;  pF
End If
Eadr = Eadrcmin parasitic capacitance of the cable and
&
Writeeeprom Cmin , Eadr
reduce the effects of nearby objects on
End Sub
Sub Calclevel
the sensor cable capacitance.
 ensure that: Hmax>Hmin and
 calibrate Maximaum Value
Cmax>Cmin
Sub Calibmax
If Cap < Cmin Then Cap = Cmin
Software
Print  Maximum Calibration
K = Hmax - Hmin
Bitwait Pind.6 , Set The Bascom project Level.bas also
D = Cmax - Cmin
Cmax = Cap
If D = 0 Then D = 0.01  avoid uses the serial interface and the LCD.
Print  Cmax ; Cfix ;  pF
division by zero
In addition to the frequency and the
Eadr = Eadrcmax
K = K / D
capacitance, it shows the liquid level
Writeeeprom Cmax , Eadr
D = -k
in millimetres on the display. A pair
End Sub
D = D * Cmin
of buttons connected to PD6 and PD7
can be used for calibration, with the
5/2009 - elektor 45
C sensor
PROJECTS MICROCONTROLLERS
calibration values being stored in mately 1 mm per 20 °C. It s even easier if you can allow the
EEPROM. The default values assign a If this is not acceptable, you will have electrolyte to make electrical contact
height of 0 to a capacitance of 7 pF and to measure the temperature of the with a sensor electrode and the elec-
a height of 300 mm to a capacitance of electrolyte as well and use a table to trolyte is electrically conductive (which
52 pF. If you adjust the liquid level to a determine the actual dielectric con- is the case with normal water). In this
height of 0 mm and press the first but- stant. Unfortunately, the simple cali- case the electrolyte acts as the outer
ton (PD7), the measured capacitance bration procedure is no longer feasi- electrode of the capacitor (see Fig-
is copied to Cmin and stored in mem- ble in this case, and the liquid level ure 8). Here again there is a linear
ory. After this, you can fill the sensor must be determined using the theo- relationship between the capacitance
tube to the 300-mm level and press the retical formulae. With this approach, and the liquid level. The temperature
second button (PD7) to copy the cor- the accuracy of the sensor tube con- dependence of the electrolyte is largely
responding value to Cmax. This data struction, the exactness of the dielec- irrelevant as long as the conductivity
is held in non-volatile memory, so it is tric constants of the tube insulation of the electrolyte is much greater than
available the next time you switch on and the insulation of the centre elec- the conductivity of the insulation of the
the instrument (see Listing 2). trode, and the accuracy of the reference inner electrode. This is always the case
If the parasitic capacitance of the inductor and the frequency measure- with tap water.
cable (approximately 33 pF) is taken ment are very important for obtaining
into account, the measured values good results. In addition, the parasitic Constructing the sensor is a bit tricky
are amazingly close to the theoreti- capacitance of the connecting cable in this case because the inner electrode
cally determined values. From this we must be measured exactly. cannot be clamped at both ends. The
can conclude that a method based on best approach is to use a thin brass
purely theoretical calculation (without tube (from a DIY shop) and insulate it
Choice of materials
calibration of the minimum and maxi- with heat-shrink tubing so the brass
mum levels), and taking the tempera- A wire with polyethylene (PE) insula- does not come in contact with the
ture dependencies of the electrolytes tion is a better choice for the inner con- electrolyte. Now the trick is to devise
into account, could be implemented ductor than one insulated with poly- brackets that hold the inner tube and
with a reasonable amount of effort. vinyl chloride (PVC) because the die- the outer tube of the sensor (the outer
As already mentioned, the simple lectric constant of polyethylene has a tube can be made from stainless steel
approach only works if you assume very small range of variation and lies or copper) such that they are accu-
that the dielectric constant of the elec- between 2.28 and 2.3. A good way to rately concentric. Depending on the
trolyte (in this case water) remains obtain such a wire is to remove the diameter of the outer tube, an arrange-
more or less the same after calibration. sheath and braid from a length of coax ment using plastic champagne corks
The error due to electrolyte tempera- cable. If the dielectric is transparent, it with a hole drilled through the centre
ture variation depends on the dimen- is solid polyethylene with µr = 2.3. Nat- is reasonably effective. Don t forget to
sions of the sensor tube, and with the urally, you can also use a glass tube ( r also drill a vent hole.
prototype arrangement it is approxi- range: 6 to 8) for the sensor. (080707-I)
46 elektor - 5/2009