1
Task of Constructor Design
Jakub Betiuk
Abstract - A new capacitance measurement system, based
on differential amplifier principle for electrical
capacitance tomography has been developed.
It is a novel methods no using yet, the resolution of
measured depend of input signals, and frequency of this
signals.
Keywords - Measurement, Capacitance, Circuit,
Tomography.
I. INTRODUCTION
Electrical capacitance tomography (ECT), started in the mid1980s, is a method for measuring spatial distribution of
dielectric constant.
Dielectric constant is measured via capacitance between two
electrodes.
It is quite difficult problem because, this capacitance is
changing in order of magnitude 1fF. A measured system also
must correctly work witch large standing capacitance derived
from connectors between measured systems and sensors [1].
.
II. DESCRIPTION
In this method, the measurement capacitance is a part of
differential amplifier circuit. One of the measured capacitor
electrode is connected to AC signal generator [2]. The other
capacitor electrode is connected to operational amplifier
which works in differential configuration
This can be expressed mathematically as:
(1)
I C  C dUdtIN
If we multiply slew rate of input signal then value of Ic - which
represent capacitance- multiply too, and increase SNR.
Output voltage in this circuit is given as:
U OUT  R2C2
dU IN
dt
(2)
where:
- R2 constance value (feedback loop);
- C1 measured capacitance;
dU
The output voltage depend of R2 and dtIN (slew rate) value.
In this circuit we can use a large value of this parameters and
get a high sensitive to change capacitance.
For example to get difference output voltage in order of
magnitude 10 mV while measuring difference of capacitance
in order of magnitude 1 fF we have to use: -R2 value order of
magnitude M and large value of dUdtIN  10M Vs .
Differential amplifier is sensitive to high frequency noise,
because its gain rise with input signal frequency. The grate
part of noise have high frequency character.
To lower susceptibility of the measurement circuit on high
frequency noise additional elements R1, C2 were added.
For signals of frequency much higher then:
(3)
f  max 2R12C2 , 21R1C1


Gain of measured circuit is finite and given as:
Auf
R22  X C2

R X
2
1
2
2
C1
(4)
For frequency that fulfil condition Eq.3 reactance XC1 and
resistance R2 can be omitted and gain of measurement circuit
can be expressed mathematically as:
R ||X
AU  R  X
2
1
Fig. 1.Differential amplifiers.
Electronic circuit is shown on Fig. 1.
It is a differential circuit with additional capacitance C2 and
resistance R1. Those elements prevent from amplifying high
frequency signals. The C1 is a measured capacitance. During
rising edge of input triangle signal UIN there is a constant
voltage on output of the measurement circuit which is
proportional to slew rate of edge and measured capacitance.
Jakub Betiuk

 0
 
f 
C2

 0
f 
C1

 R1
f 
(5)
In practice shown circuit does not amplify high frequency
Eq.3 noise but also it does not muffle it according to
expression Eq.5.
In this circuit I use low-noise, wide-band operational
amplifiers witch low value of input bias current. To reduce a
influence of input offset voltage bipolar output circuit have to
be use. That kind of circuit is show in Fig. 2.
Technical University of Łódź
E-mail: jbetiuk@kis.p.lodz.pl
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE
2
on Industrial Process Tomography , Buxton, Greater
Manchester April 14-17 1999.
[2] Baoliang Wang, Zhiyao Huang, Haiqing Li “A Novel
Capacitance Measurement Circuit for Electrical
Capacitance Tomography”
2nd Word Congress on
Industrial Process Tomography, Hannover, Germany, 29 th
– 31st August 2001.
III. CONCLUSION
Fig. 2. Circuit witch bipolar signal output.
The UIN is triangle signal. Output signal UOUT is negative
when input edge is falling and positive when this edge is rising
as show in Fig. 3.
Presented circuit is highly sensitive for low level changes of
capacitance. Measurement range can be easily changed
through slew rate change of UIN. Slew rate change could be
easily implement with DDS generator. There is still problem
with uncompensated input current of amplifier.
Fig. 3. Bipolar signal
The offset voltage of operational amplifier is added to bought
polarity signal. In next step the active rectifier separate bipolar
signal. This separated signal is given to differential
operational amplifier as show in Figure 2.. In this case output
voltage UCAP is given by:
U CAP  U OUTp  Vos   U OUTn  Vos 
U CAP  U OUTp  Vos  U OUTn  Vos
(5)
U CAP  U OUTp  U OUTn
where:
-
UCAP – output signal.
-
UOUTp – positive part of bipolar signal.
-
UOUTn – negative part of bipolar signal.
-
VOS – offset voltage of operational amplifier
As wee can see the offset voltage VOS is reduce and output
signal is increase twofold.
REFERENCES
[1] Yang W, Q. “Evaluation of Integrated Electrodes for
Electrical Capacitance Tomography” 1st Word Congress
CADSM’2007, February 20-24, 2007, Polyana, UKRAINE