Mashhour M. Bani Amer , Assistant Professor
Department of Biomedical Engineering, Faculty of Engineering, Jordan University of Science and
Technology, P.O.Box 3030, Irbid 22110, Jordan.
Abstract
Precise capacitance- to - voltage (C/V) converters research is reviewed. A comparison of direct and indirect C/V converters is briefly presented. The design techniques of C/V converter circuits are discussed. The practical investigations of designed C/V converters are explained with examples to illustrate the achievable characteristics.
1. Introduction
Capacitance is a valuable parameter in electronics and therefore many devices have been developed to convert it to measurable electrical signal [1]-[5]. The conversion of a capacitance - to - voltage plays an important role in capacitive transducers as well as for characterizing RC active circuits. Capacitive transducers are widely used especially in biomedical engineering, for example, for measurement of blood pressure, acceleration, displacement, moisture of material and component concentration in multi component fluids [6], [7]. The operation of capacitance sensors is based on conversion of measured physical parameter (pressure, acceleration, and displacement) into capacitance.
Therefore, to measure the capacitance, which is proportional to the desired physical parameter by electrical method, this capacitance must be converted into electrical signal (usually voltage). The electronic circuit used for this purpose is called capacitance - to - voltage converter (C/V). The C/V converters are usually integrated within the sensor in one package to form a capacitance - to - voltage transducer [8],
[9].
The C/V circuits can be divided into direct or indirect converters. The direct C/V converters convert the capacitance - to - voltage directly while the indirect ones convert first the capacitance into frequency or time and then this frequency or time is converted into voltage.
Of course, before designing the direct or indirect C/V converters, a lot of requirements that decide about the quality of designed C/V converter must be established. These requirements are:
1. Nonlinearity
2. Resolution
3. Sensitivity
4. Accuracy
5. Stability
6. Reliability
7. Generated total output noise
8. Cost
Unfortunately, a lot of recent researches in this field do not take into consideration all of the above requirements which may lead to erroneous C/V conversion, caused by poor reliability, short - term stability, bad linearity or low
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accuracy [10]-[14]. The present paper deals with experimental analysis and practical design of C/V converters taking into accounts all of the above requirements.
2. Direct Capacitance - to - Voltage Converters
To simplify the presentation of the direct C/V converters, they are divided into two categories: conventional C/V converters (impedance bridge and diode quad circuit) and the proposed C/V converter (capacitive voltage divider).
2 .1. The conventional direct C/V converters
The conventional impedance bridge, as described by Lion [10], is shown in Figure
1(a). A square - wave generator E i , drives the network with a frequency f , and the output voltage V o
, is given by the following equation, [10] :
V o
= [ E i
f R R
L
(R+2R
L
) (C
1
-C
2
) ] / (R+R
L
) .................(1)
To improve the design flexibility and reduce the power consumption the resistor R and R
1
Fig.1(a) are usually replaced by two diodes (Fig.1(b)).
Fig. 1. The conventional Capacitance - to - voltage converter [10]
(a) Twin bridge circuit
(b) Modified bridge circuit
The diode quad circuit is a modification of the conventional C/F converter shown in
Fig.1(b). It is based on using commercially available matched diode quads which simplifies the circuit and improves its stability. Although, the diode quad circuit is an improved derivation of the circuit in Fig.1(b), it has the following disadvantages:
(i) The full - scale output range is limited due to non-linearity and
(ii) gain roll-off.
The sensitivity and resolution of this circuit is reduced due to effects of diodes stray capacitances and elements interconnection.
(iii) The electronic circuit, which recovers the measured capacitance
(iv)
C x
from the voltage V o
is not simple. This decreases the accuracy of C x
measurements (caused by error propagation) and reliability of the designed system.
It needs two square signal sources which increases the cost of the
C/V converter.
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2.2. The proposed direct C/V converter
The previously discussed two methods were published in literature for directly conversion of capacitance to voltage. These methods have many drawbacks. This is why a decision was taken to design a simple, precise and reliable C/V converter free from previously discussed disadvantages. This simple C/V converter is shown in
Fig.3. If a sinusoidal signal V in
is applied to the input terminals of the capacitive voltage divider as shown in Fig.2, then the output voltage V out
can be given by:
V out(rms)
= V in(rms)
* C x
/ (C
1
+C x
) .............................. (2)
where C x
is the measured capacitance while C
1 is a fixed capacitance .
Figure 2. Circuit diagram of the proposed C/V converter (capacitive voltage divider).
Of course, the linearity of this circuit is depending directly upon the ratio
C x
/(C
1
+ C x
). Thus, in order to achieve good linearity, the fixed capacitance C
1
must be at least ten times bigger than the measured C x
. If this condition is achieved then equation 3 is reduced to:
V out
(rms) = V in
(rms) * C x
/ C
1
...........................(3)
Therefore, the measured capacitance C x
, can be expressed as :
C x
= V out
(rms) * C
1
/ V in
(rms) ..........................(4)
Of course, C
1
and V in are known and have fixed values. Thus, if we assume that
C
1
/ V in
(rms)= a, then:
C x
= a V out
(rms) .............................................(5)
Equation (5) implies that the proposed C/V converter has a linear characteristic between the measured capacitance C x
and its output voltage (V out
). Moreover, in comparison with the previously discussed conventional C/V converter, this circuit is cheaper, more reliable and has better stability.
The output signal (V out
) of the capacitive voltage divider is sinusoidal signal. The measured capacitance is proportional to the root mean square (rms) value of the output voltage (Eq.5). Thus, to simplify the electronic recovering of the capacitance using
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Eq.5, this AC voltage must be converted into DC voltage that will represent the
V out
(rms). Of course, the designed AC/DC converter must be precise and accurate.
Thus, the classical bridge rectifier circuit cannot be used because a voltage drop of
1.4V occurs across the diodes. Moreover, the output voltage of any rectifier circuit is directly proportional to the average value but not to the rms value of its input voltage. So, these problems must be taken into consideration during the design of
AC/DC converter, otherwise an erroneous results may occur. To overcome these problems, a new AC/DC converter is proposed (Fig. 3). In this circuit, the capacitor
C is a rectifier filter while the identical diodes D
1
and D
2
form a half-wave rectifier and these diodes are arranged in a way in which no drop in the output voltage of the capacitive voltage divider across these diodes will occur. Furthermore, the value of R
1 and R
2
were selected to ensure that the proposed AC/DC converter gives a DC output equals to the V out(rms) of the capacitive voltage divider. Thus, the proposed converter is a precise one because there is no loss of the output signal of the capacitive voltage divider during its conversion into DC.
The complete circuit diagram of the designed C/V converter is shown in Fig.4. The input stage of the circuit in Fig.4 is a sine wave oscillator with an oscillation frequency f=1.6 kHz and 5 V amplitude. Of course, this circuit can be easily integrated to obtain a miniature IC C/V converter.
Fig. 3. Circuit diagram of designed precise AC-to-DC converter.
Fig. 4. The complete circuit of the proposed C/V converter.
The above circuit is experimentally tested for different ranges of C x
. A sample of the obtained results for the measured capacitance C x
in the range of 1

F to 1 mF is
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shown in Fig. 5. From this Figure, it is easy to see that this C/V converter has a linear capacitance-voltage characteristic.
400
300
200
100
0
0 100 200 300 400 500 600
Measured Capacitance
700 800 900 1000
Fig. 5. Capacitance-Voltage characteristic of the proposed C/V converter.(C
3 is set to 10 mF)
. Indirect Capacitance-to-Voltage Converters
The indirect conversion of capacitance-to-voltage is based on conversion of capacitance changes into frequency or time periods. However these indirect C/V converters have many troubles . First, the output frequency, which is proportional to the measured capacitance, cannot be easily converted into voltage if it is necessary.
Second, the control of switches requires a relatively complex electronic system. This is why attempt has been made to study the problem of indirect C - to - V conversion.
This study was lead to design a linear, accurate, simple, reliable and cheap C/V converter.
The simplest way to convert the capacitance to frequency can be done by using the 555 timer in the a stable mode (Fig. 6), [18]. The output frequency of 555 timer in case of operation in the a stable mode is given by equation (6).
f = 1.44/{C ext
* (R
1
+ 2R
2
) } ..............................(6)
Therefore, if R
1
and R
2
are fixed resistors then the frequency f will be function of measured capacitance C ext
only. Thus the change in the capacitance C ext
will cause a change in the output frequency f of 555 timer. This frequency can be converted into voltage using the linear frequency-to-voltage (F/V) LM2917 converter [19].
Unfortunately, the capacitance-frequency (C-F) characteristic curve of 555 timer is nonlinear (Fig.7). So, it does not easy to recover the measured capacitance by simple analog electronic system which increases the complexity and decreases the reliability of the designed C/V converter.
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Fig. 6. Circuit diagram of 555 timer configured as C/F converter
16
14
12
10
8
6
4
2
0
0 200 400
C ext
[pF]
600 800 1000
Fig. 7. C-F characteristic curve of 555 timer in case of R
1
= R
2
=1 M

To eliminate these disadvantages, a simple and linear C/V converter is built using the LM2917 as C/V converter instead of its usual use as F/V converter. This is made possible by building an external square-wave generator using the 555 timer with f=1136 Hz that drives the LM2917 and connecting RC elements with LM2917 that ensure its operation as C/V converter (Fig. 8). Then, the obtained circuit is experimentally tested and the obtained C-V characteristic curve is shown in Fig. 9.
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Fig. 8. The proposed indirect Capacitance-to-Voltage Converter
14
12
10
8
6
4
2
0
0 100 200 300 400 500
C
1
(pF)
600 700 800 900 1000
Figure 9. Capacitance-to voltage characteristic curve of the proposed indirect C/V converter.
The relationship between the measured capacitance (C x
), and output voltage (V out
) of
C/V converter shown in Fig.10, can be expressed mathematically by:
V out
= f in
* C x
* R
3
* V cc
..............................(7)
where
f in
- the frequency of output signal of 555 timer
R
3
- the resistance that is connected to pin 3 of LM2917.
V cc
- supply voltage that is connected to LM2917
Thus, if f in
, R
3
and V cc
have fixed values then the change of output voltage (V out
) will be directly proportional to the change of measured capacitance. Therefore, the suggested circuit in Figure 10 forms a linear C/V converter. Of course, the selection of values of f in
, R
3
and V cc
depends on application range of the C/V converter .
The proposed C/V converter was applied to design a capacitance meter to measure the capacitance in the range 0.1 nF to 10 mF by setting f in
= 1 KHz , V cc
=
10V and R
3
= 1 M

. The obtained results using this C/V converter were precise. The parameters of the proposed C/V converter could be improved by its integrating to
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obtain it in the form of IC C/V converter.
4. Experimental Results
The proposed C/V converters shown in Figures 4 & 8 and the diode quad C/V converter (modified version of Fig(1.b)) were built in the laboratory and experimentally tested to evaluate their linearity, resolution, sensitivity, accuracy, stability and generated output noise.
To determine the nonlinearity of each C/V converter a lot of experimental measurements were performed. The measuring principle was based on measurement the output voltage for tested C/V converter at each change of the measured capacitance C x
. The results obtained are presented on Fig.5 and Fig.9. The nonlinearity measured over 0

F-1000

F range was found to be less than 100 ppm for the capacitive voltage divider and about 215 ppm for the C/V converter shown in
Fig. 8. For the diode quad C/V converter which is the best C/V converter among the previously discussed conventional converters, the measured nonlinearity was 137 ppm over the range 0

F-1000

F.
The resolution of C/V converter can be defined as the largest change in the measured capacitance that can occur without any corresponding change in the output voltage. From experimental point of view, it is difficult to realize small variations in the range of aF of the measured capacitance. However, to overcome this problem,
SPICE simulations were carried out with small changes (less than 10 aF) of the measured C x
. The resolution obtained was 60 aF for the C/V converter, 62 aF for the capacitive voltage-divider, and 83 aF for the circuit shown in Fig. 8.
The sensitivity is the rate of change of the output voltage with respect to the change in the measured capacitance. The, sensitivity is found to be 0.40 mV/ the capacitive-voltage divider C/V converter, 3.23 mV/ shown in Fig.8, and 0.27 mV//

F for the diode quad C/V converter.

F for

F for the C/V converter
The accuracy of the conventional or proposed C/V converters is influenced by two main sources of errors: no idealities and nonlinearity. The nonidealities in the C/V converters lead to additive and multiplicative errors. The main source of these errors is the operational amplifier (op-amp) nonidealities that include the op-amp input offset voltage and currents, input offset voltage drift with temperature and slew rate.
The additive and multiplicative errors can be eliminated using the three-signal approach [1]. Therefore, the nonlinearity is the only error source that affects the accuracy of C/V converter. Thus, the accuracy of the C/V converters is nearly equal to the nonlinearity, provided that the three-signal approach is applied to determine C x
.
The reliability cannot be measured experimentally. However, the probability of fault occurrence in the proposed direct C/V converters is less than the conventional
C/V converters.
The stability of the proposed and conventional C/V converters was also experimentally evaluated. This was done by making use of a millivoltmeter connected at the C/V converter output to measure the drift of converter output voltage during a certain period of time. For each C/V converter, the value of measured capacitance C x was selected to obtain a 10 mV output signal (V out
= 10 mV). The conventional and proposed C/V converters were placed in shielded boxes at ambient temperature. After
24 hours, the output signal was 10 mV, with small slow fluctuations with maximum amplitude of 2 mV for the capacitive-voltage divider C/V converter, 7 mV for the indirect proposed C/V converter, and 6 mV for the diode quad C/V converter.
Practically, this means that the voltage-divider C/V converter has better stability than the conventional C/V converters.
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Each element in C/V converter circuit generates a noise . Therefore, it is very important to measure experimentally the total output noise originated from C/V converter. The spectral density of the output noise voltage of the proposed and conventional converters was experimentally measured with a spectrum analyzer
HP35670A. The obtained total output noise voltage was 38 nV/ Hz for the capacitive-voltage divider C/V converter, 54 nV/ Hz for the indirect C/V converter shown in Fig. 8 and 58 nV/ Hz for the diode quad C/V converter.
5. Conclusions
From the experimental investigations discussed previously, it can be concluded that the designed C/V converters have many advantages over the conventional C/V converters such as long-term stability, simplicity, good sensitivity, high linearity and reliability and low cost (Tab.1).
Table 1. Summary results of a comparison between the conventional and proposed
C/V converter
Parameter
C/V converters
Conventional C/V converter
Diode quad
Proposed C/V converters
Capacitive-Voltage
Divider (Fig.4)
Indirect C/V
Converter (Fig.8)
137 ppm 100 ppm 215 ppm Nonlinearity
Resolution
Sensitivity
Accuracy
60 aF
0.27 mV/

F
170 ppm
62 aF
0.40 mV/

F
100 ppm
83 aF
3.23 mV/

F
120 ppm
Stability
Generated Output
Noise
Reliability
Cost
Stable
58 nV/
High
Low
Hz
Long-term stability
38 nV/ Hz
The highest
The lowest
Stable
54 nV/
High
Hz
Low
The suggested in this paper C/V converters are universal. This means that they can be used to convert the capacitance change of a capacitive transducer into voltage or a capacitance of discrete capacitors into voltage with better accuracy and linearity than the conventional C/V converters. Moreover, the designed direct or indirect C/V converters do not require other circuits to convert capacitance to voltage. But, the published C/V converters such as impedance bridge or diode quad circuit require additional electronic circuits such as square-wave oscillators and a complex system for recovering the capacitance from the output voltage of these C/V converters which increases the cost and decreases the reliability of these C/V converters in comparison with the proposed converters. Furthermore, the suggested converters can be easily adapted for different applications because the selection of components that appear in these converters is simpler than the conventional converters.
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