IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 45, NO. 2, APRIL 1996
A Very Accurate Measurement System
for Multielectrode Capacitive Sensors
Ferry N. Toth, Gerard C. M. Meijer, and I-Iarry M. M. Kerkvliet
Abstruct- A very accurate capacitance-measurement system
consisting of a discrete capacitance-dependent oscillator and a
microcontroller has been developed. It can measure multielec-
trode capacitors with capacitances up to 2 pF, with an accuracy
of 100 ppm with respect to a reference capacitor. The resolution
amounts to 50 aF with a total measurement time of 300 ms.
HE capacitance-measurement system presented here is
T based on earlier work [I]. The previous design involved a
linear capacitance-controlled oscillator (the so-called modified
Martin oscillator) that allowed several capacitors and an offset
capacitance to be measured in exactly the same way. By ap-
plying continuous auto-calibration, gain and offset errors were
reduced to an insignificant level. However, the previous system
had two major disadvantages when applied in capacitive sensor
First, it only measured capacitances with a common elec-
trode. More advanced multi-electrode structures, which are
often required in capacitive position sensors -, call for
multiplexing on both sides of the capacitances. Unfortunately,
adding an additional multiplexer at the input of the system can
disturb the continuous auto-calibration scheme, since the par-
asitic capacitances must not change during the measurement
Second, it could only measure accurately over a 50 f F range.
With a 2 pF range the accuracy degraded to 0.4%. Applications
in accurate weighing equipment, angular encoders  and
position sensors require a much higher accuracy over a 1 pF
The new circuit design implements double-sided multiplex-
ing and also improves the linearity by more than one order of
magnitude. The concepts presented in  and  are used to
reduce the offset, the gain and the effect of the capacitance
of the connecting cables to an insignificant level. The circuit
can be integrated on a chip or realized using readily available
components, which allows an economical production of both
small and large series.
Manuscript received April 24, 1995; revised December 26, 1995. This work
was sponsored by Enraf BV and STW, the Duth Technology Foundation.
The authors are with the Faculty of Electrical Engineering-DIMES,
University of Technology, Mekelweg 4, 2628 AG Delft, The Netherlands.
Publisher Item Identifier S 0018-9456(96)03514-0.
Fig. 1. Elirnination of parasitic capacitances.
11. BASIC PRINCIPLES
The system is based on a capacitance-controlled oscillator.
Because a microcontroller is used to measure the period
and to control the multiplexer, several capacitances can be
measured sequentially. A number of measures have been taken
to minimize the effect of the main nonidealities. Each of these
will be diiscussed in turn below.
Several parasitic capacitances can be seen in Fig. 1. As will
be shown below, the effects of cable capacitances Ccable, a and
since the parasitic capacitor C,,,
Cz,a it cannot be eliminated electronically. Still it can be
sufficiently reduced by shielding the terminals A and B.
zn will be reduced to an insignificant level. However,
is parallel to the measurand
B. Two-Port Measurement
Although shielding reduces C,,, , it greatly increases cable
Capacitances Ccable, i and (?,-able, in. It is useful to look at the
capacitance as a two-port (Fig. 1). In that case, the effect of
Ccable,i can be eliminated by connecting an ideal voltage
source to terminal A, and Ccable,in can be eliminated by
connecting an ideal current meter to terminal B. In both cases,
the cable capacitances are effectively shorted.
A practical circuit is shown in Fig. 2. Here the NAND-
gates operate as low-impedance voltage sources with on/off
switches. The op amp operates together with Cf as a low-
impedance charge amplifier. The capacitance CO, results from
0018-9456/96$05.00 0 1996 IEEE