amplifier has to satisfy the following condition:
fT??T12CfCf?Cp2 (9)
where T is the period of the input signal.
Since Cp2 consists of cable capacitances and the input capacitance of the op amp, it may indeed be larger than Cf and can not be neglected.
IV. THE CONCEPT OF THE SYSTEM
The system uses the three-signal concept presented in [2], which is based on the following principles. When we measure a capacitor Cx with a linear system, we obtain a value:
Mx?mCx?Moff (10)
where m is the unknown gain and Moff, the unknown offset.By performing the measurement of a reference quantity Cref, in an identical way and by measuring the offset, Moff,by making m = 0, the parameters m and Moff are eliminated.The final measurement result P is defined as:
P?Mref?MoffMx?Moff (11)
In our case, for the sensor capacitance C, it holds that:
Cx??Axd0??d (12)
where Ax is the area of the electrode, do is the initial distance between them, ε is the dielectric constant and △d is the displacement to be measured. For the reference electrodes it holds that:
Cref??Arefdref (13)
with Aref the area and dref the distance. Substitution of (12) and (13) into (10) and then
into (11) yields:
P?Aref?d0??d?Axdref?a1?d?a0 (14) drefHere, P is a value representing the position while a1 and a0 are unknown, but stable constants. The constant a1 =Aref/Ax is a stable constant provided there is a good mechanical matching between the electrode areas. The constant ao = (Arefd0/(Axdref) will also be a stable constant provided that do and dref are constant. These constants can be determined by a one-time calibration. In many applications this calibration can be omitted; when the displacement sensor is part of a larger system, an overall calibration is required anyway. This overall calibration eliminates the requirement for a separate determination of a1 and a0.
V . THE CAPACITANCE-TO-PERIOD CONVERSION
The signals which are proportional to the capacitor values are converted into a period, using a modified Martin oscillator [4] (Fig. 5j.
When the voltage swing across the capacitor is equal to that across the resistor and the NAND gates are switched off, this oscillator has a period Toff:
Toff = 4RCoff. (15)
Since the value of the resistor is kept constant, the period varies only with the capacitor value. Now, by switching on the right NAND port, the capacitance CX can be connected in parallel to Coff. Then the period becomes:
Tx=4R(Coff+Cx)=4RCx+Toff (16)
The constants R and Toff are eliminated in the way described in Section IV.
In [2] it is shown that the system is immune for most of the nonidealities of the op amp and the comparator, like slewing, limitations of bandwidth and gain, offset voltages,and
input bias currents. These nonidealities only cause additive or multiplicative errors which are eliminated by the three-signal approach.
VI. PERIOD MEASUREMENT WITH A MICROCONTROLLER
Performing period measurement with a microcontroller is an easy task. In our case, an INTEL 87C51FA is used,which has 8 kByte ROM, 256 Byte RAM, and UART for serial communication, and the capability to measure periods with a 333 ns resolution. Even though the counters are 16 b wide, they can easily be extended in the software to 24 b or more.
The period measurement takes place mostly in the hardware of the microcontroller. Therefore, it is possible to let the CPU of the microcontroller perform other tasks at the same time (Fig. 6). For instance, simultaneously with the measurement of period Tx, period Tref and period Toff,the relative capacitance with respect to Cref is calculated according to (11), and the result is transferred through the UART to a personal computer.
Fig. 5. Modified Martin oscillator with microcontroller and electrodes.
Fig. 6. Period measurement as background process.
Fig. 7. Position error as function of the position and estimate of the nonlinearity.
VII. EXPERIMENTAL RESULTS
The sensor is not sensitive to fabrication tolerances of the electrodes. Therefore in our experimental setup we used simple printed circuit board technology to fabricate the electrodes, which have an effective area of 12 mm × 12 mm. The guard electrode has a width of 15 mm, while the distance between the electrodes is about 5 mm. When the distance between the electrodes is varied over a 1 mm range, the capacitance changes from 0.25 pF to 0.3 pF.Thanks to the chosen concept, even a simple dual op amp (TLC272AC) and CMOS NAND’s could be used, allowing a single 5 V supply voltage. The total measurement time amounts to only 100 ms, where the oscillator was running at about 10 kHz.
The system was tested in a fully automated setup, using an electrical XY table, the described sensor and a personal computer. To achieve the required measurement accuracy the setup was autozeroed every minute. In this way the nonlinearity, long-term stability and repeatability have been found to better than 1 μm over a range of 1 mm (Fig.7). This is comparable to the accuracy and range of the system based on a PSD as described in [2].
As a result of these experiments, it was found that the resolution amounts to approximately 20 aF. This result was achieved by averaging over 256 oscillator periods. A further increase of the resolution by lengthening the measurement time is not possible due to the l/f noise produced by the first stages in both the integrator and the Comparator.
The absolute accuracy can be derived from the position accuracy. Since a 1 mm displacement corresponds to a change in capacitance of 50 fF, the absolute accuracy of 1 μm in the position amounts to an absolute accuracy of 50 aF.
CONCLUSION
A low-cost, high-performance displacement sensor has been presented. The system is implemented with simple electrodes, an inexpensive microcontroller and a linear capacitance-to-period converter. When the circuitry is provided with an accurate reference capacitor, the circuit can also be used to replace expensive capacity-measuring systems.
REFERENCES
[1] G. C. M. Meijer and R. Schner, “A linear high-performance PSD displacement transducer with a microcontroller interfacing,” Sensors and Actuators, A21-A23, pp. 538-543, 1990.
电容触摸屏控制设计外文文献及中文翻译
