# Patent

## Title
Circuit and method for sensing a differential capacitance

## Abstract

A circuit for sensing a differential capacitance includes a charge-storing circuit to generate a first output voltage and a second output voltage related to capacitances at two terminals of the differential capacitance, respectively, an operational amplifier to amplify the difference between the first and second output voltages to generate a sensing value, a first sampling capacitor having one terminal connected to the negative input terminal and the other terminal receiving the first or second output voltage, and a second sampling capacitor having one terminal connected to the negative input terminal and the other terminal switched to the output terminal of the operational amplifier. The second sampling capacitor stores a non-ideal error value to offset the non-ideal effect of the operational amplifier imparted on the sensing value.

## Background
This application is a divisional application of U.S. patent application Ser. No. 13/461,483, filed on May 1, 2012, the content of which is incorporated herein by reference in its entirety.


FIELD OF THE INVENTION
The present invention is related generally to a circuit and method for sensing a differential capacitance and, more particularly, to a circuit and method for sensing a differential capacitance capable of reducing the non-ideal effects of an operational amplifier imparted on the output sensing result.
BACKGROUND OF THE INVENTION
Differential capacitance is also referred to as electrode capacitance, which is the difference between the capacitances established at two electrodes. Sensors working thereupon have been developed and extensively used for sensing capacitive variations caused by physical factors, such as pressures, acceleration, linear displacement and rotational angles. While the circuit layouts may vary with practical sensing requirements, such sensors generally produce the sensing value according to the difference between the individual capacitances of two electrodes therein.
U.S. Pat. No. 6,949,937 has proposed a sensing circuit as depicted in FIG. 1, which includes a switched capacitor front-end 12 and an amplifier stage 14. A differential capacitance 10 is a capacitance between two electrodes and may be regarded as a combination of a pair of variable capacitors CT1 and CT2. The switched capacitor front-end 12 that includes a switching circuit 16 and a charge-storing circuit 18 is connected to the capacitors CT1 and CT2 at sensing terminals Input1 and Input2, respectively. By switching switches S1-S8 in the switching circuit 16, the capacitors CT1 and CT2 are connected to power sources VDD and VSS for supplying charges as desired. Then the charges of the capacitors CT1 and CT2 are repeatedly transferred to the capacitors C1 and C2 in the charge-storing circuit 18. Afterward, the charges of the capacitors C1 and C2 are stored into two terminals of a floating capacitor CD, so that the potential difference VCD between the two terminals of the capacitor CD is representative of the difference between the capacitances CT1 and CT2. At last, the two terminals of the capacitor CD are connected to the inputs of the amplifier stage 14, so that the amplifier stage 14 amplifies and then outputs the potential difference VCD, thereby accomplishing measurement of the differential capacitance 10. FIGS. 2A-2E illustrate operation of the switched capacitor front-end 12 shown in FIG. 1. This art repeats operation as shown in FIGS. 2A-2D in an over-sampling manner without resetting switches SR1 and SR2, thereby repeatedly charging and discharging the capacitors CT1 and CT2, and repeatedly transferring the charges to the individual storing capacitor C1 or C2 inside the charge-storing circuit 18, so as to collect charge averages within the switched capacitor front-end 12 and in turn suppress RF interference or power source noises. Afterward, as shown in FIG. 2E, the charges of the capacitors C1 and C2 are stored to the two terminals of the capacitor CD, and then amplified and output by the amplifier stage 14 that is at the back-end part of FIG. 1 and connected to the two terminals of the capacitor CD. Since this art performs averaging measurement by repeatedly operating only the switched capacitor front-end 12 in the front-end part instead of repeatedly operating the entire circuit, it helps to reduce power consumption.
However, the amplifier stage 14 uses an operational amplifier to directly amplify the difference VCD between the corresponding output voltages VOUT1 and VOUT2, so the non-ideal effects of the operational amplifier, e.g. offset, flicker noise and finite gain error, are output through the output terminal of the operational amplifier as well, making the sensing performance deteriorated.
In addition, the above operation is not effective enough in noise reduction. Taking the capacitor C1 for example, according to the law of charge conservation, the output voltage after n rounds of charge transfer is determined as




  
    
      
        
          
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    where X is typically between 0.1 and 0.5, and VDDi may be regarded as incorporating RF interference and power source noises while the equivalent power source VDD varies over time. According to the equations Eq-1, Eq-2 and Eq-3, after n rounds of charge sampling and transfer, all the sampled results are affected by the factor X except for that of the n-th round. Since X<1, the earlier sampled result affects the final output less. In other words, VOUT1 will approximate Vn, so the over-sampling operation under this configuration will not effectively average the sampled results to reduce noise.


SUMMARY OF THE INVENTION
An objective of the present invention is to provide a circuit for sensing a differential capacitance capable of reducing the non-ideal effects of an operational amplifier imparted on the output sensing result.
According to the present invention, a circuit for sensing a differential capacitance includes a pair of sensing terminals connected to two terminals of the differential capacitance, respectively, a switching circuit connected to the pair of sensing terminals for being switched to make the two terminals of the differential capacitance get connected to a high-voltage source or a low-voltage source or perform charge transfer, a charge-storing circuit coupled to the switching circuit for storing charges transferred from the differential capacitance in response to the switching of the switching circuit, to generate a first and second output voltages related to the capacitances at the two terminals of the differential capacitance, and an amplifier stage for generating a sensing value according to the difference between the first and second output voltages. The amplifier stage includes an operational amplifier having a positive input terminal connected to a common reference-voltage source, a first switch to receive the first output voltage, a second switch to receive the second output voltage, a first sampling capacitor having one terminal connected to a negative input terminal of the operational amplifier and the other terminal connected to the first and second switches, a third switch connected between the negative input terminal and an output terminal of the operational amplifier, and a second sampling capacitor having one terminal connected to the negative input terminal of the operational amplifier and the other terminal connected to the common reference-voltage source or the output terminal of the operational amplifier by a fourth and fifth switches.



BRIEF DESCRIPTION OF THE DRAWINGS
These and other objectives, features and advantages of the present invention will become apparent to those skilled in the art upon consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a conventional circuit for sensing a differential capacitance;
FIGS. 2A-2E illustrate operation of the switched capacitor front-end shown in FIG. 1;
FIG. 3 is a first embodiment of a circuit for sensing a differential capacitance according to the present invention;
FIGS. 4A-4C illustrate operation of the amplifier stage shown in FIG. 3;
FIG. 5 is a second embodiment of a circuit for sensing a differential capacitance according to the present invention using a two-tier capacitor; and
FIG. 6 is a third embodiment of a circuit for sensing a differential capacitance according to the present invention.



DETAILED DESCRIPTION OF THE INVENTION
The amplifier stage of the present invention operates based on a pseudo correlated double sampling technique to input the sampled voltages by a front-end in different transfer rounds, and uses a capacitor to store an error value of the non-ideal characteristics of an operational amplifier to offset the non-ideal characteristics of the operational amplifier.
FIG. 3 is a first embodiment of a circuit for sensing a differential capacitance according to the present invention, which includes a switching circuit 16, a charge-storing circuit 20 and an amplifier stage 22. The charge-storing circuit 20 includes a plurality of storing capacitors. During operation, it uses switches to make the charges sampled in each transfer round stored into a different storing capacitor, and then connects all the storing capacitors in parallel for outputting, so as to average the sampled inputs and noises. The switching circuit 16 is connected to capacitors CT1 and CT2 at sensing terminals Input1 and Input2, respectively. By switching switches S1-S8 in the switching circuit 16, the capacitors CT1 and CT2 are connected to a low-voltage source or a high-voltage source. The charges of the capacitors CT1 and CT2 are repeatedly transferred to the charge-storing circuit 20, as shown in FIGS. 2A-2D. For all the embodiments described herein, the power source VSS is referred to as the low-voltage source and the power source VDD is referred to as the high-voltage source, which supply charges as desired. The charge-storing circuit 20 includes storing circuits 24 and 26 having a substantially same structure. The storing circuit 24 includes multiple capacitors CS11, CS12 and CS13. During operation, switches SC11, SC12 and SC13 make the charges transferred by the capacitor CT1 in different sampling rounds into different capacitors CS11, CS12 and CS13. At last, the switches SC14, SC15 and SC16 are turned on at a same time to connect all the capacitors CS11, CS12 and CS13 in parallel, so as to generate an output voltage VOUT1. The storing circuit 26 includes multiple capacitors CS21, CS22 and CS23. During operation, switches SC21 SC22 and SC23 make the charges transferred by the capacitor CT2 in different sampling rounds into different capacitors capacitor CS21, CS22 and CS23. At last, the switches SC24, SC25 and SC26 are turned on at a same time to connect all the capacitors CS11, CS12 and CS13 in parallel, so as to generate an output voltage VOUT2. The amplifier stage 22 includes an operational amplifier 28, switches SW1-SW6 and sampling capacitors CA and CB. The operational amplifier 28 has a positive input terminal connected to a common reference-voltage source. The switch SW1 is connected to the storing circuit 24 to receive the output voltage VOUT1, and the switch SW2 is connected to the storing circuit 26 to receive the output voltage VOUT2. The switch SW3 is connected between a negative input terminal and an output terminal of the operational amplifier 28. The sampling capacitor CA has one terminal connected to the negative input terminal of the operational amplifier 28, and the other terminal connected to the switches SW1 and SW2. The sampling capacitor CB has one terminal connected to the negative input terminal of the operational amplifier 28, and the other terminal connected to the switches SW4 and SW5, so that the sampling capacitor CB is connected to the common reference-voltage source or the output terminal of the operational amplifier 28. The switch SW6 is used to reset the sampling capacitor CA. In one embodiment, the power source VSS is used as the common reference-voltage source. In another embodiment,




  
    
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    is used as the common reference-voltage source.


FIGS. 4A-4C illustrate operation of the amplifier stage 22. At the beginning, as shown in FIG. 4A, the switch SW6 is first turned on to reset the sampling capacitor CA, and at the same time a non-ideal error value Verr at the negative input terminal of the operational amplifier 28 is stored into the sampling capacitor CB. Then, as shown in FIG. 4B, the switches SW1 and SW4 are turned on to sample the output voltage VOUT1 by the sampling capacitor CA. At last, as shown in FIG. 4C, the switches SW2 and SW5 are turned on to make the sampling capacitor CB connected between the negative input terminal and output terminal of the operational amplifier 28, and sample the output voltage VOUT2 by the sampling capacitor CA. After amplified by the amplifier stage 22, the voltage across the sampling capacitor CB is VCB=[(VOUT1-VOUT2)×(CA/CB)+Verr]+(−Verr), where the non-ideal error value Verr is neutralized by the non-ideal effect of the operational amplifier 28, and thus the sensing value VSENS=(VOUT1-VOUT2)×(CA/CB), which is only related to the difference between the output voltages VOUT1 and VOUT2.
For separately storing the charges in different sampling rounds, the charge-storing circuit 20 may use a multi-tier storage approach. For example, as shown in. FIG. 5, the charge-storing circuit 20 has two-tier structure, in which the storing circuits 24 and 26 have a substantially same structure, a two-tier storage structure. An example herein is that the storing circuit 24 repeatedly samples the capacitor CT1, as shown in FIGS. 2A-2B. The charges transferred in a first sampling round are stored into the capacitor CS111, and the charges transferred in a second sampling round are stored into the capacitor CS112. Afterward, the switches SC113 and SC114 are turned on to transfer the charges of the capacitors CS111 and CS112 to the capacitor CS121 for storage. Then the switches SR111 and SR112 are turned on to reset the capacitors CS111 and CS112. The third and fourth transfer rounds are performed in the same manner with the charges stored into the capacitor CS111 and CS112, respectively, before transferred to the capacitor CS122. The fifth and sixth transfer rounds are performed in the same manner with the charges stored into the capacitors CS111 and CS112, respectively, before transferred to the CS123. Then the switches SC124, SC125 and SC126 are turned on, so the output voltage VOUT1 is the average of the 2×3=6 transfer rounds. The capacitor CT2 is sampled in the same manner. Sampling to the capacitor CT1 and the capacitor CT2 may be performed alternately, to further facilitate reducing noises. Operation of the foregoing multi-tier storage structure is described by referring to a two-tier storage structure constructed from N first-tier capacitors and M second-tier for repeatedly sampling the capacitor CT1 for n=N×M rounds. According to the law of charge conservation, the output voltage




  
    
      
        
          
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    where CS1 is the common capacitance of all the first-tier capacitors, and CS2 is the common capacitance of all the second-tier capacitors. By applying the equations Eq-5 and Eq-6 to the equation Eq-4, it is found that the multi-tier storage structure such stores the transferred charges that the input signals and noises are effectively averaged, thereby reducing the impact of noises. Therefore, by designing the charge-storing circuit 20 as a multi-tier storing circuit, the output voltage is close to the average output voltage obtained by performing transfer rounds in the number equal to the product of the amount of capacitors in all the tiers of the multi-tier structure. In other embodiments, the charge-storing circuit 20 may be designed as a storing circuit with three or more tires in the same way.


FIG. 6 is a third embodiment of the circuit for sensing a differential capacitance according to the present invention, which includes a switching circuit 16, a charge-storing circuit 30 and an amplifier stage 22. Similar to the embodiment of FIG. 3, the charge-storing circuit 30 also performs oversampling by using plural storing capacitors, but has three storing circuits 32, 34 and 36, wherein the principle of multiple storing capacitors is applied to the storing circuit 36 floated between the storing circuits 32 and 34. In this system, capacitors CS1 and CS2 in the storing circuits 32 and 34 sample capacitors CT1 and CT2, as shown in FIGS. 2A-2D. After the first transfer round, switches SCD1 and SCD2 are turned on to store charges into the capacitor CD1. Then the capacitors CS1 and CS2 are reset, so that the charges similarly sampled in the second transfer round are stored into the capacitor CD2. Again, the capacitors CS1 and CS2 are reset to make the charges sampled in the third transfer round stored into the capacitor CD3. At last, the capacitors CD1-CD3 are connected in parallel and output, so as to achieve even sampling between the inputs and noises. In other embodiments, the storing circuits 32 and 34 also have multiple storing capacitors or a multi-tier storing capacitor, as the storing circuit 24 or 26 shown in FIG. 3 or FIG. 5 so as to further improve the output.
While the present invention has been described in conjunction with preferred embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and scope thereof as set forth in the appended claims.

## Claims

1. A circuit for sensing a differential capacitance, comprising:
a first sensing terminal and a second sensing terminal connected to two terminals of the differential capacitance, respectively;
a switching circuit connected to the first and second sensing terminals, being switched to make the two terminals of the differential capacitance connected to a high-voltage source or a low-voltage source or to perform charge transfer;
a charge-storing circuit coupled to the switching circuit, storing charges transferred by the differential capacitance in response to switching of the switching circuit, to generate a first output voltage and a second output voltage related to capacitances at the two terminals of the differential capacitance; and
an amplifier stage operative to generate a sensing value according to a difference between the first and second output voltages, the amplifier stage including:
an operational amplifier having a positive input terminal connected to a common reference-voltage source;
a first switch being switched to receive the first output voltage;
a second switch being switched to receive the second output voltage;
a first sampling capacitor having one terminal connected to a negative input terminal of the operational amplifier, and the other terminal connected to the first and second switches;
a third switch connected between the negative input terminal and an output terminal of the operational amplifier; and
a second sampling capacitor having one terminal connected to the negative input terminal of the operational amplifier, and the other terminal connected to the common reference-voltage source or the output terminal of the operational amplifier by a fourth switch and a fifth switch.

2. The circuit of claim 1, wherein the charge-storing circuit comprises:
a first storing circuit including a plurality of first storing capacitors to store charges sampled at one of the terminals of the differential capacitance in different transfer rounds, to generate the first output voltage; and
a second storing circuit including a plurality of second storing capacitors to store charges sampled at the other terminal of the differential capacitance in the different transfer rounds, to generate the second output voltage.

3. The circuit of claim 2, wherein the first and second storing circuits connect the plurality of first storing capacitors in parallel and the plurality of second storing capacitors in parallel to generate the first and second output voltages, respectively.

4. The circuit of claim 2, wherein the plurality of first storing capacitors or the plurality of second storing capacitors comprise:
a plurality of first-tier capacitors for each storing the charges sampled in one of the rounds; and
a plurality of second-tier capacitors for each storing charges of the parallel-connected first-tier capacitors in one of the rounds.

5. The circuit of claim 2, wherein the charge-storing circuit further comprises a third storing circuit having at least one third storing capacitor connected to the first and second storing circuits, for storing charges in the first and second storing circuits into two terminals of the third storing capacitor.

6. The circuit of claim 2, wherein the charge-storing circuit comprises:
a first storing circuit storing charges at one terminal of the differential capacitance into a first storing capacitor;
a second storing circuit storing charges at the other terminal of the differential capacitance into a second storing capacitor; and
a third storing circuit having a plurality of third storing capacitors, each of the third storing capacitor having two terminals connected to the first and second storing circuits, respectively, for storing charges in the first and second storing circuits into different ones of the third storing capacitors in different ones of the rounds, and connecting the plurality of third storing capacitors in parallel to generate the first and second output voltages at two terminals thereof.

7. The circuit of claim 1, wherein the amplifier stage comprises:
a first switch pair connected to the first sensing terminal, having first upper-bridge and lower-bridge switches connected to the high-voltage source and the low-voltage source, respectively;
a second switch pair connected to the second sensing terminal, having second upper-bridge and lower-bridge switches connected to the high-voltage source and the low-voltage source, respectively;
a third switch pair connected to the first storing circuit, being switched to make the first storing circuit connected to either or both of the first and second sensing terminals for charge transfer; and
a fourth switch pair connected to the second storing circuit, being switched to make the second storing circuit connected to either or both of the first and second sensing terminals for charge transfer.