WO2007111611A1

WO2007111611A1 - Methods and apparatus for differential signaling using absolute pressure sensors

Info

Publication number: WO2007111611A1
Application number: PCT/US2006/011568
Authority: WO
Inventors: Mark E. Schlarmann; Todd F. Miller
Original assignee: Freescale Semiconductor, Inc.
Priority date: 2006-03-29
Filing date: 2006-03-29
Publication date: 2007-10-04
Also published as: EP2002268A4; EP2002268A1

Abstract

A differential circuit (100) is configured to accept a differential excitation voltage (101) across its input terminals (102, 104) and, in conjunction with a pair of capacitive absolute pressure sensors (106, 108), is configured to produce a differential output (115). The excitation voltage (101) at one terminal (102) with respect to a common mode voltage is opposite in polarity from the voltage of the second terminal (104) with respect to the common mode voltage. In this way, absolute pressure sensors can be used in a way that achieves the benefits of differential circuits - e.g., high linearity and increased common mode noise rejection.

Description

METHODS AND APPARATUS FOR DIFFERENTIAL SIGNALING USING ABSOLUTE PRESSURE SENSORS

TECHNICAL FIELD

[0001] The present invention relates generally to pressure sensor devices and, more particularly, to signaling techniques used in conjunction with absolute pressure sensors

BACKGROUND

[0002] Pressure sensor devices utilizing micro-electromechanical systems (MEMS) technology are popular in a wide range of applications. Depending upon the nature of the application, two types of pressure sensors are commonly used: absolute pressure sensors and differential pressure sensors.

[0003] An absolute pressure sensor is a sensor that has an electrical output related to the absolute pressure of an external environment with respect to a known, constant pressure. A differential pressure sensor, on the other hand, is a sensor whose electrical output is related to a difference in pressures between two regions. Thus, an absolute pressure sensor (for example, a MEMS sensor) typically includes a semiconductor membrane separating the external environment from an internal sealed volume having a known pressure, while a differential sensor includes a semiconductor membrane separating two ports coupled to two different pressure levels.

[0004] Because absolute pressure sensors are single-ended (i.e., a single output related to the sensed pressure), the circuits used in connection with absolute pressure sensors are also typically single-ended. In contrast, differential pressure sensors are typically coupled to differential circuits, which offer higher linearity and greater noise immunity than single-ended circuits - particularly with respect to common-mode noise (i.e., noise related to the power supply and ground).

[0005] Absolute pressure sensor are more easily produced in a standard MEMS process flow than are differential sensors. Accordingly, it would be advantageous to use absolute pressure sensors in conjunction with differential circuitry. It is difficult to do so, however. In a traditional differential circuit, the capacitor sizes are fixed and the input quantity is a differential voltage. With differential pressure sensors, the input voltage is fixed, and the capacitance values of the sensors vary. The differential output voltage is then proportional to deviations in the sensor. [0006] Simply replacing the differential pressure sensor with a pair of absolute pressure sensors is ineffective. As the two variable capacitors (i.e., the absolute pressure sensors) vary in unison with pressure rather than varying differentially, the differential output is always zero.

[0007] Accordingly, it would be desirable to provide absolute pressure sensor circuits capable of providing increased linearity and improved noise immunity. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in conjunction with the following figures, wherein like reference numbers refer to similar elements throughout the figures.

[0009] FIG. 1 is a schematic overview of a differential circuit in accordance with one embodiment;

[0010] FIG. 2 is a conceptual, cross-sectional illustration of an exemplary absolute pressure sensor device; and

[0011] FIG. 3 is a schematic overview of a circuit in accordance with another embodiment.

DETAILED DESCRIPTION

[0012] The following detailed description is merely illustrative in nature and is not intended to limit the scope or application of possible embodiments. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary or the following detailed description. [0013] Various embodiments may be described herein in terms of functional and/or logical block components and various processing steps. It should be appreciated that such block components may be realized by any number of hardware, software, and/or firmware components configured to perform the specified functions. For the sake of brevity, conventional techniques related to semiconductor processing, MEMS processing, and analog circuitry are not described herein. [0014] Referring to FIG. 1, a differential circuit 100 in accordance with one embodiment is configured to accept a differential input (or "excitation voltage") 101 across terminals 102 and 104. Acting in conjunction with a pair of absolute pressure sensors 106 and 108 (whose capacitance values are responsive to absolute pressure) and corresponding integration capacitors 118 and 120, the circuit is configured to produce a differential output 115 across terminals 114 and 116.

[0015] As shown in FIG. 1, the bias values at output terminals 114 and 116 are respectively referred to herein as V_op (positive output voltage) and V_0n (negative output voltage). The differential output V_ocι is defined as V_op-V_on. Similarly, the bias values at terminals 102 and 104 are referred to as V_EP (positive component of excitation voltage) and V En (negative component of excitation voltage), where

V_EP and Vε_n have antipodal values with respect to a common mode voltage V_CM, shown conceptually in FIG. 1.

[0016] Differential circuit 100 includes a differential operation amplifier ("op amp" or "amplifier") 130 having signal inputs 131 and 129 coupled to respective integration capacitors (or simply "capacitors") 110 and 112, whose second terminals are coupled to respective outputs 114 and 116 as shown. In the illustrated embodiment, capacitors 110 and 112 have substantially the same capacitance value, designated C₂. As is known in the art, differential op-amp 130 will exhibit a common mode input voltage V_CM- [0017] It will be appreciated by those skilled in the art that the illustrated circuit is simplified for clarity, and that the system will typically include other conventional components and connections. For example, the circuit of FIG. 1 might also include various resistors, reference values, clock circuits, supply voltages, and the like. [0018] Switch components (or simply "switches") 121 and 123 are provided on inputs 102 and 104 respectively, as are switches 122 and 124, which lead to respective ground nodes. A pair of switches 118 and 120 are also provided in parallel with capacitors 110 and 120 as shown. The switching circuitry comprises switches 118, 120, 121, 122, 123, and 124, which are coupled to one or more clock circuits (not shown) and receive respective clock signals suitable for producing a differential output 115. The switch components may be any appropriate device, including switching MOSFETs or the like. [0019] The switching circuitry is configured to selectively charge and discharge the integration capacitors (110, 112) and pressure sensors (106, 108). An exemplary clock signal (not shown) has an even phase (E) and an odd phase (O). In the illustrated embodiment, switches 118 and 120 are closed during the E phase, but are open during the O phase. Similarly, switches 121 and 123 as well as switches 122 and 124 operate in phase with or out of phase with switches 118 and 120, depending upon the particular embodiment. For example, in one embodiment, switches 121 and 123 are closed during the E phase, and switches 122 and 124 are closed during the O phase. Alternatively, switches 121 and 123 are closed during the O phase, and switches 122 and 124 are closed during the E phase.

[0020] The frequency of the clock (or clocks) used to drive the switches may be selected in accordance with known design parameters ~ depending, for example, on the various capacitance values in the circuit. In one embodiment, the clock frequency (and consequently the pulsed output 115) has a frequency of about 500 KHz to 2 MHz. The present invention is not so limited, however.

[0021] Absolute pressure sensors (or simply "sensors") 106 and 108 are coupled to respective input terminals 121 and 123 and respective signal inputs 131 and 129 of op amp 130. As mentioned previously, an absolute pressure sensor is a sensor that has an electrical output related to the absolute pressure of an external environment with respect to a known, constant pressure. In contrast, a differential pressure sensor is a sensor whose electrical output is related to a difference in pressures between two regions. Thus, an absolute pressure sensor typically includes a semiconductor membrane separating the external environment from an internal sealed volume having a known pressure, while a differential sensor includes a semiconductor membrane separating two ports coupled to two different pressure levels.

[0022] Sensors 106 and 108 may be any suitable type of absolute pressure sensor. In one embodiment, sensors 106 and 108 are a matched pair of MEMS pressure sensors. Referring to the conceptual diagram shown in PIG. 2, for example, a typical MEMS pressure sensor 106 includes a diaphragm or other such structure 202 that encloses an environment 210. The position of structure 202 with respect to a stationary capacitive plate 208 is function of the difference between the pressure of internal chamber 210 and external environment 211.

[0023] Thus, the effective capacitance of the structure (C i_a) varies in a known way with external pressure, as the internal pressure is substantially constant. The relationship between absolute pressure and capacitance is referred to herein as the sensor capacitance function, which may be linear within certain ranges and non-linear within other ranges, as is known in the art. In one embodiment, for example, sensors 106 and 108 have respective capacitance values that vary between about 380 and 400 fF (femto-Farads) in accordance with the sensor capacitance function. In such an embodiment, C_∑ may be on the order of 800 fF. It will be appreciated, however, that these values are provided for the purpose of example only, and that the invention is not so limited.

[0024] Referring again to FIG. 1, sensor 106 is suitably modeled as a capacitor having a value Cj_n, and sensor 108 is modeled as a capacitor having a value C^. It will thus be appreciated that the sensors will have substantially the same capacitance value c as a function of external pressure p:

^Xa = c(_P)

^Llb = c(_P)

[0025] In accordance with one embodiment, Vβ_P 102 has a voltage that is opposite in polarity with and equal in magnitude to V _En 104 with respect to the common mode voltage V_CM- That is, given an excitation voltage VE = Vsp-Vs_n-

V_Ep = V_CM +^- ; and

v_En =v_CM -^

[0026] As a result, it can be shown that, during operation of the switching circuitry, the differential output V_od varies linearly with the sensor capacitance function and the excitation voltage as follows:

V^ -2-^-V,

[0027] Thus, although sensors 106 and 108 are absolute rather than differential sensors, the electric signaling in the resulting circuit is differential. Since the excitation voltage has positive and negative polarities with respect to the common mode voltage, the output is directly proportional to the product of the excitation voltage and the sensor capacitance function, and inversely proportional to the integration capacitor value. In this way, differential circuit techniques traditionally only used with differential pressure sensors can be employed with absolute pressure sensors, leading to higher linearity and greater noise immunity as compared to traditional circuits used in conjunction with absolute pressure sensors.

[0028] The operating voltages of differential input 101 and other components may be selected to achieve any particular output 115 depending upon, for example, the supply voltage, the nature of op-amp 130, etc. In one embodiment, with a nominal 5 V supply, the differential circuit has the following approximately input values: V_CM=2.5V, Ve_n=OJ V, V_Ep=4:5 V, and V_£=4.0 V.

[0029] FIG. 3 depicts an alternative embodiment, wherein switches 121 and 124 are in phase with the "E" phase of switches 118 and 120, and switches 122 and 123 are in phase with the "O" phase of switches 118 and 120. Alternate phasing is shown in parenthesis, as with FIG. 2. In this embodiment, the use of alternating phases eliminates the need for a differential input voltage. Rather, a single ended input 101 is used, and the output during the odd phase exhibits a relationship as described above. [0030] It will appreciated that the various components of circuit 100, including pressure sensors 106 and 108, may be implemented in a variety of ways and employ any number of components and semiconductor devices. In one embodiment, sensors 106 and 108 are integrated monolithically on a semiconductor chip that also includes the active and passive electrical components of circuit 100. In this regard, capacitors 110 and 112, resistors 118 120, 121, 122, 123, and 124, and op amp 130 may be fabricated in accordance with conventional semiconductor processing techniques (including conventional surface micromachining and MEMS techniques) known in the art. [0031] In summary, what has been described is, in accordance with one embodiment, a differential circuit comprising: a differential input having a first input terminal, a second input terminal, and an excitation voltage applied therebetween, wherein a first voltage at the first input terminal with respect to a common mode voltage is opposite in polarity from a second voltage at the second input terminal with respect to the common mode voltage; a first pressure sensor coupled to the first input terminal and having a first capacitance that varies with an absolute pressure in accordance with a sensor capacitance function; a second pressure sensor coupled to the second input terminal and having a second capacitance that varies with the absolute pressure in accordance with the sensor capacitance function; and a differential amplifier coupled to the first pressure sensor and the second pressure sensor, the differential amplifier having a first output terminal and a second output terminal that together produce a differential output voltage linearly related to the sensor capacitance function. In one embodiment, the first and second pressure sensors are micro-electromechanical system (MEMS) pressure sensors. [0032] In accordance with one embodiment, the differential output voltage is directly proportional to the product of the excitation voltage and the sensor capacitance function. For example, given a sensor capacitance function of C(p), an excitation voltage of V_E, and a circuit further including a first integration capacitor coupled to the differential amplifier and the first pressure sensor and a second integration capacitor coupled to the differential amplifier and the second pressure sensor (wherein the first and second integration capacitors have a value C₂) the differential output voltage is substantially equal to - [2OP)VE)IC₂.

[0033] In accordance with another embodiment, the circuit further includes: a first integration capacitor coupled to the differential amplifier and the first pressure sensor; a second integration capacitor coupled to the differential amplifier and the second pressure sensor; and switching circuitry configured to selectively charge and discharge the first and second integration capacitors and the first and second pressure sensors. In one embodiment, the first pressure sensor has a capacitance range of about 380-400 fF. [0034] The switching circuitry may include: a first switch coupled in parallel with the first integration capacitor; a second switch coupled in parallel with the second integration capacitor; a third switch coupled between the first input terminal and the first pressure sensor; a fourth switch coupled between the second input terminal and the second pressure sensor; a fifth switch coupled between the first input terminal and a ground node; a sixth switch coupled between the second input terminal and the ground node; a clock signal having an odd phase and an even phase, wherein: the first switch and the second switch are activated during the even phase; the third switch and the fourth switch are activated, in a first mode, during the even phase, and in a second mode, during the odd phase; and the fifth switch and the fifth switch are activated, in the first mode, during the odd phase, and in a second mode, during the even phase.

[0035] In accordance with another embodiment, a semiconductor device comprises: a first absolute pressure sensor having a first capacitance that varies with an absolute pressure in accordance with a sensor capacitance function (e.g., a linear or non-linear function), the first absolute pressure sensor connected between a first node and a second node; a second pressure sensor having a second capacitance that varies with the absolute pressure in accordance with the sensor capacitance function, the second absolute pressure sensor connected between a third node and a fourth node; a differential input having a first input terminal at the first node set to a first voltage with respect to a common mode voltage and a second input terminal at the third node set to a second voltage with respect to the common mode voltage, wherein the difference between the first voltage and the second voltage defines an excitation voltage, and wherein the second voltage has a magnitude that is the same as the first voltage and has a polarity that is opposite of the first voltage; a differential amplifier having a first signal input coupled to the second node, a second signal input coupled to the fourth node, a first output terminal connected to a fifth node, and a second output terminal coupled to a sixth node; and a first capacitor coupled between the second and fifth nodes, and a second capacitor coupled between the fourth and sixth nodes, wherein the first capacitor and the second capacitor have substantially the same capacitance value.

[0036] In a further embodiment, the device includes: a first switch coupled between the second and fifth nodes; a second switch coupled between the fourth and sixth nodes; a third switch coupled between the first node and a ground node; a fourth switch coupled between the third node and the ground node: a fifth switch coupled between the first node and a source of the first voltage; a sixth switch coupled between the third node and a source of the second voltage; a clock signal having an odd phase and an even phase, wherein the first switch and the second switch are activated during the even phase; the third switch and the fourth switch are activated, in a first mode, during the even phase, and in a second mode, during the odd phase; and the fifth switch and the sixth switch are activated, in the first mode, during the odd phase, and in a second mode, during the even phase.

[0037] In a particular embodiment, the first and second absolute pressure sensors (e.g., surface micromachined MEMS sensors) have a capacitance value of between approximately 375 and 400 fF.

[0038] In one embodiment, the differential amplifier comprises an operational amplifier circuit integrated, on a semiconductor die, with the first and second absolute pressure sensors. The first and second capacitors may be integrated, on the semiconductor die, with the operational amplifier circuit and the first and second absolute pressure sensors.

[0039] In accordance with one embodiment, the first and second output terminals of the differential amplifier produce a differential output voltage that is proportional to sensor capacitance function and the excitation voltage, and is inversely proportional to the capacitance value of the first and second capacitors. The clock signal may, for example, have a frequency of between approximately 2 MHz and 500 KHz.

[0040] In accordance with another embodiment, a method for producing a differential signal output using absolute pressure sensors includes: providing a first absolute pressure sensor having a first capacitance that varies with an absolute pressure in accordance with a sensor capacitance function; providing a second pressure sensor having a second capacitance that varies with the absolute pressure in accordance with the sensor capacitance function; applying, to the first absolute pressure sensor, a first voltage having a first magnitude and a first polarity with respect to a common mode voltage; applying, to the second absolute pressure sensor, a second voltage having the first magnitude and a second polarity opposite the first polarity with respect to the common mode voltage, wherein the first and second voltages define an excitation voltage; receiving, at a differential amplifier, a first signal from the first absolute pressure sensor and a second signal from the absolute pressure sensor; and producing, at the differential amplifier, a differential output voltage that is directly proportional to the product of the first magnitude and the sensor capacitance function.

[0041] In a particular embodiment, the differential amplifier includes a pair of integration capacitors having a first capacitance value, and wherein the value of the differential output voltage is equal to the product of: a constant (e.g., about -0.5), the excitation voltage, the sensor capacitance function applied to the absolute pressure, and the inverse of the first capacitance value.

[0042] While at least one example embodiment has been presented in the foregoing detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the example embodiment or embodiments described herein are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing the described embodiment or embodiments. It should be understood that various changes can be made in the function and arrangement of elements without departing from the scope of the invention as set forth in the appended claims and the legal equivalents thereof.

Claims

CLAIMSWhat is claimed is:

1. A differential circuit (100) comprising: a differential input (101) having a first input terminal (102), a second input terminal (104), and an excitation voltage applied therebetween, wherein a first voltage at the first input terminal (102) with respect to a common mode voltage is opposite in polarity from a second voltage at the second input terminal (104) with respect to the common mode voltage; a first pressure sensor (106) coupled to the first input terminal (101) and having a first capacitance that varies with an absolute pressure in accordance with a first sensor capacitance function; a second pressure sensor (108) coupled to the second input terminal (104) and having a second capacitance that varies with the absolute pressure in accordance with a second sensor capacitance function; and a differential amplifier (130) coupled to the first pressure sensor (106) and the second pressure sensor (108), the differential amplifier (130) having a first output terminal (114) and a second output terminal (116) that together produce a differential output voltage in accordance with the first and second sensor capacitance functions.

2. The differential circuit of claim 1, wherein the first and second pressure sensors (106, 108) are micro-electromechanical system (MEMS) pressure sensors.

3. The differential circuit of claim 1, wherein the differential output voltage is directly proportional to the product of the excitation voltage and the first and second sensor capacitance functions, and wherein the first and second sensor capacitance functions are substantially equal.

4. The differential circuit of claim 3, wherein the first sensor capacitance function is C(p), the excitation voltage is V_E, further including: a first integration capacitor (118) coupled to the differential amplifier (130) and the first pressure sensor (106); and a second integration capacitor (112) coupled to the differential amplifier (130) and the second pressure sensor (108); wherein the first and second integration capacitors (110, 112) have a value C₂, and wherein the differential output voltage is substantially equal to -(2C(P)V_E)/C₂.

5. The differential circuit of claim 1, further including: a first integration capacitor (118) coupled to the differential amplifier (130) and the first pressure sensor (106); a second integration capacitor (112) coupled to the differential amplifier (130) and the second pressure sensor (108); and switching circuitry (121, 122, 123, 124, 118, 120) configured to selectively charge and discharge the first and second integration capacitors (110, 112) and the first and second pressure sensors (106, 108).

6. The differential circuit of claim 5, wherein the switching circuitry comprises: a first switch (118) coupled in parallel with the first integration capacitor (110); a second switch (120) coupled in parallel with the second integration capacitor (112); a third switch (121) coupled between the first input terminal (102) and the first pressure sensor (106); a fourth switch (123) coupled between the second input terminal (104) and the second pressure sensor (108); a fifth switch (122) coupled between the first input terminal (102) and a ground node; a sixth switch (124) coupled between the second input terminal (104) and the ground node; a clock signal having an odd phase and an even phase, wherein: the first switch and the second switch are activated during the even phase; the third switch and the fourth switch are activated, in a first mode, during the even phase, and in a second mode, during the odd phase; and the fifth switch and the fifth switch are activated, in the first mode, during the odd phase, and in a second mode, during the even phase.

7. The differential circuit of claim 4, wherein the first pressure sensor (106) has a capacitance range of about 380-400 fF.

8. A semiconductor device comprising: a first absolute pressure sensor (106) having a first capacitance that varies with an absolute pressure in accordance with a first sensor capacitance function, the first absolute pressure sensor connected between a first node and a second node; a second pressure sensor (108) having a second capacitance that varies with the absolute pressure in accordance with a second sensor capacitance function, the second absolute pressure sensor connected between a third node and a fourth node; a differential input having a first input terminal (102) at the first node set to a first voltage with respect to a common mode voltage and a second input terminal (104) at the third node set to a second voltage with respect to the common mode voltage, wherein the difference between the first voltage and the second voltage defines an excitation voltage, and wherein the second voltage has a magnitude that is the same as the first voltage and has a polarity that is opposite of the first voltage; a differential amplifier (130) having a first signal input coupled to the second node, a second signal input coupled to the fourth node, a first output terminal connected to a fifth node, and a second output terminal coupled to a sixth node; and a first capacitor (118) coupled between the second and fifth nodes, and a second capacitor (120) coupled between the fourth and sixth nodes, wherein the first capacitor (118) and the second capacitor (120) have substantially the same capacitance value.

9. The device of claim 8, further comprising: a first switch (118) coupled between the second and fifth nodes; a second switch (120) coupled between the fourth and sixth nodes; a third switch (122) coupled between the first node and a ground node; a fourth switch (124) coupled between the third node and the ground node; a fifth switch (121) coupled between the first node and a source of the first voltage; a sixth switch (123) coupled between the third node and a source of the second voltage; a clock signal having an odd phase and an even phase, wherein: the first switch and the second switch are activated during the even phase; the third switch and the fourth switch are activated, in a first mode, during the even phase, and in a second mode, during the odd phase; and the fifth switch and the sixth switch are activated, in the first mode, during the odd phase, and in a second mode, during the even phase.

10. The device of claim 8, wherein the first and second absolute pressure sensors (106, 108) have a capacitance value of between approximately 375 and 400 fF.

11. The device of claim 8, wherein the first and second absolute pressures sensors (106, 108) are micro-electromechanical systems (MEMS) sensors.

12. The device of claim 11, wherein the first and second absolute pressure sensors (106, 108) are surface-micromachined MEMS sensors.

13. The device of claim 11, wherein the differential amplifier (130) comprises an operational amplifier circuit integrated, on a semiconductor die, with the first and second absolute pressure sensors (106, 108).

14. The device of claim 13, wherein the first and second capacitors (118, 120) are integrated, on the semiconductor die, with the operational amplifier circuit and the first and second absolute pressure sensors (106, 108).

15. The device of claim 8, wherein the first and second output terminals (114, 116) of the differential amplifier (130) produce a differential output voltage that is proportional to first and second sensor capacitance functions and the excitation voltage, and is inversely proportional to the capacitance value of the first and second capacitors (110, 112).

16. The device of claim 8, wherein the first and second sensor capacitance functions are non-linear.

17. The device of claim 8, wherein the clock signal has a frequency of between approximately 2 MHz and 500 KHz.

18. A method for producing a differential signal output using absolute pressure sensors, the method comprising: providing a first absolute pressure sensor (106) having a first capacitance that varies with an absolute pressure in accordance with a sensor capacitance function; providing a second pressure sensor (108) having a second capacitance that varies with the absolute pressure in accordance with the sensor capacitance function; applying, to the first absolute pressure sensor (106), a first voltage having a first magnitude and a first polarity with respect to a common mode voltage; applying, to the second absolute pressure sensor (108), a second voltage having the first magnitude and a second polarity opposite the first polarity with respect to the common mode voltage, wherein the first and second voltages define an excitation voltage; receiving, at a differential amplifier (130), a first signal from the first absolute pressure sensor (106) and a second signal from the second absolute pressure sensor (108); producing, at the differential amplifier (130), a differential output voltage that is directly proportional to the product of the first magnitude and the first and second sensor capacitance functions.

19. The method of claim 15, wherein the differential amplifier (130) includes a pair of integration capacitors (110, 112) having a first capacitance value, and wherein the value of the differential output voltage is equal to the product of: a constant; the excitation voltage; the sensor capacitance function applied to the absolute pressure; and the inverse of the first capacitance value.

20. The method of claim 16, wherein the constant is substantially equal to negative two.