OF A SENSOR FOR OFFSET AND SENSITIVITY

VARIATION WITH TEMPERATURE

FIELD OF THE INVENTION

The present invention relates generally to sensors and more particularly to

improving the calibration of such sensors.

BACKGROUND OF THE INVENTION Piezoresistive and capacitive sensors are being used in increasingly higher

accuracy applications for sensing various changes in pressure and the like in a variety of

environments. Because the output of these sensors typically varies over temperature, the sensors require compensation and calibration in order to achieve the accuracy and temperature stability requirements of these application The calibration of sensors typically requires the adjustment of four parameters to achieve optimum output

performance over temperature - offset, offset temperature coefficient (OTC), signal

gain, and gain temperature coefficient (GTC)

In general the transfer function of a sensor is given by

Vsens = Offset, ■(\ + a _] - T+ a ₂ - T ² +...+a„ - T" ) + S„ ^■ (l + /?, ^• T + β ₂ ^■ T ² +...+ ?„ • T" ) • 0

Equation 1

where:

Vsens is the sensor output voltage

Offset^ is the sensor offset (output with zero excitation) at a reference temperature (e.g.

25°C)

ai is the first order temperature coefficient of the sensor offset

a is the second order temperature coefficient of the sensor offset

a„ is the n ^th order temperature coefficient of the sensor offset

T is the temperature difference from the reference temperature

So is the sensor sensitivity or span at the reference temperature (e g 25°C)

βι is the first order temperature coefficient of the sensor sensitivity

β ₂ is the second order temperature coefficient of the sensor sensitivity

β„ is the n ^th order temperature coefficient of the sensor sensitivity

Q is the physical parameter being sensed (e g pressure, acceleration, etc )

For most sensor applications, all but the first order terms can be ignored so that Equation l becomes

Vsens = Offset ₀ • (l + a ^■ T) + S ₀ • (l + β ^■ f) ^■ Q Equation 2

However, for high accuracy sensor applications, the second order terms are usually included so that Equation 1 becomes

Vsens = Offset ₀ ■ (l + a , • T + a ₂ ^■ T ² ) + S ₀ • (l + /?, ^■ T + β ₂ ^■ T ² ) • Q Equation 3

To compensate this signal, a signal conditioning circuit is required which must

subtract out the offset terms and provide amplification which varies with temperature to

counteract the effect of the sensor span (TC) Traditionally, the signal conditioning has

been done with opamps and laser trimmed resistors However, this type of signal conditioning circuit is usually limited to providing first order correction of the temperature dependent terms In addition this method is expensive as it requires the use of a laser and the solution is typically not monolithic (on a single integrated circuit) as

the opamps and resistors are usually built on separate substrates

An embodiment of a conventional digital compensation circuit 100 is shown in

Figure 1. In this embodiment, the differential signal from the sensor 5' is fed into an amplifier 102 which may have a gain of 1 or greater depending on the application The output of this amplifier is fed into another amplifier stage 104 whose gain is controlled

by the contents of a gain register 106 In addition, the offset and offset TC terms are added at summation point 1 14 in this stage using DACs 108, 1 10, 1 12 controlled by

digital parameters. The compensation of the sensor sensitivity TC is done in the third stage 1 16 after the offset, offset TC and gain compensation The third stage 1 16 may also have a gain of 1 or greater depending on the application The final stage is an output buffer 1 1 1

In this circuit, the temperature, T, is sensed using an on-chip proportional to

absolute temperature (PTAT) circuit 122. The analog signal representing T is digitized

using an analog-to-digital converter 124 The digital word representing 7 ^' is then used to control two DACs 1 10 and 120, one for the offset TC compensation and the other for the gain TC compensation Digital information representing the values of the

compensation terms, is serially fed into an on-chip control unit 125 The individual bits

are decoded and sent to the various DACs 106, 108, 1 12, and 1 18 Once the correct binary code has been selected to center the sensor characteristic in the specified range, the code is stored using a digital storage method such as zener-zap, EEPROM or fuse link The transfer function of this circuit 100 is given by Equation 4

Vo t = (Vsens + Voff + Vote ^■ T) ^■ Gam ₀ - (1 + δ - T) Equation 4

Combining equations 3 and 4 gives:

Vout = + δ- T)

Equation 5

Vout is the calibrated sensor output voltage (output of conditioning circuit) Gai o is the gain of the compensating amplifier at the reference temperature

Voff is the offset added by the conditioning circuit

Votc-T is the temperature dependent component of the offset added by the conditioning

circuit

δ is the temperature dependent component of the gain of the compensating amplifier which counteracts the temperature dependent component of the sensor sensitivity

The calibration of the sensor involves making measurements of Vout at various

values of Q and various temperatures and thereby deducing the values of Voff Vote,

Gam ₀ and δ to minimize the error between Vout and the ideal sensor characteristic Ideally the Voff, and Gaιn ₀ terms would be found first using measurements at the initial calibration temperature at minimum and maximum Q The temperature dependent terms would then be found by an additional set of measurements at high (or low) temperature

By setting

Voff = -Off seta

Vote = -Offseto-a,

and δ ^* = -β, equation 5 becomes:

Vout = S ₀ - Q - Ga ₀ ^■ [l + T ^{2 ■} (β ₂ + δ ^■ /J, ) ₂ + T ^{3 •} δ ^■ β ₂ ] + Offset, - a ₂ - Gam, - (] + δ - T) r ²

Equation 6

The desired term is simply So O Gamo All the other terms arise because this circuit only

corrects for linear variations of the sensor offset and sensitivity with temperature In

high accuracy applications these extra terms may limit the usability of the sensor since it may be impossible to calibrate the sensor within the desired specification

Accordingly, what is needed is a system and method to allow for more accurate

calibration of sensors The system and method should be easy to implement and cost

effective. The present invention addresses such a need

SUMMARY OF THE INVENTION

A digital compensation circuit for calibrating a sensor is described The

compensator circuit comprises a serial communication circuit for receiving data relating to a plurality of parameters, and means coupled to serial communication circuit for providing piece-wise linear compensation of a temperature coefficient (TC)

The piece-wise linear compensation means further comprises detector means for

detecting a threshold for a digital temperature and providing an output, and a plurality of

registers coupled to the detector means and the serial communication circuit, a first of

the plurality of registers for providing a first value if the digital temperature is above the

threshold, a second of the plurality of registers for providing a second value if the digital temperature is below the threshold The piece-wise linear compensation means further includes a selector means coupled to the detector means and the plurality of registers, for selecting one of the first and second of the plurality of registers dependent upon the

output of the detector means for providing piece-wise linear compensation of a temperature coefficient.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a diagram of a sensor conventional calibration circuit.

Figure 2 is a block diagram of a high accuracy calibration system 200 in accordance with the present invention

Figure 3 shows typical sensor offset behavior together with a linear approximation and a piece-wise-linear approximation using the present invention Figure 4 illustrates the residual errors in the offset term for both the linear

approximation and the piece-wise-linear approximation method

Figure 5 illustrates a multi-part piece-wise-linear function

DETAILED DESCRIPTION The present invention relates to an improvement of a calibration system for a sensor The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and

its requirements. Various modifications to the preferred embodiment will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments Thus, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles

and features described herein.

The present invention is an improvement over conventional calibration schemes. In the present invention the second order behavior of sensor offset and sensitivity with temperature are approximated by a piece-wise-linear function In the present invention,

the offset and sensitivity behavior is approximated by two different linear functions, one

for low temperature and one for high temperature The switch-over point from one

function to another is known as the pivot temperature and is the value at which the

temperature T is zero (reference temperature). In so doing a highly accurate sensor

calibration is provided To more particularly describe the features of the present invention refer now to the following discussion in conjunction with the Figures

Figure 2 is a block diagram of a high accuracy calibration system 200 in accordance with the present invention As is seen system 200 has many of the common

components as those shown in system 100 of Figure 1 Those components are given

similar designations as described in Figure 1.

The piece-wise-linear approximation for offset TC correction is implemented by providing two offset TC registers 204 and 206. The value in one register 204 is fed to

the offset TC DAC 214 for low temperature and the value in the other register is fed to the offset TC DAC 214 for high temperature The circuit 212 detects when the

temperature crosses the zero point and switches the inputs to the offset TC DAC 214

from one register to the other

The piece-wise linear approximation for gain TC correction is implemented by two gain TC registers 208 and 210 The value in one register 208 is fed to the gain TC

DAC 216 for low temperature and the value in the other register 210 is fed to the gain

TC DAC 216 for high temperature The circuit 212 detects when the temperature

crosses the zero point and switches the inputs to the DAC from one register to the other

In a preferred embodiment, the temperature T is represented as a ten (10) bit digital word with 512 being the value at the pivot temperature In this way the detector

circuit for the pivot temperature is, for example, a simple logic inverter connected to

the most-significant-bit (MSB) of the temperature word When this bit is logic 1 , the digital temperature word is greater than or equal to 512 and therefore, the temperature T

is greater than or equal to zero If the MSB is logic 0, the digital temperature word is less than 512 and therefore 7 ^' is less than zero.

In addition, in the preferred embodiment is included means for providing piece- wise-linear compensation for both sensor offset TC and gain TC although one of

ordinary skill in the art will recognize that a particular sensor may require piece-wise

linear compensation of offset TC but not of sensitivity TC or vice versa and it would be within the spirit and scope of the present invention to provide piece-wise-linear compensation of that one parameter only

Figure 3 shows typical sensor offset behavior 302 together with a linear

approximation 304 such as that provided by the circuit 100 in Figure 1 and a piece- wise- linear approximation 306 such as that provided by the circuit 200 of Figure 2 of the present invention As is seen the piece-wise linear approximation more closely follows the offset behavior Similarly, a piece-wise-linear approximation can be used for

correcting the sensitivity temperature behavior

To further illustrate this point, Figure 4 is a waveform that shows the residual errors in the offset term for both the linear approximation 402 and the piece-wise linear approximation 404 As is seen, the piece-wise-linear approximation error is clearly

smaller thus allowing for higher accuracy compensation

An extension of this method is the use of multiple registers to approximate the

offset or sensitivity TC behavior of the sensor with more than two linear functions In

this way the operating temperature region of the sensor can be broken up into multiple segments and different linear functions used to approximate the offset or sensitivity behavior in each region. In this case the detection circuit must detect multiple thresholds

and in addition it must perform some arithmetic functions to avoid discontinuities at the

segment switch-over points For example, suppose the offset characteristic in Figure 3 were to be approximated by a three part piece-wise-lmeai function between 7=0, and 7=7 such as that shown in Figure 5 (502) The switch-over points are 7-7 _/ and 7=7?

The equations of the approximating function are given by equations 7a-7c Segment 1, 0 < 7 < T,

ConφensatmgOffset = Voff + Votc _a 7 Equation 7a

Segment 2, T,< 7 < 7 ₂

Co pensattngOffset = Voff + Votc _a T + Votc _b (l - V, ) Equation 7b

Segment 3, 1 ₂ < I < 7 ?

Co pen satmgOffsel = Voff + Vote , /, + Vot , ( J l _] ) t- Vofc _t ( / - 7, )

Equation 7c

Note that in each segment the constant portion of the compensating function is

different The additional terms, Votc _a T segment 2 and \ otc _a / , t Votc _h {I-> - 1 ) in

segment 3 can be inserted into the signal path via anothei oftset DAC or they can be combined with Voff and inserted using the existing otiset DAC Since these terms are

known at time of calibration they can be stored in memory and simply added in at the appropriate temperature The detection circuit would therefoi e include an adder circuit

to calculate the extra terms in addition to calculating the terms 7-7/ and T-l ₂

Although the preferred embodiment ony includes means for pioviding piece- wise-linear compensation for sensor offset TC and sensitivity I C it should be clear that the present invention can also be used to correct for the temperature coefficient of the sensor linearity error The sensor linearity error is the deviation of the sensor transfer

characteristic (that is, sensor output versus 0 where O is the parameter being sensed) from an ideal straight line In addition, one of ordinary skill in the art will recognize that

a particular sensor may require piece- wise linear compensation of offset TC or of

sensitivity TC or of linearity TC and it would be within the spirit and scope of the present invention to provide piece-wise-linear compensation only of those parameters requiring it. Although the present invention has been described in accordance with the

embodiments shown, one of ordinary skill in the art will readily recognize that there

could be variations to the embodiments and those variations would be within the spirit and scope of the present invention Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the spirit and scope of the

appended claims.