110 have a different sensitivity to the physical parameter (e.g. pressure). This means that the magnitude and/or the sign of the sensitivity (e.g. caused by a change in resistance of the sensing element) are different.

There is a strong correlation between each of the 3 signals, because of their dependency on the same physical input. If the change in resistance for piezoresistors is considered to be linear, then only an offset and gain are needed to get the desired linear output curve. Typically the sensor is also temperature dependent and the offset and gain of each measured differential signal should be calibrated at multiple temperatures. In embodiments of the present invention the calibrated output curves can be used for detecting the correct functionality of the sensor.

In the following simplified example, the sensing elements are resistors which are pressure dependent. The resistance R1 of the first sensing element 110a is increasing X with pressure, the resistance R2 of the second sensing element 110b is decreasing X with pressure, the resistance R3 of the third sensing element is increasing X/2 with pressure and the resistance R4 of the fourth sensing element is decreasing X/2 with pressure. In this exemplary embodiment it is, for simplicity, assumed that the nominal resistance of the sensing elements is the same. It is, furthermore, assumed that the bias currents for biasing the sensing elements are the same. In the following this bias current is referred to as I. If the sensing device is connected with a readout circuit, the readout circuit may for example measure VR1-VR2 (changing 2*X*I), VR3-VR4 (X*I), VR1-VR4 (1.5*X*I). Therefore if the voltage changes between nodes 112a and 112b U volts, then the corresponding change between nodes 112d and 112c needs to be half of the change U, if the resistors function correctly. Similarly, the corresponding voltage change between nodes 112a and 112c should be ¾ times U.

FIG. 2 shows a circuit diagram of a sensing device 100, in accordance with embodiments of the present invention, which comprises only 3 sensing elements 110a, 110b, 110c. Similarly to FIG. 1, the three sensing elements have second nodes 112a, 112b, and 112c connected to current sources 240a, 240b, and 240c providing currents I1, I2, and I3 respectively, and the voltages of the second nodes 112a, 112b, and 112c are referred to as VR1, VR2, and VR3 respectively.

In the configuration of FIG. 2 only a minimum number of nodes of the sensing device are required. The common node 111 is shared between the sensing elements and is accessible for biasing this node. The second nodes 112a, 112b, and 112c are accessible by the readout circuit. In this example the readout circuit is not completely shown. Only current sources are shown which are connected to the second nodes of the sensing elements. The sensing elements may for example be sensor resistors. With three sensor resistors R1 (sensing element 110a), R2 (sensing element 110b), R3 (sensing element 110c) connected to a common node, three differential signals can be measured. In case, for example, the sensor resistors are biased with a current source, 3 differential voltages can be measured: VR1-VR2 can be measured between second nodes 112a (VR1) and 112b (VR2), VR1-VR3 can be measured between second nodes 112a (VR1) and 112c (VR3), and VR2-VR3 can be measured between second nodes 112b (VR2) and 112c (VR3). Note that the third measurement can be calculated from the other two measurements. In embodiments of the present invention the third measurement is used to find measurement errors. Remark that the negated voltages like VR2-VR1 are not considered as they basically measure the same signals.

In embodiments of the present invention each sensing element (e.g. resistor) has a different sensitivity to the sensed physical parameter. The difference in the sensitivity can be seen e.g. in the magnitude and/or sign. When each sensing element measures the same physical parameter value (e.g. pressure), there is correlation between e.g. the resistance values of the sensing elements. In embodiments of the present invention 2 of the 3 differential voltages are independent. There is a correlation between each of the 3 differential voltages, because they measure the same physical parameter. This correlation can be measured upfront, so that it is known. This can be achieved e.g. by measuring the differential voltages at 2 or more pressure values and fitting a curve to the measured voltages for each differential measurement. This way it is possible to calculate for every voltage a corresponding pressure. It can be made more accurate by applying offset, gain or other corrections for each differential voltage separately.

Since we know the pressure value corresponding to a differential voltage value for each differential voltage, it is straight-forward to obtain the correspondence between the differential voltages. Here the correspondence between the differential voltages of VR1-VR2 and VR1-VR3 is marked with C12_13, the correspondence between the differential voltages VR2-VR3 and VR1-VR3 with C13_23 and the correspondence between the differential voltages VR1-VR2 and VR2-VR3 with C12_23.

In that case any fault which is only influencing one of the three sensor resistors or one of the three (not-common) sensor nodes can be detected by comparing two differential measurement results with their known correspondence. When for example measuring VR1-VR2 and VR1-VR3, the equation

VR
⁢
1
-
VR
⁢
3

=

C12_
⁢
13
⁢

(

VR
⁢
1
-
VR
⁢
2

)

⁢

should
⁢

hold
.

A mismatch versus the known correspondence means that a fault is present. The fault could be located at the sensing element (e.g. resistance drift, leakage current) or at the readout circuit (e.g. drift of bias current, leakage current).

Remark that in the exemplary embodiment where the sensing elements are resistors it is advantageous that all 3 resistors have nominally the same or a similar resistance value, to keep the signal small without pressure. Alternatively, in the case where the resistance values differ substantially between the resistors, their biasing currents can be made different in order to get nominally the same voltage over the sensor resistors. This ensures that the differential voltages remain small. For example in case 1 resistor has double the resistance value of the 2 others, then one could have half the bias current to get a similar voltage over this resistor as for the other 2 resistors.

In an exemplary embodiment of the present invention the resistance R1 of a first sensing element is increasing with pressure, the resistance R2 of a second sensing element is decreasing with pressure and the resistance R3 of a third sensing element is significantly less dependent (or totally not dependent) on pressure. The resistance R3 of the third sensing element can for example be made pressure independent by changing the position (e.g. aside of a membrane or at a position where longitudinal and transversal stress compensate each other) or the orientation. It can also be made significantly less sensitive by combining 2 or more resistor parts that react differently on pressure, e.g. a series (or parallel) connection of a resistor that increases with pressure and a resistor that decreases with pressure. To get nominally the same resistance, the first sensing element could be made by the series connection of 2 resistors that both increase with pressure and the second sensing element could be made by the series connection of 2 resistors that both decrease with pressure.

The errors may be quantized as follows. Suppose 3 resistors which are sensitive to physical parameter P, with sensitivities S1, S2 and S3, and which all have the same resistance R0 with P=0. Suppose all 3 resistors are biased with the same current I0 and suppose the first node of the 3 resistors is ground.

Then the following voltage is obtained at the second node of the different resistors:

VR
⁢
1

=

I
⁢
0
*
R
⁢
0
*

(

1
+

S
⁢
1
*
P

)

⁢

VR
⁢
2

=

I
⁢
0
*
R
⁢
0
*

(

1
+

S
⁢
2
*
P

)

⁢

VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

1
+

S
⁢
3
*
P

)

In that case the differential voltages are:

VR
⁢
13

=

VR
⁢
1
-
VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

S
⁢
1
-
S
⁢
3

)

*
P

⁢

VR
⁢
23

=

VR
⁢
2
-
VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

S
⁢
2
-
S
⁢
3

)

*
P

These differential voltages may be calibrated using calibration factors G13 and G23:

Y
⁢
13

=

VR
⁢
13
*
G
⁢
13

⁢

Y
⁢
23

=

VR
⁢
23
*
G
⁢
23

The calibration is preferably such that:

Y
⁢
13

=

Y
⁢
23

=

Y
⁢
0
⁢

(

with
⁢

Y
⁢
0
⁢

the
⁢

ideal
⁢

output

)

This requires that:

G
⁢
13
/
G
⁢
23

=

(

S
⁢
2
-
S
⁢
3

)

/

(

S
⁢
1
-
S
⁢
3

)

The output error (e.g. in case of a fault at the sensor) is Y13-Y0 and Y23-Y0. To monitor if a fault is present, Y13-Y23 may be checked, which should ideally be 0. In the following different error cases are explained.

Error Case 1:

Suppose an offset error x is present for VR1. In that case:

Y
⁢
13

=

Y
⁢
0

+

x
*
G
⁢
13

⁢

Y
⁢
23

=

Y
⁢
0

⁢

Y
⁢
13
-
Y
⁢
23

=

x
*
G
⁢
13

In that case the error is x*G13 and the output, which may be monitored for determining correct functionality of the sensor system, may be configured such that it outputs x*G13.

Error Case 2:

Suppose an offset error x is present for VR3. In that case:

Y
⁢
13

=

Y
⁢
0

-

x
*
G
⁢
13

⁢

Y
⁢
23

=

Y
⁢
0

-

x
*
G
⁢
23

⁢

Y
⁢
13
-
Y
⁢
23

=

x
*

(

G
⁢
23
-
G
⁢
13

)

In that case the error is-x*G13 and −x*G23 and the output, which may be monitored for determining correct functionality of the sensor system, may be configured such that it outputs x*(G23-G13).

It is noted that if the difference between S1 and S2 is decreasing, then also the difference between G13 and G23 will be decreasing, so Y13-Y23 will be decreasing, and will be smaller than in error case 1. This case is therefore more difficult to detect, while the error is still in the same order as in case 1. Note that if S1=S2, then G13=G23 and Y13−Y23=0. In that case the error will not be detected, illustrating the need for different sensitivities.

If the sensitivity difference (S1-S2) becomes bigger, then also G23-G13 becomes bigger and the error will be easier detected.

In the simplified case of S3=0 and assuming small difference between S1 and S2, then s % difference in sensitivity between S1 and S2 would need approximately s % difference in gain between G23 and G13.

So if one has an error x=1%, then a sensitivity difference of 1% would only create a difference between Y13 and Y23 of approximately 0.01% of Y0 which is hardly detectable, while an error of 1% might not be acceptable.

If one has a sensitivity difference of 10%, then Y13-Y23 would be approximately 0.1% of Y0, which might be detectable.

So it would be advantageous to have sensitivity differences of 10%, 20% or even more. One could also live with for example 5% or less at the expense of reduced sensitivity for the error detection (monitor).

In the optimal scenario S2=−S1, so also G13=−G23. In that case the monitor output is twice the error magnitude, so easily detectable.

Error Case 3:

Suppose a sensitivity error x at S1. In that case:

VR
⁢
1

=

I
⁢
0
*
R
⁢
0
*

(

1
+

(

S
⁢
1

+
x

)

*
P

)

⁢

VR
⁢
13

=

VR
⁢
1
-
VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

S
⁢
1

+
x
-

S
⁢
3

)

*
P

⁢

Y
⁢
13

=

Y
⁢
0

+

I
⁢
0
*
R
⁢
0
*
x
*
P
*
G
⁢
13

⁢

Y
⁢
23

=

Y
⁢
0

⁢

Y
⁢
13
-
Y
⁢
23

=

I
⁢
0
*
R
⁢
0
*
x
*
P
*
G
⁢
13

In that case the error is I0*R0*x*P*G13 and the output, which may be monitored for determining correct functionality of the sensor system, may be configured such that it outputs I0*R0***P*G13.

For P=0, this will result in Y13−Y23=0. In that case the S1 error will not detected by monitoring I0*R0*x*P*G13, but the sensitivity error also does not cause an error for Y13 at P=0.

For P different from 0, also Y13-Y23 will be different from zero, and therefore potentially detectable.

Error Case 4:

Suppose a sensitivity error x is present for S3:

VR
⁢
13

=

VR
⁢
1
-
VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

S
⁢
1
-
S
⁢
3
-
x

)

*
P

⁢

VR
⁢
23

=

VR
⁢
2
-
VR
⁢
3

=

I
⁢
0
*
R
⁢
0
*

(

S
⁢
2
-
S
⁢
3
-
x

)

*
P

If in this case S1=S2, then Y13−Y23=0 and the error will not be detected. So also the detection of sensitivity errors requires a difference in the sensor sensitivity.

Also other error sources which impact only 1 sensor element, 1 (second) sensor node or 1 differential output reading are better detectable with different sensitivities of the sensor elements. Even some errors which impact multiple sensor elements, sensor nodes or differential output readings may benefit from sensor elements with different sensitivities.

In a second aspect embodiments of the present invention relate to a sensor system 300. The sensor system comprises a sensor device 100 and a readout circuit 200. The readout circuit 200 is connected to the second node 112 of each sensing element and is configured for applying driving signals to the second nodes and for reading differential signals between pairs of the second nodes 112.

The readout circuit 200 may for example comprise one or more current sources for injecting a current through the sensing elements 110 or one or more voltage sources for applying a bias over the sensing elements 110. The readout circuit 200 may comprise switches for connecting the one or more current source(s) or voltage source(s) to one or more of the node(s).

The readout circuit may also comprise at least one signal path for processing the differential signals between the second nodes. A signal path may be present for each node pair, or a signal path may be multiplexed between the different node pairs. In some embodiments of the present invention hybrid cases may exist wherein the readout circuit comprises two signal paths. One fixed to one pair of second nodes, and the other multiplexed between all other pairs of second nodes. Thus, a compromise is obtained between cost and safety.

In embodiments of the present invention the differential signals are differential voltages.

In embodiments of the present invention the at least one signal path comprises an amplifier. Thus, the differential signal between the second nodes can be amplified. In some embodiments of the present invention an amplifier is not strictly required. In some cases the sensor device may be directly connected to an ADC without amplification of the differential signal.

The readout circuit 200 is, furthermore, configured for comparing the differential signals, after calibrating the differential signals taking into account the sensitivities of the sensing elements, for determining correct functionality of the sensor system 300. It is thereby an advantage of embodiments of the present invention that a redundant system is obtained with only a limited number of nodes of the sensing element. The readout circuit may comprise an ADC for converting an analog differential signal into a digital signal. The readout circuit may furthermore comprise a processing device (e.g. microprocessor, digital signal processor, field programmable gate array) for processing the digital signal. This processing comprises comparing the differential signals, after calibrating the differential signals taking into account the sensitivities of the sensing elements, for determining correct functionality of the sensor system. In embodiments of the present invention, after calibration the obtained calibrated differential signals are substantially the same, unless an error occurred in the sensor system 300.

In embodiments of the present invention the readout circuit 200 may be configured for applying a predefined voltage to the first node 111 as driving signal to the first node. In alternative embodiments the predefined voltage (e.g. ground) may be applied to the first node directly via a PCB on which the sensor device is mounted.

In embodiments of the present invention the readout circuit 200 may also be connected with the first node 111. This can for example be advantageous when the sensing elements are piczoresistors. Piezo-resistors are typically not only stress (pressure) dependent, but also temperature dependent. In that case the average voltage between the first node and the second node of a sensing element is a measure for the temperature.

FIG. 3 shows a schematic diagram of an exemplary sensor system 300, comprising a sensor device 100 and readout circuit 200, in accordance with embodiments of the present invention. In FIG. 3, the sensor device 100 and the readout circuit 200 are separate devices. The sensor device 100 comprises at least three sensing elements 110 in accordance with embodiments of the present invention. The sensor device may for example be a MEMS pressure sensor or any other type of sensor device comprising 3 sensing elements connected together to a common node and wherein at least three sensing elements have a different sensitivity to the physical parameter.

The readout circuit 200 comprises a control block 210 which comprises switches which enable the connection of any of the nodes of the sensor to an amplifier 220 and after that to an ADC and signal processing block 230, which may be connected to outside control, or it may perform the required calculations relating to sensor output and functional safety inside the sensor system 300.

The control block 210 may be configured for detecting if one of the sensing element branches is faulty and identifying it in the signal processing block 230. In case there are e.g. 4 sensing elements, the sensor system 200 may continue to be functional using the three remaining sensing elements 110.

In the exemplary embodiment illustrated in FIG. 3 the readout circuit 200 further comprises current sources 240 which are feeding the required current to the second nodes of the sensing elements