Abstract:
A sensor chip has a piezo-resistive bridge, a first resistor network that can be used for biasing when connected to an external amplifier, a second resistor network that can be used to set gain when connected to the external amplifier, and a leadout resistor that connects an output of the bridge to a common summing point of the two resistor networks. The summing point is connected to the non-inverting input of the external amplifier. The leadout resistor has a predetermined number of squares. A portion of the squares has a light implant and the remaining portion of the squares has a heavy implant. The ratio of the heavy and light implant portions provides customized span compensation of the amplified output for specific operating temperature ranges.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to pressure sensors and, more particularly, to pressure sensors having span compensation customized for a specific operating temperature range where the customization can be changed for a different specific operating temperature range. 
     BACKGROUND OF THE INVENTION 
     Piezo-resistive pressure sensors are used in a wide variety of applications including automotive, industrial, medical, and environmental applications. Such sensors typically include a silicon diaphragm incorporating an ion implanted piezo-resistive Wheatstone bridge. An applied pressure bends the diaphragm and imbalances the bridge, producing a differential, ratiometric output signal that is proportional to the product of the change in resistance (ΔR/R) caused by the pressure and the bridge excitation voltage. 
     Piezo-resistive pressure sensors formed in silicon are frequently fabricated using either bulk silicon or silicon-on-insulator (SOI) wafers. In the case of bulk silicon, the piezo-resistive pressure sensors are fabricated directly in the bulk silicon. In the case of SOI, the piezo-resistive pressure sensors are fabricated in the top silicon layer that is over the buried oxide layer of the SOI structure. 
     In the bridge configuration of piezo-resistive pressure sensors, the resistance of diagonally opposed legs varies equally and in the same direction as a function of the mechanical deformation caused by pressure. As the resistance of one set of diagonally opposed legs increases under pressure, the resistance of the other set decreases, and vice versa. 
     Bridge excitation in the form of a voltage or current is applied across two opposite nodes of the bridge. These nodes are usually referred to as excitation inputs or bridge drive inputs. Any change in resistance (such as due to a pressure input) is detected as a voltage difference across the other two nodes of the bridge, which are typically referred to as the bridge output. 
     For silicon based piezo-resistive pressure sensors, the voltage difference across the bridge output is quite small. Therefore, the bridge output is processed through a pressure channel that typically includes an amplifier to amplify the voltage difference across the bridge output. A feedback resistor around the amplifier is used to control the gain of the pressure channel that includes the amplifier. This feedback resistor is usually a light implant resistor compared to the heavy implant piezo-resistors that form the sensor bridge. 
     The full span output is defined as the difference in sensor outputs corresponding to the maximum and minimum applied pressures. The full span output (FSO) of an uncompensated piezo-resistive sensor bridge can exhibit a strong nonlinear dependence on temperature caused be the intrinsic nonlinear dependence of the piezo-resistor gauge factor (ΔR/R) on temperature, whereas the zero pressure (null) offset and null offset dependence on temperature are maintained small in comparison. Thus, a sensor is typically compensated so that it can be used in practice. 
     Span shift with temperature is defined as the span as a function of temperature divided by the span at 25° C. Accordingly, span shift(T) in percent is equal to 100·[Span(T° C.)/Span(25° C.)]. The span shift curve is nonlinear with a negative slope with temperature as illustrated in FIG.  4  and is identified as K 3 . The span shift K 3  is defined as the ratio of the pressure sensitivity (ΔR/R)) of the heavy implant piezo-resistive bridge as a function of temperature normalized to the value at 25° C. In equation form K 3 (T) is equal to [ΔR/R(T)]/[ΔR/R(25° C.)] and may be expressed by the following 5 th  order polynomial: 
     
       
           K   3 ( T )=−(6.265753E−14)· T {circumflex over ( )}5+(5.393845E−11)· T {circumflex over ( )}4−(2.440481E−08)· T {circumflex over ( )}3+(8.022881E−06)· T {circumflex over ( )}2−(2.585262E−03)· T +(1.058300) 
       
     
     The magnitude of the slope decreases with increasing temperature. A typical span shift value at 25° C. is −0.25%° C. Thus, in most applications, the sensor bridge output must be compensated, for the span shift(T) in particular, before it can be used in practice. 
     FIG. 4 also illustrates the temperature characteristics of the heavy implant resistors (K 2 ) and the light implant resistors (K 1 ). The temperature characteristics of the heavy implant resistors (K 2 ) is defined as follows: K 2 =Ratio of the resistance of the heavy implant resistor as a function of temperature normalized to the value at 25° C. In equation form, K 2 =[Rheavy(T)]/[Rheavy(25° C.)] and may be expressed by the following 5 th  order polynomial: 
     
       
           K   2 ( T )=−(3.018497E−14)· T {circumflex over ( )}5+(4.603604E−11)· T {circumflex over ( )}4−(2.282857E−08)· T {circumflex over ( )}3+(7.538750E−06)· T {circumflex over ( )}2−(2.252834E−05)· T +(0.9963789) 
       
     
     The temperature characteristics of the light implant resistors (K 1 ) is defined as follows: K 1 =Ratio of the resistance of the light implant resistor as a function of temperature normalized to the value at 25° C. In equation form, K 1 (T)=[Rlight(T)]/{Rlight(25° C.)] and may be expressed by the following 5 th  order polynomial: 
     
       
           K   1 ( T )=−(8.171496E−14)· T {circumflex over ( )}5+(9.930398E−11)· T {circumflex over ( )}4−(3.557091E−08)· T {circumflex over ( )}3+(9.691127E−06)· T {circumflex over ( )}2+(2.958093E−03)· T +0.923953 
       
     
     It is noted that the change in resistance of light implant resistors as a function of temperature K 1 (T) is much greater than that of the heavy implant resistors (K 2 (T). 
     SOI piezo-resistive pressure sensors that use the same design layout and the same ion implant concentrations as that used to fabricate bulk silicon piezo-resistive pressure sensors experience a positive span shift in the amplified pressure channel output as a function of temperature, whereas the span shift of the SOI piezo-resistive bridge-only has a negative slope with temperature, which is similar to that of bulk piezo-resistive sensors. This comparison indicates that the bridge span shift has been over-compensated by the positive temperature dependant gain of the amplifier. This over-compensation of span shift is primarily due to the higher positive TCR (temperature coefficient of resistance) of the light implant (high TCR) resistor elements in the SOI construction as used in the gain and feedback resistor networks which in turn causes an increase in the temperature dependent gain of the amplifier. As a result, the amplified pressure sensor output span is changed from being under-compensated to being over-compensated as shown in FIG.  5 . 
     For example, in bulk silicon devices, the positive TCR of the light implant feedback (gain) resistor in the pressure channel compensates approximately 85% of the negative temperature coefficient (TC) of the heavy implant pressure bridge&#39;s span shift, as shown by the curve with the delta points, which results in the amplified output to be under-compensated by approximately 15% as shown by the curve with the square points. However, for SOI devices, the increase in the TCR of the light implant gain resistor causes an over-compensation of span shift with temperature as shown by the curve with the circle points. As shown in FIG. 5, the approximate +23% span shift of the bridge output (the curve with the delta points) at −55° C. is over-compensated to approximately −3% at the amplified output. Similarly, the approximate −28% span shift of the bridge output at +225° C. is over-compensated to approximately +7% at the amplified output. 
     Known techniques have been implemented to reduce the effect of span shift over-compensation. For example, in one technique, the dopant concentration of the SOI light implant process can be reduced to provide a lower TCR and a lower sheet resistivity. This process requires extensive re-layout of all of the light implant elements, processing of product for verification, and the need to have a third implant variable in the production wafer fabrication. 
     In another technique, the effective TCR of all of the light implant feedback and bias resistors in the pressure channel is reduced by making a certain percentage of these elements heavy implant elements. This process requires extensive re-design and re-layout of all the feedback and bias resistors, and could jeopardize the exact tracking of the R feedback /R bias  ratio required for high performance and long term stability. 
     Accordingly, these known techniques are complex and are not practical. 
     The present invention optimizes span compensation that may be customized for a specific operating temperature range and permits re-customization for a different operating temperature range. A benefit of the present invention is that the same ion implant concentrations that are common to both bulk silicon and SOI pressure sensors can be retained. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the present invention, a sensor chip has first, second, third, fourth, fifth, and sixth sensor nodes and comprises a piezo-resistive bridge and first, second, third, fourth, fifth, and sixth conductive paths. The piezo-resistive bridge has first and second input nodes and first and second output nodes. The first conductive path connects the first input node to the first sensor node. The second conductive path connects the second input node to the second sensor node. The third conductive path connects the first output node to the third sensor node. The fourth conductive path connects the second output node to the fourth sensor node, the fourth conductive path includes a leadout resistance, a portion of the leadout resistance is formed as a light implant resistance, and the remainder of the leadout resistance is formed as a heavy implant resistance. The fifth conductive path connects the fourth sensor node to the fifth sensor node, and the fifth conductive path includes a bias resistance. The sixth conductive path connects the fourth sensor node to the sixth sensor node, and the sixth conductive path includes a feedback resistance. 
     According to another aspect of the present invention, a sensing system comprises a resistive sensor bridge, an amplifier, and first, second, third, fourth, fifth, and sixth conductive paths. The resistive sensor bridge has first and second input nodes and first and second output nodes. The amplifier has negative and positive inputs and an output. The first conductive path connects the first input node to a first source. The second conductive path connects the second input node to a reference potential. The third conductive path connects the first output node to the positive input of the amplifier. The fourth conductive path connects the second output node to the negative input of the amplifier, the fourth conductive path includes a leadout resistance, a portion of the leadout resistance is formed as a light implant resistance, and the remainder of the leadout resistance is formed as a heavy implant resistance. The fifth conductive path connects a second source to the negative input of the amplifier, and the fifth conductive path includes a bias resistance. The sixth conductive path connects the output of the amplifier to the negative input of the amplifier, and the sixth conductive path includes a feedback resistance. 
     According to still another aspect of the present invention, a method of fabricating a sensor chip comprises the following: forming a resistive sensor having at least a first resistance and a second resistance, wherein the resistive bridge has first and second input nodes and at least one output node; forming a first conductive path connected to the first input node; forming a second conductive path connected to the second input node; and, forming a third conductive path connected to the output node, wherein the third conductive path comprises a third and fourth resistances, wherein each of the first, second, and third resistances is a heavy implant resistance, and wherein the fourth resistance is a light implant resistance. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features and advantages will become more apparent from a detailed consideration of the invention when taken in conjunction with the drawings in which: 
     FIG. 1 illustrates a sensor chip layout according to an embodiment of the present invention; 
     FIG. 2 illustrates the sensor chip layout of FIG. 1 in circuit schematic form; 
     FIG. 3 illustrates the sensor chip layout of FIG. 1 in circuit schematic form and coupled to an external amplifier; 
     FIG. 4 illustrates the temperature characteristics of heavy implant resistors and of light implant resistors and further illustrates the span shift of a heavy implant piezo-resistive bridge as a function of temperature; 
     FIG. 5 illustrates the span shift of the output of an SOI sensor without the customized compensation provided by the present invention, the span shift of the output of a bulk silicon sensor with compensation, and the span shift in the sensor bridge only case; 
     FIG. 6 compares the span shift of the output of an SOI sensor without the compensation of the present invention to the span shift of the output of an SOI sensor with the span shift compensation customized for one temperature range; 
     FIG. 7 compares the span shift of the output of an SOI sensor without the compensation of the present invention to the span shift of the output of an SOI sensor with the span shift compensation customized for another temperature range; and, 
     FIG. 8 compares the span shift of the output of an SOI sensor without the compensation of the present invention to the span shift of the output of an SOI sensor with the span shift compensation customized for still another temperature range. 
    
    
     DETAILED DESCRIPTION 
     As shown in FIGS. 1 and 2, a sensor chip  10  may be fabricated using standard SOI processing techniques. The sensor chip  10  includes a substrate  12 , which may be the top silicon layer of an SOI structure. The substrate  12  is provided with terminals V 1 -V 4  and A-F that permit external connections to be made to various points of the sensor chip  10 . Also, the sensor chip  10  may be provided with an epitaxial layer (such as an n type epitaxial layer) and a shield layer (not shown) as are known in the art. 
     The sensor chip  10  includes a piezo-resistive bridge  14  having piezo-resistors  16 ,  18 ,  20 , and  22  connected in a Wheatstone bridge configuration. The piezo-resistive bridge  14  has first and second excitation input nodes  24  and  26 , and first and second output nodes  28  and  30 . The piezo-resistor  16  is connected between the first excitation input node  24  and the first output node  28 , the piezo-resistor  18  is connected between the second excitation input node  26  and the first output node  28 , the piezo-resistor  20  is connected between the first excitation input node  24  and the second output node  30 , and the piezo-resistor  22  is connected between the second excitation input node  26  and the second output node  30 . 
     Also, the sensor chip  10  includes various leadout resistors and other resistors. Accordingly, a leadout resistor  32  connects the first output node  28  of the piezo-resistive bridge  14  to the terminal V 1 , and a pair of leadout resistors  34  and  36  connects the second output node  30  of the piezo-resistive bridge  14  to the terminal V 2 . (As described hereinafter, the leadout resistor  34  is a heavy implant resistor and the leadout resistor  36  is a light implant resistor. FIGS. 1 and 2 imply that the leadout resistor  36  is formed adjacent to the terminal V 2 . However, the light implant that the forms the leadout resistor  36  can instead be formed closer to the bridge so that a heavy implant region, then a light implant region, and then a heavy implant region in series connect the node  30  to the terminal V 2 . This arrangement would then be shown by three series resistors connected between the node  30  to the terminal V 2 . However, for simplicity, all such arrangements are represent by only two resistors, i.e., the resistors  34  and  36 .) Additionally, a resistor  38  connects the terminal V 2  to the terminal D, a resistor  40  connects the terminal D to the terminal E, a resistor  42  connects the terminal E to the terminal F, a resistor  44  connects the terminal V 2  to the terminal C, a resistor  46  connects the terminal C to the terminal B, and a resistor  48  connects the terminal B to the terminal A. Further, the first excitation input node  24  is connected to the terminal V 3 , and the second excitation input node  26  is connected to the terminal V 4 . 
     During the formation of the sensor chip  10 , the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 , and the leadout resistor  36  are formed as light implant resistors, and the piezo-resistors  16 ,  18 ,  20 , and  22  and the leadout resistor  34  are formed as heavy implant resistors. The implanting material, for example, may be Boron. As a result of this implanting, the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 , the leadout resistors  32 ,  34 , and  36 , and the piezo-resistors  16 ,  18 ,  20 , and  22  each have a predetermined resistivity. 
     The ratio of the resistivity of a light implant resistor to the resistivity of a heavy implant resistor, for example, may be on the order of seven to one. In a first example, a light implant resistor may have a resistivity of 860 ohms per square, and a heavy implant resistor may have a resistivity of 120 ohms per square. Thus, in this first example, each of the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 , and the leadout resistor  36  may have a resistivity of 860 ohms per square, and each of the piezo-resistors  16 ,  18 ,  20 , and  22  and the leadout resistors  32  and  34  may have a resistivity of 120 ohms per square. In a second example, a light implant resistor may have a resistivity of 2064 ohms per square, and a heavy implant resistor may have a resistivity of 288 ohms per square. Thus, in this second example, each of the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 , and the leadout resistor  36  may have a resistivity of 2064 ohms per square, and each of the piezo-resistors  16 ,  18 ,  20 , and  22  and the leadout resistors  32  and  34  may have a resistivity of 288 ohms per square. However, other ratios and/or resistivities may be used. 
     Moreover, the dopant concentration of the light implant resistor is the same for both resistivities of 860 and 2045 ohms per square. Likewise, the dopant concentration of a heavy implant resistor is the same for both resistivities of 120 and 288 ohms per square. For example, the light implant resistivities may have a dopant concentration in the order of 3×10{circumflex over ( )}17 ions per cubic cm, and the heavy implant resistivities may have a dopant concentration in the order of 1×10{circumflex over ( )}19 ions per cubic cm. Both combinations of light and heavy implant resistivities of the two above examples are achieved using the same wafer mask set and wafer process. The change in the resistivity levels is determined by the parameters of the wafer starting material that control the finished thickness of the resistors. 
     By appropriate external connection to the terminals V 1 -V 4  and A-F, the sensor chip  10  may be coupled to a pressure channel that includes an external amplifier. Thus, as shown in FIG. 3, the terminal V 1  is externally connected to a positive (non-inverting) input of an external amplifier  50 , the terminal V 2  is externally connected to a negative (inverting) input of the external amplifier  50 , the terminals V 3  and E are externally connected to an external excitation source V ref , the terminal V 4  is externally connected to an external reference potential such as ground, and the terminal B is externally connected to the output of the external amplifier  50 . The output of the external amplifier  50  is designated VP and is defined by the following equation, which shows the relationship of the resistors  34  and  36  to the amplifier gain: 
       V Pout as % of  V ref=100·{1+( R   44 + R   46 )·[(1 /R   22 )·(1−( R   16 · R   22 )/( R   18 · R   20 ))/(1+(( R   34 + R   36 )/ R   20 )·(1 +R   20 / R   22 ))−(1/( R   38 + R   40 ))·( R   16 / R   18 )]}/[1+( R   16 / R   18 )] 
     As shown in FIG. 3, the leadout resistors  34  and  36  connect the second output node  30  of the piezo-resistive bridge  14  to the negative input of the external amplifier  50  and, therefore, are part of the input resistance R in  that partially determines the gain of the external amplifier  50 . By lightly implanting a predetermined portion of the input resistance R in  (i.e., the leadout resistor  36 ), the TCR of the input resistance R in  can be made higher. This increase in the TCR of the input resistance R in  reduces the rate of increase of the gain with increasing temperature thereby reducing the span shift discussed above. Accordingly, by using a light implant, for a portion of the input resistance R in , span compensation can be customized while retaining the same geometry of the bridge and leadout resistors, while not changing any other part of the design of the sensor chip  10 , and while using the same ion implant concentrations that are common to bulk silicon and SOI devices. 
     The resistors  38 ,  40 , and  42  may be referred to as bias resistors. Any combination of these resistors may be selected in order to provide a desired bias to the terminal V 2 . The resistors  44 ,  46 , and  48  may be referred to as feedback resistors. Any combination of these resistors may be selected in order to provide a desired feedback resistance for the external amplifier  50 . 
     Table 1 shows a first example of the relative sizes and values for the piezo-resistors  16 ,  18 ,  20 , and  22 , the leadout resistors  32 ,  34 , and  36 , and the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 # of 
                 Resistivity 
                 Resistance 
               
               
                   
                 Resistor 
                 Squares 
                 (ohms/square) 
                 (ohms) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 16 
                 85.075 
                 120 
                 10,209 
               
               
                   
                 18 
                 85.075 
                 120 
                 10,209 
               
               
                   
                 20 
                 85.075 
                 120 
                 10,209 
               
               
                   
                 22 
                 85.075 
                 120 
                 10,209 
               
               
                   
                 32 
                 0.89 
                 120 
                 106.4 
               
               
                   
                 34 
                 7.30 
                 120 
                 875.8 
               
               
                   
                 36 
                 1.00 
                 860 
                 860.0 
               
               
                   
                 38 
                 90.89 
                 860 
                 78,167.6 
               
               
                   
                 40 
                 17.34 
                 860 
                 14,914.1 
               
               
                   
                 42 
                 22.37 
                 860 
                 19,240.0 
               
               
                   
                 44 
                 72.89 
                 860 
                 62,684.0 
               
               
                   
                 46 
                 13.71 
                 860 
                 11,791.9 
               
               
                   
                 48 
                 16.64 
                 860 
                 14,313.7 
               
               
                   
                   
               
             
          
         
       
     
     It is noted that the number of squares of the resistor  34  plus the number of squares of the resistor  36  equal is preferably constant (8.3 squares). Thus, if the number of squares of the resistor  36  is increased, for example, then the number of squares of the resistor  34  is decreased by the same amount. 
     FIGS. 6,  7  and  8  are graphs that show the SOI sensor pressure channel&#39;s amplified output as a function of temperature, each illustrating a customized span compensation for a different temperature range. 
     In FIG. 6, for example, the span compensation has been customized for the temperature range of −55° C. to +225° C. The curve with the solid circle points shows the span output over temperature without customized compensation where both of the leadout resistors  34  and  36  are heavy implant resistors. The curve with the non-solid circle points shows the span output with customized span compensation resulting when the leadout resistor  36  is changed from being one square of a heavy implant resistor to one square of light implant resistor. At +225° C., for example, the span shift is reduced from approximately +7% to near zero, and at −55° C. the span shift is reduced from approximately −3% to near zero. Over the entire range of −55° C. to +225° C., the span shift error is less than approximately 1.5%. As can be seen, making the leadout resistor  36  a light implant resistor, customized for −55° C. to +225° C. according to the present invention, significantly reduces span shift. 
     In FIG. 7, for example, the span compensation has been customized for the temperature range of −55° C. to +125° C. The curve with the solid circle points shows the span output over temperature without customized compensation where both of the leadout resistors  34  and  36  are heavy implant resistors. The curve with the non-solid circle points shows the span output with customized span compensation resulting when the leadout resistor  36  is changed from being 1.3 squares of a heavy implant resistor to 1.3 squares of light implant resistor. At +125° C., for example, the span shift is reduced from approximately +5% to approximately +0.5%, and at −55° C. the span shift is reduced from approximately −3% to approximately +1.0%. Over the entire range of −55° C. to +125° C., the span shift error is less than approximately 1.0%. As can be seen, making the leadout resistor  36  a light implant resistor, customized for −55° C. to +125° C. operation according to the present invention, significantly reduces span shift. 
     In FIG. 8, for example, the span compensation has been customized for the temperature range of −30° C. to +100° C. The curve with the solid circle points shows the span output over temperature without customized compensation where both of the leadout resistors  34  and  36  are heavy implant resistors. The curve with the non-solid circle points shows the span output with customized span compensation resulting when the leadout resistor  36  is changed from being 1.52 squares of a heavy implant resistor to 1.52 squares of light implant resistor. At +100° C., for example, the span shift is reduced from approximately +4.2% to approximately +0.2%, and at −55° C. the span shift is reduced from approximately −3% to approximately +0.2%. Over the entire range of −30° C. to +100° C., the span shift error is less than approximately 0.25%. As can be seen, making the leadout resistor  36  a light implant resistor, customized for −3° C. to +100° C. operation according to the present invention, significantly reduces span shift. 
     Table 2 shows a second example of the relative sizes and values for the piezo-resistors  16 ,  18 ,  20 , and  22 , the leadout resistors  32 ,  34 , and  36 , and the resistors  38 ,  40 ,  42 ,  44 ,  46 , and  48 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 # of 
                 Resistivity 
                 Resistance 
               
               
                   
                 Resistor 
                 Squares 
                 (ohms/square) 
                 (ohms) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 16 
                 85.075 
                 285 
                 24,246.4 
               
               
                   
                 18 
                 85.075 
                 285 
                 24,246.4 
               
               
                   
                 20 
                 85.075 
                 285 
                 24,246.4 
               
               
                   
                 22 
                 85.074 
                 285 
                 24,246.4 
               
               
                   
                 32 
                 0.89 
                 285 
                 252.7 
               
               
                   
                 34 
                 7.30 
                 285 
                 2,080.0 
               
               
                   
                 36 
                 1.00 
                 2,045 
                 2,045.0 
               
               
                   
                 38 
                 90.89 
                 2,045 
                 185,875.4 
               
               
                   
                 40 
                 17.34 
                 2,045 
                 35,464.4 
               
               
                   
                 42 
                 22.37 
                 2,045 
                 45,750.9 
               
               
                   
                 44 
                 72.89 
                 2,045 
                 149,056.7 
               
               
                   
                 46 
                 13.71 
                 2,045 
                 28,040.0 
               
               
                   
                 48 
                 16.64 
                 2,045 
                 34,036.7 
               
               
                   
                   
               
             
          
         
       
     
     Certain modifications of the present invention have been described above. Other modifications of the invention will occur to those skilled in the art. For example, the present invention has been described above in relation to pressure sensors. However, the present invention may be used on other types of sensors such as temperature sensors. 
     Also, the terminals V 1 -V 4  and A-F are described above as terminals that permit external connections to be made to the sensor chip  10 , and the external amplifier  50  is referred to as an external amplifier. However, the terminals V 1 -V 4  and A-F may instead be referred to as sensor nodes. Such sensor nodes can be terminals that permit external connections to be made to the sensor chip  10 , or such sensor nodes can be simply connections points indicating internal connections of the sensor chip  10 . In this latter case, the external amplifier  50  may be an internal amplifier formed as part of the sensor chip  10 , or the amplifier may be an external amplifier connected to the sensor chip  10  through the use of external connections. 
     Moreover, the sensor chip  10  is described above as including a Wheatstone pressure bridge. However, the pressure bridge of the sensor chip  10  may instead include fewer that four resistors. For example, the pressure bridge of the sensor chip  10  may include a half bridge having two resistors connected between excitation inputs and having a junction forming an output. 
     Accordingly, the description of the present invention is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention. The details may be varied substantially without departing from the spirit of the invention, and the exclusive use of all modifications which are within the scope of the appended claims is reserved.