Classifications

• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01C—RESISTORS
  • H01C17/00—Apparatus or processes specially adapted for manufacturing resistors
  • H01C17/22—Apparatus or processes specially adapted for manufacturing resistors adapted for trimming
  • H01C17/232—Adjusting the temperature coefficient; Adjusting value of resistance by adjusting temperature coefficient of resistance
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01C—RESISTORS
  • H01C7/00—Non-adjustable resistors formed as one or more layers or coatings; Non-adjustable resistors made from powdered conducting material or powdered semi-conducting material with or without insulating material
  • H01C7/06—Non-adjustable resistors formed as one or more layers or coatings; Non-adjustable resistors made from powdered conducting material or powdered semi-conducting material with or without insulating material including means to minimise changes in resistance with changes in temperature

Definitions

• the invention relates to resistors and resistor networks which are electro- thermally trimmable, and more specifically, to thermal trimming of these resistors to adjust resistance, temperature coefficient of resistance and relative temperature coefficient of resistance.
• Non-laser trimming technique is known to adjust the resistance of thin film resistors. This technique is based on thermal trimming of a resistor made from a thermally mutable material. Resistor trimming is achieved by heating using electric current pulses passed through the resistor itself or through an adjacent auxiliary heater (US Patents 4210996, 5635893, 5679275). Instead of direct physical removal of 14830-2SFUl
• thermal trimming directly modifies the physical properties of the material such as resistivity and TCR.
• TCT Temporal Coefficient of Trimming
• Non-zero TCT generates a new problem (not existing in typical cutting-based trimming techniques), which can be illustrated by the following example.
• An embodiment of the present invention compensates (or minimizes) RTCR 0 (TCR mismatch) resulting from non-zero TCT of a thermally trimmable resistor network by constructing a compound resistor from at least two resistive portions having different resistance and TCR values. 14830-/5F(J l )
• An embodiment of the present invention achieves independent adjustment of resistance ratio and RTCR of a thermally trimmable resistor network, the RTCR being adjusted to near-zero or intentionally to a non-zero value.
• a trimmable resistor network with adjustable non-zero RTCR can be used in various different applications where
• a method for providing a trimmable resistive component having a predetermined behavior of temperature coefficient of resistance (TCR) as a function of trimming comprising: selecting materials to form a compound resistor having at least a 0 first portion and a second portion, at least the first portion including a first resistor Ri, that is thermally trimmable and has a first resistivity, a first temperature coefficient of resistance value ⁇ &, and a trimming-induced shift of temperature coefficient ⁇ x , which defines a change in the oto per fraction of trimming x of the first resistivity, the second portion including at least a second resistor, R 2 , having a second resistivity value, and a 5 second temperature coefficient of resistance value / S 0 ; determining how the TCR value of the resistive component changes as at least the first portion is trimmed, by generating a function of the TCR versus trim-fraction x, with Ri and R 2 as variable parameters and oto,
• a trimmable resistive component having a predetermined behavior of temperature coefficient of resistance (TCR) as a function of trimming comprising: a first 5 portion composed of a first resistor that is thermally trimmable and has a first resistivity, a first temperature coefficient of resistance value do, and a trimming-induced shift of temperature coefficient ⁇ x , which defines a change in the c ⁇ per fraction of trimming x of the first resistivity; and a second portion composed of at least a second resistor having a second resistivity value and a second temperature coefficient of resistance 0 value ⁇ o, the first portion and the second portion having specific values for R) and RT or
• Ri /R 2 to provide the resistive component with the predetermined behavior of the TCR value; wherein the predetermined behavior of the TCR is defined by a function of the TCR versus trim-fraction x, with Ri and R 2 as variable parameters and OQ, ⁇ o, and ⁇ x as fixed parameters, thereby incorporating an effect of the ⁇ ⁇ in the resistive component with ⁇ x being a function, ⁇ x (x), representing fixed behavior of ⁇ x as a function of trim- fraction x.
• an application specific circuit having an adjustable parameter of the circuit and an adjustable temperature coefficient of the parameter, the circuit comprising: at least one compound resistor including: a first portion comprising a first resistor, Ri, that is thermally trimmable and has a first resistivity, a first temperature coefficient of 0 resistance (TCR) value Ob, and a trimming-induced shift of temperature coefficient ⁇ ⁇ , which defines a change in the C ⁇ per fraction of trimming x of the first resistivity; and a second portion comprising a second resistor, R 2 , having a second resistivity value and a second TCR value ⁇ o, the first portion and the second portion having specific values for at least one of Ri and R 2 and Ri /R 2 to provide the compound resistor with the 5 predetermined behavior of the TCR value; wherein the predetermined behavior of the TCR is defined by a function of the TCR versus trim-fraction x, with Ri and R 2 as variable parameters and 0/0, /
• trimming algorithms such as those disclosed in PCT publications WO04/097859, WO04/097860, and WO04/083840 are used.
• control circuitry such as that described in PCT publications WO03/023794 and WO04/097859 to trim resistors is also preferred.
• An embodiment of the present invention can be used for making precision 5 adjustable resistors and resistor networks. Electro-thermal trimming used for the adjustment in general changes not only resistance value but also TCR of trimmable material.
• the proposed solutions allow the designer/user to achieve:
• compound resistor is to be understood as a resistor composed of more than one identifiable resistor, which can have the same or different resistances, resistivity, sheet resistances, trim amounts, and other physical properties.
• a “resistive component” can be a single resistance, a network of resistances,
• the analysis done to generate the function can be numerical (when computer- 0 based simulation tools are used), analytical (based on classic electricity laws), or experimental (when set of curves TCR(x) is generated experimentally) and should not be limited to any one of these techniques.
• basic electrical laws to be used in generating the function as described above can be Ohm's Law (relating current, voltage and resistance in a 5 resistor), Kirchoffs current law (for summing of currents at a node), Kirchoffs voltage law (regarding the sum of voltages around a closed electrical loop), and equations describing how the component values of electrical components (e.g. resistance) vary with temperature.
• resistivity units: ohm-cm
• sheet resistance units: ohms/square
• Fig. l is a schematic of a compound resistor consisting of two parts connected in series, as per an embodiment of the present invention
• Fig. 2 is a comparative graph of the TCR of a single trimmable resistor Ri and the TCR of a compound resistor as in fig 1 ;
• Fig. 3 is a graph showing TCR of a compound resistor configured as shown in 0 Fig. 1 vs. relative trimming of its resistance value, for several different ratios of R 20 /R 10 ;
• Fig. 4 is a schematic of a compound resistor in a parallel configuration, as per another embodiment of the present invention.
• Fig. 5 is a comparative graph of the TCR of a single trimmable resistor Ri and the TCR of a compound resistor as in fig 4;
• Fig. 6 is a graph which shows the dependence of the TCR of a compound resistor R comp , composed of two trimmable portions in series, Ri(x), R 2 (y), as a function of relative trimming of the compound resistor;
• Fig. 7 shows a series connection of two compound resistors, each compound resistor consisting of two trimmable resistors;
• Fig. 8 shows a series connection of a compound resistor as in Fig. 1 , along with a third resistor which is trimmable;
• Fig. 9 shows an alternative circuit configuration for a compound resistor, with two resistors forming the first portion and one resistor forming the second portion;
• Fig. 10 shows a full Wheatstone bridge, Rbi, Rb2, Rb3, R M , each with a trimmable 5 compound resistor, R comp i, R CO m P 2, Rco m p h Rcom P4 , connected in parallel, and a simplified representation where each bridge resistor and its associated compound resistor is combined and represented as Rb compi, Rb_com P 2, Rb compi, Rb compi
• Fig. 1 1 shows two different configurations of trimmable compound resistors, one where R ⁇ (x) and Ri(y) are connected in series, and the other where Rj(x) and Rj(y) 0 are connected in parallel;
• Fig. 12 is a graph of overall TCR of an example of one R t comp compound resistor having a series connection, as a function of its own normalized resistance, as one of the trimmable portions is trimmed down, where trimming R 2 (y) increases the TCR while trimming Ri (x) decreases the TCR;
• Fig. 13 is a graph of overall TCR of an example of one Rb_ C om P compound resistor having a series connection, as a function of its own normalized resistance, as 5 one of the trimmable portions is trimmed down, where trimming R 2 Cy) changes the TCR by a much larger amount than does trimming Ri (x);
• Fig. 14 is a graph of overall TCR of an example of one Rb_ ComP compound resistor having a series connection, as a function of its own normalized resistance, as one of the trimmable portions is trimmed down, where trimming Ri (x) decreases the 0 TCR by a larger amount than the increase caused by trimming R 2 (y);
• Fig. 15 is a graph of overall TCR of an example of one Rb C o mP compound resistor having a parallel connection, as a function of its own normalized resistance, as one of the trimmable portions is trimmed down, where trimming R 2 (y) increases the TCR by a larger amount than the decrease caused by trimming Ri (x);
• Fig. 16 is a graph of overall TCR of an example of one R b _ COmP compound resistor having a parallel connection, as a function of its own normalized resistance, as one of the trimmable portions is trimmed down, where the magnitudes of the changes in TCR are smaller than those in figure 15;
• Fig. 17 is a graph of overall TCR of an example of one R b _ COmP compound 0 resistor having a parallel connection, as a function of its own normalized resistance, as one of the trimmable portions is trimmed down, where trimming R 2 (y) causes a larger increase in TCR than the decrease in TCR caused by trimming Ri (x);
• Fig. 18 shows the trimming behavior of one compound resistor R b comp having several different values of the nominal TCR ( ⁇ b ) of the bridge resistor (R b ), where the 5 changes in TCR and relative resistance remain almost the same, for the three different values of ⁇ b,'
• Fig. 19 shows a scheme of TCR compensation of the bridge as a whole, where the trimmable compound resistor R5 is connected in parallel with the whole bridge, such that it experiences the entire voltage applied to the bridge, U b , 0
• Fig. 20 shows an example of trimming the TCR of the overall bridge using resistor Rs, connected in parallel with the entire bridge;
• Fig. 21 shows another scheme of TCR compensation of the bridge as a whole, where the trimmable compound resistor R & is connected in series with the whole bridge, such that it experiences the same current as that applied to the bridge;
• Fig. 22 shows the temperature coefficient of bridge voltage (upper graph), and 5 the ratio U ⁇ /U (lower graph, where U is the excitation voltage of the circuit shown in Fig. 21), as functions of normalized resistance of the trimmable resistor R ⁇ f ⁇ f ⁇ om Fig. 21 ;
• Fig. 24 shows TCR of a parallel-compound resistor configures as shown in Fig. 4, as a function of trimming fraction of the trimmable portion (-0.4 ⁇ x ⁇ 0), for the single trimmable portion (upper graph), and for the compound resistor (lower graph); and
• Fig. 25 shows a series-connected compound resistor with an additional R p in 15 parallel.
• Fig. 1 shows a schematic of a compound resistor consisting of two parts connected in series, a trimmable resistor R t with TCR ⁇ %, negative TCT ⁇ (x), and ballast resistor R 20 (non-trimmable) with TCR ⁇ o.
• resistor Ri is trimmable in a range of ⁇ 15% from a "middle" resistance value Rio'. 25
• R 1 (X) K 10 (I + X) (1) where x is the trim fraction and -0.15 ⁇ x ⁇ 0.15.
• the resistance and TCR of the compound resistor can be expressed as:
• Fig. 2 depicts the variation of TCR with x, for a single trimmable resistor R / , and in the lower part of Fig. 2, the TCR of a compound resistor (such as shown in Fig. 1), as a function of resistance trimming relative to a "middle" 0 value Rio.
• TCT compensation for a resistor having negative TCT is possible only in the case when the ballast resistor R 20 has a more negative TCR than the trimmable resistor.
• compensation for a 0 trimmable resistor having is possible when the ballast resistor R 2 0 has TCR /? ⁇ 500ppm/K.
• Another example of possible compensation is and /? ⁇ -4200ppm/K.
• the compound resistor has a trimming range narrower than that of a single trimmable resistor by a factor of 1/(1 +k).
• a simple guideline for this is to use resistor materials with low TCT ⁇ i(x) and high initial TCR difference ao- ⁇ o- Application-specific cases where an intentionally narrow trimming range of the compound resistor is needed also may exist. Equations (4,5) can be used to make an effective choice of the resistor materials.
• 5 Fig. 3 is a graph which shows the TCR of the compound resistor vs. relative trimming of its resistance value.
• trim-fractions at which the compound resistor becomes ideally TCT-compensated can be pre-determined (designed by the user), by proper selection of the resistor values and properties. It should be understood that Ri (x), ⁇ (x) are not as- 0 manufactured resistance and TCR of the first portion but its actual values reached at a certain trimming level (at these "predetermined trim-fractions").
• a procedure for implementing an embodiment of the method of the present invention is as follows (for a circuit as shown in Fig. 1):
• the materials are chosen for the two portions of the resistor (with specific sheet resistance and TCR for both portions, and TCT for the first portion). 5 2. The trimming range required for a given application is chosen.
• the as-manufactured resistance ratio of two portions is defined (based on the known sheet resistances, TCR's and TCT), such that the compound resistor reaches ideal TCT-compensation (defined by eq.(6)) approximately at the middle of the desired trimming range, thus providing relatively "flat" TCR vs. trimming in that entire desired 0 trimming range.
• TCT is a function of x — ⁇ i is ⁇ i(x).
• TCT is a function of x — ⁇ i is ⁇ i(x).
• the "optimum" initial ratio of as-manufactured resistances R 2 o/Rio may be quite different 0 from that predicted by Eq.4 or Eq.6 or the procedure described a few paragraphs above, and should be based on Eq. 3b.
• a somewhat modified procedure would be: 1.
• the materials are chosen for the two portions of the resistor (with specific sheet resistance and TCR for both portions, and ⁇ j(x) for the first portion).
• the as-manufactured resistance ratio of the two portions is defined (based 5 on the known sheet resistances, TCR's and TCT), such that the compound resistor reaches ideal TCT-compensation approximately at the middle of the desired trimming range, thus providing relatively "flat" TCR vs. trimming in that entire desired trimming range.
• R 2 o/Rio one can solve analytically Eqs.3-4 (if an analytical form is available), or, more generally, simulate a set of curves "TCR vs. trim- 0 fraction" using equation 3b, and choose that ratio which provides the optimal "flat" TCR behaviour vs. trim.
• the overall TCR of the compound resistor has been shifted closer to zero over its entire trim range.
• This technique (connection of a third resistive portion in parallel with the other two portions), allows shifting of the entire TCR curve, without appreciably changing the shape of the curve of TCR vs trim, where one or both of the 5 series-connected portions is trimmed. This is effective whether the TCT behaviour is linear or non-linear.
• R p has negative TCR, then it will act to make the overall TCR of the compound resistor more negative. In the above example, this moves the overall TCR closer to zero. On the other hand, if R p has a positive TCR, then it will act to make the 0 overall TCR of the compound resistor more positive. In the context of the above example, this would move the overall TCR of the compound resistor farther above zero. In this way, one may use such R p to adjust the overall TCR of the compound resistor in a desired manner. Similarly, one may add a portion of resistance (R s ) in series with a parallel- compound resistor to adjust the overall TCR of the compound resistor.
• the value of R p should be relatively large in order to not disturb the shape of the curve of TCR vs trim, here the 5 value of R s should be relatively small compared to the parallel-connected portions, if one wants to avoid disturbing the shape of the curve of TCR vs trim.
• Fig. 4 shows a schematic of the analogous compound resistor with two resistive parts connected in parallel, instead of in series.
• the resistance of the compound resistor and its TCR can be found as:
• the compound resistor has a trimming range narrower than that of a single 0 trimmable resistor by a factor of k/(l+k). Therefore, to maintain a substantial trimming range for the compound resistor, it is again preferable to choose materials with high TCR difference ⁇ -cco so as to maximize the parameter k.
• Fig. 5 plots the TCR of a single trimmable resistor Ri and the TCR of a compound resistor composed of two resistors connected in parallel, as a 5 function of resistance trimming relative to its "middle" value Rio-
• the resistance value of the resistor R 2 0 used for TCT compensation and calculated from eq. (10) equals 0.6i? /0 .
• Fig.24 shows TCR as a function of trimming fraction of the trimmable portion (-0.4 ⁇ x ⁇ 0), for the single trimmable portion (upper graph) and the parallel compound resistor (lower graph).
• the above-described compound trimmable resistors with compensated TCT can 0 be used in designing various resistor networks.
• a resistor divider can be built from two TCT-compensated trimmable resistors. Resistance ratio adjustment of this divider can be performed with near-zero RTCR variations as will be explained further below.
• thermally mutable materials for example polysilicon doped with different types of dopants, may have significantly different TCT.
• polysilicon doped with Boron has much lower TCT than polysilicon doped with Arsenic (D. Feldbaumer, J. Babcock, C. Chen, Pulse 5 Current Trimming of Polysilicon Resistors, Trans, on Electron Devices, vol. 42 (1995), pp. 689-696).
• Polysilicon samples doped with one type of dopant but at different doping levels also may have different TCT (US patent 6306718).
• Thermally trimmable single resistors with different TCR and TCT are proposed to be used in a compound resistor to provide independent adjustment of resistance value 0 and TCR.
• TCR and TCT of the two resistive portions are: for the first resistor, and for the second resistor.
• Each of the two single resistors are 5 trimmable as and where x and y are the respective trimming fractions.
• Fig. 6 shows the dependence of the TCR of this series-connected compound resistor R comp as a function of its relative trimming.
• resistor Ri(x) is trimmed by 0 fraction x
• the TCR of the compound resistor remains almost constant while its total resistance, R COmp , changes.
• trimming of the resistor R 2 (y) by fraction y results in a significant change in the TCR o ⁇ R comp , with a slope of approximately -40ppm/K per 1% of trimming of the compound resistor, or -13ppm/K per 1% of trimming of the resistor R 2 .
• the possibility of trimming the resistance value of the compound resistor 5 with different slopes of TCR vs. R comp trimming fraction is useful for building resistors with independent adjustment of resistance and TCR, and resistor networks with independent adjustment of resistance ratio and RTCR.
• the variations with trim of the temperature coefficients of resistance may be different for the two (or more) trimmable portions.
• these variations 0 with trim of the temperature coefficients of resistance may each be linear or non-linear, with different coefficients ( ⁇ ) of non-linearity.
• the fundamental requirement is that the two trimmable portions have significantly different variations of TCR with trim-fractions: [a o + ⁇ i(x)x] must be significantly different from [ ⁇ o+/ 2 (y)y]-
• Kic Omp Ki(1 + *i ) + K2(1 + yi ) (12a)
• K 2comp K 1 O + * 2 ) + K 2 O + / 2 ) (12C)
• Resistor R 22 5 (whose trimming significantly changes the TCR of the compound resistor), can be used for this purpose.
• the desired trimming fractions xj and y 2 can be found from by solving the system of two equations derived from Equations (12a-d):
• RTCR up to 4ppm/K. It should be understood that depending on the technical requirements (precision and trimming range), an appropriate method of calculation of trimming values should be chosen. It could be based on analytical or numerical solution of equations (12a-d), or usage of look-up tables. 0 Note that the necessity to adjust the resistance ratio of two trimmable resistors and their RTCR may exist not only for the resistor divider circuit as described in the examples, but also for other resistor networks where two trimmable resistors are not necessarily connected in series. The principle of the adjustment of such a circuit remains the same as described in the examples 1 - 8.
• the overall circuit output may depend on (a) ratio(s) (or relationship) of a number of resistors, not necessarily in a simple series or parallel combination (not necessarily connected directly to each other). 5
• the main idea is that the compound resistor behaves differently when we trim one or the other, provided that they have different TCT.
• Fig. 8 shows a schematic of a resistor divider consisting of a compound TCT- compensated trimmable resistor R comp plus a single trimmable resistor R 3 , connected in series.
• the circuit can be used in applications where one needs essentially non-zero 0 RTCR of the voltage divider.
• a voltage divider with the resistor R comp having TCR 900ppm/K higher than that of resistor Rs.
• the as-manufactured resistance value of R 3 should be chosen intentionally 10% higher, so that subsequent trimming down by -10% allows both the required RTCR adjustment and the required resistance ratio.
• the present invention is suitable in a broad range of cases where 5 thermal trimming of thermally-mutable resistance is possible. This does not necessarily require special thermal isolation of the resistors beyond what is typically found in standard integrated circuit host processes.
• the present invention does not necessarily require bidirectional trimming, and can function effectively even if individual resistors are trimmed largely only in a downward direction. It can also function effectively in 0 cases where the range is limited for trimming upwards from a trimmed-down value.
• thermal trimming is typically much faster in the downward direction than in the upward direction, the required trim signals may be short enough that special thermal isolation is not needed (and thus this technique may work with thermally-trimmable resistors which are integrated on the same chip with other circuitry, such as those provided by standard CMOS processes).
• the invention can be used in a variety of applications, such as for zero compensation of a Wheatstone bridge.
• Fig.10 The scheme depicted in Fig.10 is an example of the invented method applied for zero compensation (compensation of zero offset and temperature coefficient of zero offset) of the Wheatstone bridge.
• trimmable compound resistors R com pi, Rcomp2, 5 R c o m pi-, Rco mp4 are each connected in parallel to the corresponding bridge resistors Rb/,
• R b2 , Rb 3 , R b4 - Each pair of resistors thus forms a new compound resistor, represented in the figure by Rb comph Rb_comp2, Rb compS, Rb_comp4-
• trimmable compound resistors each consisting of two trimmable portions Ri(x) and R 2 (y) made from different materials 0 (where x and y are the trimming fractions of each single resistor within a compound 148J6-25FCT
• resistor These portions can be connected in series or in parallel, as shown in Fig. 11. Each resistive portion is independently trimmable:
• R 2 (y) R 20 (I + y) (17b)
• R;o and R 2 o are as-manufactured resistance values.
• FIGs 12 - 14 show three different examples, plotting the overall ("net") TCR of one of the compound resistors (parallel combination of one of the bridge resistors R b with its corresponding R COm p, called genetically Rb_ comp ),as a function of its own normalized resistance (Rt co m p)-
• Rb by itself
• R comp has TCR of 1600ppm/K
• R comp having the parameters 5 specified in Fig. 12
• the overall TCR of the resultant R b _co mP is approximately 1275ppm/K.
• Rb co mp i and Rb co mP3 are each trimmed “down” by ⁇ 3%, but that said trimming is the result of trimming "down” of 5 resistor Ri by ⁇ 31 % in the compound resistor R COm pi, and trimming "down of resistor R 2 by ⁇ 31% in the compound resistor R COmp i-
• the trimming-induced ⁇ TCR in Rb_compi is about -70ppm/K
• the trimming-induced ⁇ TCR in Rb_com P 3 on the opposite side of the bridge, is about +50ppm/K, for a total ⁇ TCR having magnitude approximately 120ppm/K.
• the bridge zero offset can be significantly adjusted using thermally-trimmable resistors, without significantly unbalancing the relative TCR of the system (without causing additional 0 ⁇ TCR).
• the range of bridge zero offset adjustment can be further doubled if the corresponding (same-numbered) single resistors Ri or R 2 in pair R CO mpi, Rcom P 4, and in 5 pair R comp2 , R comP 3, are trimmed simultaneously. For example, one would trim down Ri in R com pi and R comp 4, and trim down R 2 in R CO mp2 and R comp 3.
• Figs. 15 - 17 show examples similar to those shown in Figs. 12 - 14, where the single trimniable resistors R / and R 2 are connected in parallel instead of in series. Again the overall (net) TCR of the compound resistor Rb co m p is shown as a function of 0 normalized resistance Rb C o mp when single trimmable resistors Ri and R 2 are trimmed down.
• Fig. 18 shows the trimming behaviour of compound resistor Rb co mp with several different values of the nominal TCR ( ⁇ b) of each of the four bridge resistors (R b ). Note that in Fig. 18 the slope of this overall bridge TCR with trimming depends on the value 0 of ⁇ b while trimming range of ⁇ TCR and relative resistance change remains almost the same, for each of the three values of ⁇ b .
• trimming-compensation circuit consisting of four compound resistors with resistance value of approximately 5 times higher than resistance of resistors of the bridge allows RTCR adjustment in the range of ⁇ 240ppm/K 5 (2 x 120ppm/K) and relative resistance adjustment of ⁇ 12% (2 x 2 x 3%).
• Some sensor-based applications where the sensing element(s) is/are configured in a Wheatstone bridge, require increasing the bridge-voltage (e.g. Ub in Fig. 21) with temperature (applying a positive bridge-voltage tempco), to compensate for negative 5 temperature-induced drift of the sensitivity of the sensing element(s).
• Examples of these types of sensors include piezo-resistive pressure sensors and resistive magnetic field sensors.
• the calibration procedure of a particular sensor involves adjustment of bridge-voltage tempco, in order to achieve temperature-stable full-scale output.
• Bridge TCR compensation scheme trimable resistor in parallel with the 0 bridge:
• the shift of the bridge TCR (shown in Figs. 12-17) caused by connection of "zero-offset-compensation" compound resistors R Comp i-R comP4 (Fig.10), must be included into consideration.
• the "zero-offset-compensated" bridge with parameters shown in Fig. 15 is to be “TCR-compensated” using the scheme depicted in Fig. 19.
• the bridge TCR is already shifted (prior to any trimming), from its initial 1600ppm/K to approximately 1450ppm/K.
• Bridge TCR compensation scheme (trimmable resistor in series with the bridge): Adjustment of the bridge-voltage tempco (temperature coefficient) is possible not only by the scheme shown in Fig. 19, with trimmable resistor Rs(x) connected in parallel with 0 the bridge, but also with trimmable resistor R ⁇ (x) connected in series with the bridge (having equivalent resistance R b , since all four bridge resistors have resistance Rb), as shown in Fig. 21.
• Fig. 22 shows bridge voltage tempco and ratio U ⁇ /U (where U is the excitation voltage) as functions of normalized resistance of the trimmable resistor R ⁇ (x).
• U is the excitation voltage
• a trimmable resistor having constant, nominally-zero TCR it must be trimmed from 0 to 85%-down from its as- 0 manufactured resistance, in order to cover a particular desired bridge voltage temperature coefficient range between 1100 and 1500ppm/K. It is also important to note that the as-manufactured resistance value of the trimmable resistor, 15 times greater than the bridge resistance, results in reduction of ratio U ⁇ /U to 0.1 - 0.3, with corresponding reduction in sensor sensitivity. Therefore, a desired normal operating bridge voltage of, say, IV requires 3-lOV of excitation voltage.
• Compound resistor R comp consisting of two single trimmable resistors Ri and R 2 connected in series (Fig. 11) and bridge resistor Rb (Fig. 11) form net compound resistor R b _ COm p-
• Resistance and TCR of single resistors are functions of their trimming fraction x 5 and y correspondently:
• R dT dR b _ comp (R 1 (X) + R 2 (y)f
• ⁇ b is TCR of the resistor R b .
• Compound resistor R comp consisting of two single trimmable resistors R / and R 2 connected in parallel (Fig. 1 1) and one bridge resistor R b (Fig. 10) form net compound resistor R b _ C o mP -
• Resistance of the compound resistor R b comp equals:
• TCR of the compound resistor can be expressed as:

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