CA1115980A - Bridge circuit - Google Patents

Abstract

E. A. Romo 2X

BRIDGE CIRCUIT

ABSTRACT OF THE DISCLOSURE
A circuit including a strain gage bridge having a con-stant current supply at a constant temperature and otherwise variable with temperature. Linearization and accuracy are ob-tained through a feedback connection. The constant current and temperature compensation features and common mode rejection are also employed to improve accuracy.

Description

E. A. Romo 2X

BRI~GE CIRCUI~r BACKGROUND OF THE INVE _ ION_ This invention relates to a bridge having an element connected therein, the resistance of which changes with some variable, and more particularly to a strain gage bridge or the 5 like.
In the past, strain gage bridge circuits have suf~ered from inaccuracies due to asymmetrical strain gages, amplifier distortion, and other non-linearities.
PRIOR ART STATEMENT
__ The voltage regulator disclosed in this application may be similar to or identical to voltage regulator 127 disclosed in U.S. Patent No. 3,725,665 issued April 3, 1973.
The utility of the invention of this application may include but not be limited to a combination where the circuit of 15 the invention is substituted for that shown in Fig. 4 of U.S.
Patent No. 3,722,264 issued March 27, 1973.
Regarding U.S. Patent No. 3,532,869 issued October 6, 1970, see the abstrac-t.
Regarding U.S. Patent No. 3,161,821 issued 20 December 15, 1964, note amplifiers 11, 11', 15, 15', 34 and 42.
Regarding U.S. Patent No. 3,434,343 issued March 25, 1969, note column 3, line 46 et seq.
Regarding U.S. Patent No. 3,518,886 issued July 7, 1970, see circuit 19 in E`ig. 1.
Regarding U.S. Patent No. 3,568t044 issued March 2, 1971, see resistor 42.
Regarding U.S. Patent No. 3,841,150 issued October lS, 1974, see the abstract and resistor 77 in Fig. 3.
Regarding U.S. Patent No. 3,847,017 issued 30 November 12, 1974, see amplifiers A3 and A4.
Regarding U.S. Patent No. 3,967,188 issued June 29, 1976, see the abstract.
SUMMAR~ OF THE INVENTION
_~___ _ According to the present invention, there is provided a 35 detector circuit comprising: a Wheatstone bridge having first, second, third and fourth corner junctions; a first leg connected between said fourth and first corner junctions; a second leg connected between said first and second corner junctions; a third leg connected between said second and third corner ~' ~
. ,~

E. A. Romo 2X

junctions; a fourth leg connected between said third and fourth corner junctions; a main differential amplifier having inverting and noninverting inputs, and an output; first means to supply a voltage to said main differential amplifier noninverting input 5 regulated with respect to ground, said main differential amplifier output being connected -to said secotld corner junction, said fourth corner junction being connected to said main differential amplifier inverting input; second means providing resistance connected from said fourth corner junction to ground, 10 the current from the output of said main differential amplifier being constant when the resistance of any of said legs changes;
output means connected from said first and third corner junctions; and utilization means connected from said output means~

In the accompanying drawings which illustrate exemplary embodiments of the present invention:
Fig. 1 is a schematic diagram of the circuit oE the present invention;
Fig. 2 is a schematic diagram of a Wheatstone bridge; and Fig. 3 is a schematic diagram of an alternative embodiment of the present invention.
_ SCRIPTION OF THE PREFERRED EMBODIMENT
In the drawings, a battery is provided at 10 connected to input junctions 11 and 12 through diode 13 and resistor 14, respectively. Diode 13 is poled to be conductive from a positive pole of battery 10 to junction 11.
Battery 10 has a negative pole connected to junction 12 30 through resistor 14. A voltmeter calibrated in differential pressure is provided at 15 and connected in parallel with resistor 14. The lead between battery 10 and diode 13 may he very long, if desired. The same is true of the lead ~rom resistor 14 to junction 12.
Junction 12 is connected to ground. An output resistor is provided at 16 connected from a junction 17 to junc-tion 12.
Other junctions are connected through the figure as Eollows.
There is a junction 18, a junction 19, a junction 20, a ~unction 21, a junction 22, a junction 23, a junction 24, a junction 25, a junction 26, a junction 27, a junction 23, a junction 29, a .~

junction 30J a junction 31~ a junction 32, a junction 33, a junc-tion 34, a junction 35, a junction 36, a junction 37, a junction 38, a junction 39, a junction 40, a junction 41, a junction 42, a junction 43, a junction 44, a junction 45, a junction 46, a S junction 47, a junc-tion 48, a junction 49, a junotion 50 and a junction 51 shown in the drawing.
The circuitry found in dotted ~ox 5Z is a voltage regu-lator which, if desired, may be conventional. Transistors are provided at 53 and 54. Transistor 53 has a collector 55, an emitter 56 and a base 57. Base 57 is connected form junction 18.
Transistor 54 has a collector 58, an emitter 59 and a base 60.
A zen~r diode is provided at 61 connected between junctions 18 and 20. A resistor 62 is provided connected from junction 20 to emitter 56. Collector 55 is connected to junction 21. Junctions 21, 22 and 23 are connected together. A zener diode 63 is con-nected from junction 23 to ground. A resistor 64 is connected from junction 18 to jun~tion 19. Junction 19 i5 connected to ground. Base 60 is connected from junction 22. A resistor 65 is connected from emitter 59 to junction 19. Collector 58 is con~sected from junction 18.
Junction ~0 is connected from junction 11. Voltage regula-tor 52 acts as a source of potential for a differential ampliier 66 connected from junction 21 in voltage regulator 52.
Differential ampliiers are also provided at 67, 68 and 69. ~ s~rain gage bridqe is provided at 70~ Strain gages are provided at 71 and 72. Resistors are provided at 73 and 74. A
potentiometer is provided at 75 having a winding 76 and a wiper 77. The potential o~ wiper 77 is one corner of the bridc~e 70.
The other co~ners are the junctions 24, 27 and 28. A re~istor 78 is co~nected parallel with winding 76. ~uxiliary resi.stors are provided at 79 and 80. A conventional differential pressure unit i5 provided at 81 to stress strain gages 71 and 72 so thak voltmeter 15 can he calibxated in differential pressure. The differential pressure unit 81 may be of the prior art ty~e de-scribed hereinbefore. The position of wiper 77 provides a æero adjustment. The position of wiper 82 of a variable resistor 83 provides a span adjustment.

-4- E. A. Romo 2X

A temperature compensating resistor is provided at 84 connected between terminals 85 and 86. Terminals 85 and 86 are, in turn, connected to junctions 32 and 33, respectively. Depend-ing upon the algebraic sign of the ~emperature correction needed, resistor 84 is connected as shown or between terminals 87 and 88 connec~ed to junctions 34 and 35. A resistor 89 is connected between junctions 32 and 33. A resistor 90 is connec~ed between junctions 34 and 35. Linearity through feedback is provided at one of the junctions 33 and 36. As shown, the feedback is pro-vided through a resistor 91 and a jumper 9~ betwee~ terminals 93 and 94 ~o junction 36.
In its other position/ jumper 92 is connected from ter-minal 93 to a terminal 95. R~sistor 91 is connected from junc-tion 51. Junctions 27 and 30 are connected together. A resis~or lS 96 is connected between junctions 30 and 34. The inverted input of amplifier 67 is connected from junc~ion 30. A re~istor 97 is connected between junctions 31 and 32. A resistor 98 is conn~cted between junctions 23 and 31. The non-inverting inpuk of amplifier 67 is connected from junction 31.
With no change in temperature, or with a change in tem-perature, the amplifier 67 keeps the current at the output thereof and from junction 27 to junction 30 constant. The gain of ampli-~ier 67, as is conventional, may be anywhere from 100,000 or less to 500,000 or more. This means that junction 30 is always driven to the potential of junction 31.
If strain gages 71 and 72 are not symmetricaL, the con-stant curr~nt drive of amplifier 67 still maintains the output thereof accurate. ~he circuit connected from wiper 77 and junc-tion 28 is, ~or the most part, a common mode rejection circuit which also Lmproves accuracy~ A resistQr 99 is connqcted from wiper 77 to junction 37. A capacitor 100 is connected between junctions 29 and 37. ~unctions 28 and 29 are connected to the noninverting input of amplifier 66. Amplifier 68 has a ~eedback resistor 101. Amplifier 66 has a feedback resistor 102. Junc-tion 45 is connected from the output of amplifier 66. Resistor s~
-5- E. A. Romo 2X

102 is connected from junction 44 to the inverting input of ampliier 66. Junctions 44 and 45 are connected together.
JunctiQns 43 and 44 are connected together. Variable resistor 83 is connected from junction 43 to junction 42. Terminals 103, 104, 105 and 106 are connected respectively from junctions 42, 41, 40 and 39, so that resistors 107 and/or 108 and/or 109 may be shorted or opened.
Feedback resistor 101 is connectad between junctions 38 and 47. The output of amplifier 68 is connected to ~unction 47.
The noninverting input of amplifier 6a is connect~d ~rom junc tion 37. The invPrting input of an amplifier 68 is connected from junction 38. Junctio~s 38 and 39 are connected together.
A resistor 110 is connected from junction 45 to junction 46.
A resistor 111 is connected from junction 47 to junction 48. A
resistor 112 is connected fl~om junction 46 to junction 51. Junc~
tions 17 and 51 are connected together. A resistor 113 i.5 con-nected from junction 48 to ground. The invert~ng and noninvert-ing inputs of amplifier 69 are respectively connected from junc-tions 4 6 and 4 8 .
A xesis~or 114 is con~ected from the output o amplifier 69 to a base 115 of a transistor 116 having a collector 117 and an emi~ter 118. Collector 117 is connected to junction 50.
Junctions 11 and 50 ar~ connected together. Another transistor is pro~ided at 118' having a collector 119, an emitter 120 and a base 121. Emitter 118 is connected to junction 49. Bass 121 is connected from junction 4g. Collector 119 is connected from junction 50. A resistor 122 is connected from collector 120 to junction 17. A resistor 49' i5 connect~d between junctions 49 and 51. Re~istors 33' and 34' have a resistance normally sub-~tantially less than that of resistors 97 and 96, respec~ively.
Some circuit component values are listed in the follow-i~g:

5~

-6-E. A. Romo 2X

Resistors _ e _ 14 10 ohms 33' 200 ohms 34~ 200 ohms 49' 4~700 ohms 62 1,500 ohms 64 22 megohms 20,000 ohms 73 7,500 ohms 74 7,50~ ohms 78 10 ohms 96 3,2~0 ohms 97 10,000 ohms 98 10,000 ohms 99 2,200 ohms 101 75,000 ohms 102 75,000 ohms 107 5,000 ohms 108 5,000 ohms 2a lO9 ; ~ ooo ohms 110 75~000 ohms 111 75,000 ohms 112 75,000 ohms 113 75,000 ohms 114 220 ohms 122 22 ohms W~, 76 100 ohms In Fig. 3, oppo~itely disposed strain gages are fixed to tho same side o a conventional cantilevered beam. For example, see U. S. Patent No. 3,518,886 issued ~uly 7, 1970.
OPER~ION
.
As stated previously, ~oltage regulator 52 may be conven-tional and may operate in the same manner as that disclosed in the said U. S. Patent No. 3,725,665.

-7- E. A. Romo 2X

The present invention can utilize two strain gages 71 and 72 in ~he same or a manner similar to that disclosed in U. S.
Patent No 3,722,264 as aforesaid. In this patant it will be recognized that when one strain gage is in tension, the other is in compression, and vice versa, as is well known. This means that the re~istance o the tension gage increases and that of the compression gage decreases.
Note tha-t ~he resis~ance between junctions 24 and 27 may change with ~emperature. Resistor 84 supplies a zero temperature adjus~ment. Feedback from junctic~n 51 through resistor 91 keeps the output voltage across resistor 14 linear with the conventional strain gage beam of DPU 81, and accurate with the differential pressure within DPU 81. The str~in-resistance ~unction of gages 71 and 72 and their beam are not quite linear and the feedback compensates for this.
Excep~ fox feedback and temperature sensitive resistor 84, resistor 98 through juncti~n 31 to ground is a voltage divider which determines the noninverting input voltage o~ differential amplifier 67. The same is true of ~he inverting input connected through junction 30 to resistor 34' ~o ground.
As stated pre~iou~ly, as is well known, ampli~ier 67 may have a gain of 500,000 and will thereore drive its inverting in-put to within, for example, 0.5 millionth of the voltage of its noninverting input. The noninverting input is essentially co~stant except for a pos~ible te~perature and/or feedback connection.
Resistor 84 supplies a zero temperature correction, as ~foresaid. The dynamic temperature correction is supplied by ampli~ier 67 which keeps the current between junctiQns ~-7 and 30 constant and e~ual to tha output ourrent of amplifier 67 ~o bridge 70. As is well known, the input impedances of amplifier~, such as ampli~iers 66, 67, 68 and 69, are so high (in the megohm range or above) that the curren~ between junctions 28 and 29, and fro~n wiper 77 through resistor 99 may be neglected.
In accordance with the foregoing, under strain, gage 71 35 is in tension when gage 72 is in compression or vice versa.

-8- E. A. Romo 2X

Amplifiærs 66 and 68 act as a common mode rejection circuit and cancel out common nonlinearities in the amplifiers and changes therein due to temperature. Note that one side of the bridge, junction 28, is connected to amplifier 66, and the other side (wiper 77) is con~ected to amplifier 68 through resistor 99 and junction 37.
~mplifier 69 then takes the difference between the o~tputs of amplifiers 66 and 68. The rea~on for this is, as is well known, the output of the bridge should be proportional to ~he difference b~tween the voltages at junction 28 and wiper 77.
Transistors 116 and 118~ form a Darlington circuit, known for many years~ that has an output current through and a voltage across resis~or 16 which is direc~ly proportional to ~he ou~put voltaye of amplifier 69, which is al o well known.
The constant current at the output of amplifier 67 solves the temperature change problem. I the voltage between junctions 24 and 27 were constant, a change in the ~ridge temperature would cause the currents in the bridge legs to vary. This would cause the potential of wiper 77 to ~ary erroneously because the curxent of the leg including strain gage 72 would change and the voltage across that leg would vary. There is no compensation at junction 28 because the res.istance of 73 i~ equal to tha~ of 74 and the voltage at 28 is always half the constant voltage between junc-tions 24 and 27.
On the other hand, with a constant output current Erom amplifier 67, the currents in all legs remain constant (reme~ber the amplifiers 66 and 68 take negligible input current because of their high input impedances). See also the algebraic proof, infra.
If the sum of the resistances in the leg of gage 71 is Ra, tho sum of those in the leg of gage 72 i5 Rb, the resistance of resistor 73 is Rc, and the resistance of resistor 74 is Rd, the voltage drop from wiper 77 to the potential of junction 28 i~

eO ~ iabRb icdRd ~1) See Fig. 2.

-9 E. ~. Romo 2X

ab a b ( 2 ) where e is the vol~age drop from junction A in Fig. 2 to ~unction B (note e is variable and i is constant).
= e (3) lcd Rc ~ Rd a = R- + R b+--R-- + Rd (4) eRb eRdR ~5 eO ~a + Rb c d RbtRC + Rd) - Rd(Ra Rb O = ~r~

(Ra + Rb) (R~ + Rd) (6) x Ra + ~ + Rc + Rd .1 Ra + Rb ~ Rc + Rd (7) loAs is convsntiona1 Rc may be equal to Rd and ~oth may be temperature insensîtive.
Equation (7) may thus ~e rewritten eO ~ ~ ~8j If Rc ~ Ra and Rc >~ Rb (10) -10- E. A. Romo 2X

eO Rb ~ a (11) If ~ ~o( b (12) and Ra = Rao(l + ~a~ ) (13) (Common equations for resistance versus temperature ~if~erence ~T from a reerence, ~b and ~a being constan~, Rbo and Rao being resistances at the reference temperature.) 1 (RbO Ra~ Rb~aT - RaOa ~T~ ~14) Thus i the leg xesistance Rbo is equal to ~he leg resis-tance Rao ~need not ~e -- may be zero corrected in the output.
circuit) and o~b Rao~a (15) eO Rbo Rao (16) ~0 and Rao are constant and independent of tem~erat re and their difference i9 w~at eO measures. The said diference is lS that sought' for as ~ linear function of differential pressure~
~ot~ again i is constant.
Tha phrase "matched legs" i~ here~y de~ined ~r use herein and in. the claim~ to mean Wheatstone bridge strain ga~es or the like constructed in accordance with equation (15).
2U No~e what happens when e = E ~17) and E is a constant voltage.
From equation (5) o = ~ c )( d a~ ~ (18) 3~
-11- E. A. Romo 2X

However in this case, the temperature sensitive Ra and do not drop out in the denomina~or of (18~ even if R = Rd (19) and R >> Ra (20) and R >> ~ (21 The same is true of ~he four strain gages in khe alterna-- tive embodiment of Fig. 3 and even if all four bridge legs are matched and have equal resistances at a single re~erence ~empera~
ture.
Applying equation ~18) to Fig. 3, let us define E~b and R~ as tension ga~e legs, Ra and Rd as compression gage legs so ~hat, from stress only, resistance changes QR

c = R + ~R (22 Ra = Rd ~ R - ~R ~23) From equation (18) eO (R + QR)2 _ (R - QR) ~24) E 4(R 1- aR) Eo R~R_ (R ~ ~R) Equation (25) ~hows that if E is constant, QR is not linear with eO for all values of R and aR.
20Even i R QR
eO ~R (26) and eO is a ~unction o chan~es in R due to tempera-ture changes. Note ~R is not a func~ion of temperature, but only a function o strain.

-12- E. A. Romo 2X

On the other hand, using constant current i, from equa-tion ( 7 ) eO ~ ~ (27) - ~R (28) 5 Thu~, with con tant curren~ i, equation (28) is independellt of the ef f ect~ .

A~S ~ rm

Claims (18)

E.A. Romo 2X

WHAT IS CLAIMED IS:

1. A detector circuit comprising: a Wheatstone bridge having first, second, third and fourth corner junctions;
a first leg connected between said fourth and first corner junctions; a second leg connected between said first and second corner junctions; a third leg connected between said second and third corner junctions; a fourth leg connected between said third and fourth corner junctions; a main differential amplifier having inverting and noninverting inputs, and an output; first means to supply a voltage to said main differential amplifier noninverting input regulated with respect to ground, said main differential amplifier output being connected to said second corner junction, said fourth corner junction being connected to said main differential amplifier inverting input; second means providing resistance connected from said fourth corner junction to ground, the current from the output of said main differential amplifier being constant when the resistance of any of said legs changes; output means connected from said first and third corner junctions; and utilization means connected from said output means.

2. The invention as defined in claim 1, wherein said first and second legs include first and second strain gages, a differential pressure unit being provided to put one of said first and second legs in compression while putting the other thereof in tension, said utilization means including a meter calibrated in differential pressure.

3. The invention as defined in claim 1, wherein said first and second means include at least first and second resistors, respectively, said first resistor being connected from said main differential amplifier noninverting input to ground, said second resistor being connected from said fourth corner junction to ground.

4. The invention as defined in claim 3, wherein third and fourth resistors are provided and are connected in series with said first and second resistors, respectively, from one end there-of to ground, and a feedback resistor connected from said output means to the ungrounded side of one of said third and fourth re-sistors, said first, second, third and fourth resistors having -14- E. A. Romo 2X
resistances R1, R2, R3, and R4, respectively, where R3 = R4, R1 >> R3, R2 >> R4, and R1 and R2 are the same order of magnitude.

5. The invention as defined in claim 1, wherein one of said first and second means are temperature sensitive.

6. The invention as defined in claim 1, wherein said output means includes a first auxiliary differential amplifier (ADA), and second and third auxiliary differential amplifiers (ADA), each of the said three of which has a noninverting input, an inverting input, and an output, said first ADA noninverting input being connected from said third corner junction, a first resistor connected from said first corner junction to said second ADA noninverting input, a capacitor connected between the non-inverting inputs of said first and second ADAs, second and third resistors connected respectively from the outputs of said first and second ADAs to the respective inverting inputs of said first and second ADAs, a variable resistor connected from the output of said first ADA to the inverting input of said second ADA, a fourth resistor connected from said first ADA output to said third ADA inverting input, a fifth resistor connected from the output of said second ADA to the noninverting input of said third ADA, a sixth resistor connected from the noninverting input of said third ADA to ground, a Darlington pair including first and second transistors each having a collector, an emitter and a base, a seventh resistor connected from the output of said third ADA to said first transistor base, the first transistor emitter being connected to said second transistor base, both of the collectors being connected together, eighth and ninth resistors connected in that order from the second transistor emitter to ground, tenth and eleventh resistors connected respectively from said first transistor emitter and from the inverting input of said third ADA to the ungrounded side of said ninth resistor, a source of D.C. potential, a twelfth resistor connected from said collec-tors to ground, and a voltmeter calibrated in differential pressure and connected in parallel with said twelfth resistor.

-15- E. A. Romo 2X

7. A detector circuit comprising: a Wheatstone bridge having first, second, third and fourth corner junctions; a first reference leg connected between said second and third corner junctions, said first leg including a resistor; a second reference leg connected between said third and fourth corner junctions, said second leg including a resistor, both of said first and second reference legs being temperature insensitive; a first active leg connected between said fourth and first corner junctions; a second active leg connected between said first and second cor-ner junctions, said first and second active legs each including a temperature sensitive strain gage; force means to increase the resistance of one strain gage while decreasing the resistance of the other strain gage; a main differential amplifier having in-verting and noninverting inputs, and an output; first means to supply a voltage regulated with respect to ground and connected to said main differential amplifier noninverting input, said main differential amplifier output being connected to said second corner junction, said fourth corner junction being connected to said main differential amplifier inverting input, second means providing resistance connected from said fourth corner junction to ground, the current from the output of said main differential amplifier being constant when the sum of the resistances of said first and second active legs changes; output means connected from said first and third corner junctions; and utilization means con-nected from said output means.

8. The invention as defined in claim 7, wherein the re-sistance Rb of said first active leg is equal to that Ra of said second active leg at a predetermined reference temperature when said strain gages are unstressed, said first reference leg having a resistance Rc equal to that Rd of said second reference leg, the following condition also being true:
Rc Rb

9. The invention as defined in claim 8, wherein said first and second active legs are matched to the extent that, when said first and second active legs are unstressed, -16- E. A. Romo 2X

Rbo.alpha.b = Rao.alpha.a where Rb = Rbo(1 + ab.DELTA.T) Ra = Rao(1 + .alpha.a.DELTA.T) Ra and Rao are Rb and Ra, respectively, at said predetermined reference temperature, .alpha.b and .alpha.a are the temperature coefficients of resistance of said first and second active legs, and .DELTA.T is the difference between ambient temperature and said predetermined reference temperature.

10. The invention as defined in claim 9, wherein said force means includes a differential pressure unit, said utiliza-tion means including a voltmeter calibrated in differential pressure.

11. The invention as defined in claim 10, wherein said first means includes a regulated voltage source, a first resistor connected from said source to said amplifier noninverting input, third means providing resistance from said amplifier noninverting input to ground including a second resistor having a terminal connected to ground, said second means also having a third resis-tor connected to ground, a feedback connection from said output means to one of said second and third resistors at a point above ground, one of said second and third means having a temperature sensitive resistor, but otherwise being substantially identical.

12. The invention as defined in claim 7, wherein said first means includes a regulated voltage source, a first resistor connected from said source to said amplifier noninverting input, third means providing resistance from said amplifier noninverting input to ground including a second resistor having a terminal connected to ground, said second means also having a third resis-tor connected to ground, a feedback connection from said output means to one of said second and third resistors at a point above ground, one of said second and third means having a temperature sensitive resistor, but otherwise being substantially identical.

-17- E. A. Romo 2X

13. A detector circuit comprising: a Wheatstone bridge having first, second, third and fourth corner junctions; a first leg connected between said second and third corner junctions, said first leg including a strain gage; a second leg connected between said third and fourth corner junctions, said second leg including a strain gage; a third leg connected between said fourth and first corner junctions; a fourth leg connected between said first and second corner junctions, said third and fourth legs each including a strain gage, all of said strain gages being temperature sensitive; force means to increase the resistance of one pair of oppositely disposed strain gages while decreasing the resistance of the other pair; a main differential amplifier having inverting and noninverting inputs, and an output; first means to supply a voltage regulated with respect to ground and connec-ted to said main differential amplifier noninverting input, said main differential amplifier output being connected to said second corner junction, said fourth corner junction being connected to said main differential amplifier inverting input; second means providing resistance connected from said fourth corner junction to ground, the current from the output of said main differential amplifier being constant when the resistance between said second and fourth corner junctions changes; output means connected from said first-and third corner junctions; and utilization means connected from said output means.

14. The invention as defined in claim 13, wherein the resistance R of each leg is the same at a predetermined refer-ence temperature when all of said strain gages are unstressed.

15. The invention as defined in claim 14, wherein each of said legs has the same temperature coefficient of resistance.

16. The invention as defined in claim 15, wherein said force means includes a differential pressure unit, said utiliza-tion means including a voltmeter calibrated in differential pressure.

-18- E. A. Romo 2X

17. The invention as defined in claim 16, wherein said first means includes a regulated voltage source a first resistor connected from said source to said amplifier noninverting input, third means providing resistance from said amplifier noninverting input to ground including a second resistor having a terminal connected to ground, said second means also having a third resis-tor connected to ground, a feedback connection from said output means to one of said second and third resistors at a point above ground, one of said second and third means having a temperature sensitive resistor, but otherwise being substantially identical.

18. The invention as defined in claim 13, wherein said first means includes a regulated voltage source, a first resistor connected from said source to said amplifier noninverting input, third means providing resistance from said amplifier noninverting input to ground including a second resistor having a terminal connected to ground, said second means also having a third resis-tor connected to ground, a feedback connection from said output means to one of said second and third resistors at a point above ground, one of said second and third means having a temperature sensitive resistor, but otherwise being substantially identical.