Triferential Subtraction in Strain Gage Signal Conditioning. Introduction

Transcription

1 Trferental Subtracton n Stran Gage Sgnal Condtonng Karl F. Anderson Vald Measurements 3751 W. Ave. J-14 Lancaster, CA (661) Introducton The general form of NASA's Anderson loop measurement crcut topology nventon depends on the dual-dfferental subtractor for ts enablng technology.[1-9] Ths form of actve subtractor tolerates random varatons n lead wre resstance between the varous stran gages n a loop as well as n lead wres and connectons between a stran gage and ts sgnal condtonng. However, many practcal stran gage applcatons do not beneft from ths level of sophstcaton because ther stran gages are, n essence, electrcally adjacent. Ths paper presents a dual-dfferental subtractor defnton and then presents a smpler trferental approach to actve subtracton for stran gages that are electrcally adjacent. Schematc dagrams for several confguratons are presented. A trferental subtractor can be mplemented wth a sngle operatonal amplfer. The Dual-Dfferental Subtracton Functon The dual-dfferental subtractor s a sx-termnal, three-port actve analog electronc crcut functon defned n Fg. 1. The subtractor presents ts analog output where t can be most usefully observed n the system. Subtractors typcally deal wth floatng nputs and may provde ether grounded or floatng outputs. The subtractor develops at ts output port the dfference between two selected (and possbly amplfed) dfferental potental dfferences observed by ts nput ports. Dfferent amplfcaton factors can be used n observng the varous loop potental dfferences and the loop can contan any practcal number of observed mpedances. The deal dual-dfferental subtractor delvers at ts output,, the dfference between two nput potental dfferences, and, observed wthout energy transfer and amplfed by gans A 1 and A 2, respectvely. The output s unnfluenced by any common mode potental dfference, v cm1 and v cm2, or nteror mode potental dfference from one nput to the other, v m. Observng Separated Stran Gages The general theory underlyng the Anderson loop combnes an actve, dual-dfferental subtractor (referred to as a subtractor for smplcty) wth Kelvn sensng of observed potental dfferences across two (or more) mpedances carryng the same current. The Anderson loop measurement crcut topology makes use of the dual-dfferental subtractor to provde the dfference between the IR voltage drops across any two of potentally several dfferent stran gage and reference resstance voltage drops (Fg. 2).

2 Dual-dffererental subtractor v cm1 = A 1 - A 2 v m v cm2 Fgure 1, The dual-dfferental subtractor R R R w4 Dual-dffererental subtractor v g = A 1 v g - A 2 v ref v ref Fgure 2, The Anderson loop measurement crcut topology In practcal applcatons, the nput mpedance of the subtractor's nput ports s suffcently hgh to develop an nsgnfcant voltage drop across lead wre and connector resstances. So, the presence of typcal and varyng lead wre resstance s essentally rrelevant. The output of the crcut s gven by: = A 1 v g A 2 v ref (1) becomes when observng the voltage drops across two stran gages n an Anderson loop. = [A 1 ( ) A 2 ( )] (2) 2

3 When = and A 1 = A 2 = 1, eq. 2 reduces to: = ( ) (3) These equatons model the measurement crcut for any reasonable resstance that may exst n the loop between stran gages, n sense wres and n ther varous connectons. Observng Adjacent Stran Gages Resstances are electrcally adjacent when they share a common crcut node. The common node s brought out through a lead wre that senses the more negatve end of one stran gage also senses the more postve end of an adjacent stran gage or other crcut resstor. Stran gage pars are typcally wred usng the standard three-wre confguraton for brdge crcuts and n ether a three- or fve-wre confguraton for loop crcuts. All pars of adjacent arms (ncludng current-carryng lead wres) n a Wheatstone brdge are electrcally adjacent resstances. Three examples of ths concept are llustrated n Fg. 3. The fve-wre confguraton has the R w4 node common to both gages. The three-wre confguratons have ther node common to both gages. The resstance adjacent to the sngle gage confguraton s a brdge-completon resstor n Wheatstone brdge sgnal-condtonng crcutry and the reference resstor n Anderson loop crcutry. R w4 R w5 Fgure 3 Adjacent-gage confguratons Crcuts wth three lead-wres start at the top wth a gage plus a current-carryng lead wre,, electrcally adjacent ther connecton to the common node. The common node followed by a crcut segment ncludng, and ether a second gage and a Wheatstone brdge completon or Anderson loop reference resstor. Of course, the order of the second resstance and, s dctated by the practcal wrng stuaton, but t s electrcally rrelevant. Wth only three voltage-sensng wres arrvng at the nput to a sgnal condtoner there s a need for only three nput wres to the four nput termnals of a dual-dfferental subtractor. Accordngly, a specal three nput-termnal case of the dual-dfferental subtractor called a trferental subtractor has been developed. 3

4 Trferental Subtracton The trferental subtractor develops at ts output port the dfference between two electrcally adjacent (and possbly amplfed) potental dfferences observed by ts nput ports. Dfferent amplfcaton factors can be used n observng the adjacent loop potental dfferences and the loop can contan any practcal number of observed adjacent mpedances. The trferental subtractor s a fve-termnal, three-port actve analog electronc crcut functon defned n Fg. 4. Trferental subtractors typcally deal wth floatng nputs and provde ungrounded outputs that are observed dfferentally. The deal trferental subtractor delvers at ts output,, the dfference between two adjacent nput potental dfferences, and, observed wthout energy transfer and amplfed by gans A 1 and A 2, respectvely. The output s unnfluenced by any common mode potental dfference, v cm. The trferental subtractor s obvously a dual-dfferental subtractor wth the nteror-mode voltage, v m, electrcally shorted. For completeness, the defnton was presented n ts entrety. Equatons 1, 2 and 3 descrbe the Anderson loop wth ether a dual-dfferental or a trferental subtractor. Trfererental subtractor = A 1 - A 2 v cm Fgure 4, The trferental subtractor Practcal Implementatons Several mplementatons of the trferental subtractor have been developed. The user can consder the varous system transfer functon tradeoffs and select an approach optmum for the ntended applcaton. In general, havng fewer amplfers nvolved n subtracton wll result n a correspondngly lower measurement nose floor and drft wth temperature. Sngle Operatonal Amplfer Desgn The smplest trferental subtractor s mplemented wth a sngle operatonal amplfer (op amp) as llustrated n Fg. 5. It s a classc nvertng operatonal amplfer crcut postoned to replcate ts nput voltage where t can be observed n seres opposton to an adjacent loop 4

5 voltage. There s a fnte (but usually nsgnfcant) current, source, drawn through the nput resstance,, and the balance network assocated wth the nverter. sense = - for = Fgure 5, A trferental subtractor usng a sngle operatonal amplfer The nput and feedback resstances, and, respectvely, are typcally dentcal wthn component tolerances and selected to be an order of magntude or two greater than the stran gage resstance. Ths mnmzes drfts by keepng any lead-wre IR voltage drop due to the sense current, sense, from sgnfcantly alterng the system output voltage. The balance adjustment vares the A 1 /A 2 rato by trmmng the / rato. Balance range resstors, and, and balance-lmt resstance,, values are selected to acheve the desred balance authorty by varyng the amplfer gan around ts nomnal 1 value. Ths approach has the nterestng effect at balance of developng an output sgnal lnear n ( / ) ( / ). So t s not necessary to use stran gages that have essentally the same resstance. It s not absolutely necessary to nclude and, but f they are omtted the balance lmt resstance,, can become unreasonably large for fne adjustment of balance. Swtchng n dfferent values of and can provde a hgh-resoluton offset adjustment whle removng a substantal ntal offset. A dual-gage fve-wre sgnal condtoner usng a sngle-op amp trferental subtractor s llustrated n Fg. 6. In all of the fgures, carres the current from the exctaton source to the gage(s). and returns ths current to the reference resstor,. The voltage drop across s used as feedback for the exctaton current regulator. The system's electrcal senstvty can be establshed by provdng a calbraton resstance at any of the ndcated locatons, cal, cal, or cal. Brdge amplfers can often supply the power to and amplfy the low-level output from a trferental subtractor. By ths means, exstng Wheatstone brdge-based sgnal condtonng can be converted for Anderson loop operaton, often by replacng the brdge completon and calbraton card wth ether a dual-dfferental or trferental subtractor. The classcal approach for dealng wth lead-wre resstance varatons n brdge crcuts s to cause a current-carryng lead wre to exst n adjacent arms of a brdge. These confguratons also apply to wrng stran gages for trferental subtracton wth the added convenence that standard wrng color codes can be used. The three-wre sngle- and dual-gage confguratons 5

6 provde ths feature. All of the benefts of current loop sgnal condtonng reman avalable except for toleratng random varatons n any lead-wre resstance. sense sense R w4 cal R w5 cal cal RC flter = ( - ) v set pont Exctaton off Fgure 6, A dual-gage fve-wre sgnal condtoner usng a sngle-op amp trferental subtractor sense sense cal cal cal RC flter = ( - ) v set pont Exctaton off Fgure 7, A dual-gage three-wre sgnal condtoner usng a sngle-op amp trferental subtractor 6

7 A dual-gage three-wre sgnal condtoner usng a sngle-op amp trferental subtractor s llustrated n Fg. 7. Note that sense s not a problem because t does not flow n a gage exctaton wre. sense sense RC flter = ( - ) R cal v set pont Exctaton off Fgure 8, A sngle-gage three-wre sgnal condtoner usng a sngle-op amp trferental subtractor The three-wre technque for connectng a sngle stran gage s llustrated n Fg. 8. In ths case, the reference resstor, and become the electrcally adjacent resstance to the stran gage and resstance. Note that the calbraton resstance, R cal, shunts the reference resstor,, to provde for I calbraton. Ths approach also has the nterestng propertes of provdng common-mode rejecton that does not requre resstor matchng and the output s sngle-ended wth respect to analog common. The sense current, sense, can become essentally rrelevant whenever voltage drop due to the sensng current through ts lead wre s suffcently small. Also, note that the stran gage exctaton current,, s regulated after any sensng current has been extracted from the loop. Multple Operatonal Amplfer Desgns A sense current can be reduced to near zero f ts sgnal lne s buffered by addng a untygan amplfer. The buffer amplfer can also contrbute to provdng a drven sheld for the leadwres from stran gages to the subtractor nput. Several approaches usng more than one operatonal amplfer follow. Dual Operatonal Amplfer Desgns A buffered trferental subtractor wth balance control and drven guard s presented n Fg. 9. It s often convenent to use two operatonal amplfers n the same ntegrated-crcut package. 7

8 R cal = - for = Fgure 9, Buffered trferental subtractor The addton of the unty-gan buffer amplfer reduces the current n ts lead-wre to essentally zero. Ths assures that ths lead-wre resstance has no apprecable effect on the crcut output. A cost of ths feature s the addtonal drft and nose njected by an addtonal amplfer n the sgnal path. Guard drve R cal R sh1 = - for = R sh2 Fgure 10, Drven guard from a buffered trferental subtractor The unty gan buffer and nvertng amplfers have a low-mpedance output that s close to the extremes of voltage across the trferental nput. The current-lmtng dvder n Fg. 10 provdes a convenent source of guard drve for the nput lead-wres. 8

9 R sh1 R w4 cal cal R w5 cal R sh2 RC flter v set pont = ( - ) Exctaton off Fgure 11, A dual-gage fve-wre buffered trferental sgnal condtoner A buffered trferental sgnal condtoner wth guard drve s presented n Fg. 11. It llustrates a fve-wre connecton to two stran gages. sense sense R w4 cal R w5 cal cal R Gn RC flter R Gfb v set pont Exctaton off = ( - )(R Gn / R Gfb ) Fgure 12, Amplfcaton of a trferental sgnal condtoner output 9

10 The output of trferental subtractors can be amplfed by usng one more operatonal amplfer to provde a hgh-level dfferental output. Illustrated n Fg. 12, the addtonal gan s proportonal to the rato of R Gfb to R Gn. 1 2 R 4 1 = - 2 = v 3 - v 4 = ( v 3 ) - ( v 4 ) v 4 2 R cal R 3 v 3 2 Fgure 13, The dual-trferental subtractor Another mplementaton of the trferental subtractor operates wth four gages. Illustrated n Fg. 13, a trferental subtractor par provdes a dfferental sgnal that can be accepted at the nput of most conventonal dc Wheatstone brdge sgnal condtonng equpment. Resstors (not shown) added n seres wth the output lnes can smulate the output mpedance of a Wheatstone brdge. An unusual feature of ths confguraton s that a lead-wre s not requred from the node at the md-pont of the stran gage group unless each "half-brdge" s to be observed ndependently. Component Selecton Nearly all of the components nvolved n trferental subtractors are processng low-level analog sgnals. Therefore, t s essental to select components havng sutable stablty, nose performance and common-mode rejecton. Resstors nvolved n subtracton should be selected wth as much attenton to ther temperature coeffcent of resstance as f t were a brdge completon resstor. The resstors that establsh the guard drve potental and lmt the guard current do not need to be partcularly precse or stable because they do not contrbute drectly to the subtracton functon. Operatonal amplfers should be selected prmarly for low offset voltage changes wth respect to temperature, for low nose at the nput resstance they experence, bandwdth and nput offset current. Chopper-stablzed operatonal amplfers are recommended to acheve the best drft performance. Remember, mcro-volts count. 10

11 Measurement Valdty Checks Competent engneerng of measurement systems always nvolves provdng means to document the valdty of acqured data. Wthn the sgnal-condtonng crcutry, the most useful features for ths purpose are an exctaton zero and a means to dentfy the overall transfer functon of the electroncs. Crcutry to accomplsh these functons s ncluded wth each sgnal condtoner fgure. Exctaton can be reduced to essentally zero by causng the current regulator's set-pont to become zero. Ths approach has the advantage of not drvng the current regulator's operatonal amplfer nto saturaton by openng the current feedback loop. Always beware that removng exctaton from stran gages upsets the thermal equlbrum of the gage-test artcle system. You may need to wat untl thermal equlbrum s reestablshed before contnung wth the test. The transfer functon of the electroncs can be accomplshed by momentarly shuntng a remote gage wth a shunt calbraton resstor connected va the sense lead-wres. Another method s to shunt ether the nput or feed back resstor n the trferental subtractor. The response to ths calbraton acton can be easly related to an equvalent stran n a gage. Summary Anderson loop stran gage sgnal condtonng does not always requre the complexty of a dual-dfferental subtractor because electrcally adjacent gages share a common crcut node. The trferental subtractor s defned to smplfy sgnal condtonng for adjacent gages. A trferental subtractor can be as smple as a classcal nverter mplemented wth a sngle operatonal amplfer and two resstors. A varety of fve- and three-wre sgnal condtonng crcuts were llustrated. Some of these crcuts can provde an Anderson loop "front end" for conventonal stran gage brdge amplfers. References 1. Anderson, Karl F., Constant Current Loop Impedance Measurng System That Is Immune to the Effects of Parastc Impedances, U.S. Patent No. 5,731,469, December Anderson, Karl F., "The Constant Current Loop: A New Paradgm for Resstance Sgnal Condtonng" NASA TM , October Parker, Allen R., Jr., "Smultaneous Measurement of Temperature and Stran Usng Four Connectng Wres, " NASA TM , November Anderson, Karl F., "Current Loop Sgnal Condtonng: Practcal Applcatons, " NASA TM- 4636, January Anderson, Karl F., "A Converson of Wheatstone Brdge to Current-Loop Sgnal Condtonng for Stran Gages, " NASA TM , Aprl Anderson, Karl F., Contnuous Measurement of Both Thermoelectrc and Impedance Based Sgnals Usng Ether AC or DC Exctaton, Measurement Scence Conference, January Hll, Gerald M., "Hgh Accuracy Temperature Measurements Usng RTDs Wth Current Loop Condtonng, " NASA TM , May Olney, Candda D. and Collura, Joseph V., "A Lmted In-Flght Evaluaton of the Constant Current Loop Stran Measurement Method, " NASA TM , August Anderson, Karl F., "The Anderson Loop: Your Successor to the Wheatstone Brdge?," IEEE Instrumentaton and Measurement Magazne, Vol. 1, No. 1, March References are avalable at 11