Basic Bridge Circuits

Transcription

1 AN7 Datafoth Copoation Page of 6 DID YOU KNOW? Samuel Hunte Chistie ( ) was bon in London the son of James Chistie, who founded Chistie's Fine At Auctionees. Samuel studied mathematics at Tinity College and, upon gaduation, taught mathematics at the Royal Militay Academy fo almost 50 yeas. Chistie made many contibutions to magnetic science, such as the dependence of magnetic foces on tempeatue and sola ay effects on teestial magnetism. In 833, he published a pape on the magneto-electic conductivity of vaious metals, illustating how wie conductance vaies invesely with length and diectly as the squae of wie diamete. Embedded in this pape was the desciption of a cicuit used to measue and compae wie conductance. Chales Wheatstone (an English physicist and invento) ecognized the value of Chistie's cicuit; he was the fist to put this cicuit, which beas his name, to extensive use and to develop many significant applications fo it. To this day (6 yeas late), the Wheatstone bidge emains the most sensitive and accuate method fo pecisely measuing esistance values. Samuel Chistie neve got ecognition fo his bidge cicuit. At a oyalty of five cents fo evey bidge cicuit used, imagine what Chistie s oiginal cicuit invention would be woth today. Basic Bidge Cicuits Peamble Bidge cicuits have been in use fo well ove 50 yeas. To date, the bidge is still the most economical cicuit technique fo accuately measuing esistance. The oiginal bidge cicuit topology has had many unique modifications and has been applied to applications such as AC measuements, automatic balancing, oscillatos, and amplifies. Pehaps the best known application fo Samuel Hunte Chistie s cicuit is the bidge stain gage fo stain type measuements in mechanical assemblies and building stuctues. Analytical investigations thoughout this document focus on the R-ohm type bidge, which means all bidge esistos ae R ohms when not exposed to the field pocess vaiables. Figue epesents the R-ohm bidge type field senso with all bidge esistos (R, R, R3, Rx) located at the point of field measuement; howeve, as esisto Rx is the bidge esistive senso element, it vaies with pocess paametes such as tempeatue, flow, pessue, level, humidity, stain, etc. In R-ohm bidge topologies, R, R, R3 ae equal to R and Rx = (R+ R) whee R is a function of pocess vaiables. This application note will focus pimaily on some subtleties of bidge cicuit excitation and associated pefomance. Analysis of all the many bidge topologies that compensate fo small second ode effects ae beyond the scope of this application note. Reades inteested in the in-depth details of complex bidge topologies and stain gage applications should exploe the intenet, which contains thousands of sites dedicated to such details. In addition, eades ae encouaged to examine Datafoth s complete line of Signal Conditioning Modules (SCMs) dedicated to stain gage bidge applications, Refeence. Excitation x a R Vout = Vab b a' R R3 Rx b' Basic Bidge Cicuits The following examples focus only on Figue type bidge cicuit topologies with a single esistive vaiable element. Output esponses, including the effects of excitation line esistance fo both voltage and cuent bidge excitation as well as bidge lineaity, ae examined. Eos due to esistances of pooly made contacts and coosive action of dissimila metals ae neglected. Moeove, the output line esistances ae neglected since it is standad pactice to measue bidge output voltages with high impedance (typically > MΩ) devices. -pai (4-wie) Connection Figue Basic Field Bidge Cicuit with Rx Vaiable y Field Location

2 AN7 Datafoth Copoation Page of 6 Examples Two categoies of R-ohm bidge topologies will be examined. Categoy bidges ae defined as bidge topologies with all bidge esistos located in the field with one o moe elements exposed to the pocess vaiable; Categoy bidges ae defined as having one o moe bidge esistive senso elements that ae located in the field exposed to the pocess vaiables, with the emaining bidge esistos located at the point of electical excitation. Bidges with one o two pocess vaiable elements ae often efeed to as quate and half bidges, espectively. Categoy R-ohm Bidge with Voltage Excitation This example is based on Figue whee the excitation souce is voltage V. The actual bidge excitation voltage, Vxy, is not constant because of voltage dops in the excitation line esistance. Bidge output voltage is Vout = (Va-Vb) = Vab. If Vab is always measued with a high impedance (typically > MΩ) device, then sense line esistances can be neglected and Vab = Va b. As an example of the effects of sense line esistances, assume line esistance of 0Ω, voltmete with MΩ input impedance, and a 0Ω bidge. The voltmete loading on teminals a -b is appoximately , wheeas the loading on teminals a-b is appoximately o a diffeence of -0.00%. Equation illustates the output voltage, Vout = Vab, of Figue, neglecting all line esistances. R Rx Vab= V* - = R+R Rx+R3 ( R*R3) -( R*Rx) ( R+R )*( R3+Rx) Eqn. Industial tansduces with bidge cicuit topologies have esisto sets that balance the bidge at a steady state value detemined by a specific steady state field paametic input. As these steady state paametes change, the bidge becomes unbalanced and the output is non-zeo. Measuing this unbalanced voltage with an appopiate scale facto applied is a diect indication of the change in field vaiable. The useful ange of these voltages falls in the micovolt to millivolt categoy; consequently, low voltage measuement techniques must be utilized. Equation is the voltage output of R-ohm bidge cicuit topologies shown in Figue, with voltage excitation including excitation line esistances. V R-Rx Vout = * Eqn. ( R+Rx ) + *( 3R + Rx) ) R If excitation line esistances ae negligible, this equation educes to: V R-Rx Vout = * R+Rx line esistances = 0 Eqn. a Figue depicts the output esponse of the 0Ω bidge topology shown in Figue to changes in Rx. In this simulation, the excitation is 5VDC, Rx anges fom 0Ω to 0Ω, and thee diffeent excitation line esistances zeo, 5Ω, and 0Ω ae used. Output line esistance is neglected, which is a valid technique, as peviously shown. Equation illustates the classic bidge balance equation, which defines a set of esisto values that balances the bidge, esulting in zeo bidge output voltage, Vab = 0. This condition occus when R*Rx = R*R3. Note: The classic bidge balance condition is valid independent of line esistance and voltage excitation value. Clealy, this makes the bidge a useful cicuit topology fo balance measuing applications. 3 Chistie s 833 pape showed that if Rx is an unknown and R = R, then the bidge output will be zeo (it was easy to measue zeo in 833) when R3 is adjusted to be equal to the unknown esistance, Rx. Many industial tansduces use bidge cicuits with one o moe bidge esistances that ae functions of pocess vaiables such as tempeatue, flow, pessue, stain, humidity, etc. In these situations, bidge topology based tansduces can not be conveniently (o economically) balanced at the field location; theefoe, non-zeo output bidge voltages ae measued. Unlike balance measuements, bidge excitation and line esistances will contibute to measuement eos. Figue Output of the 0Ω Bidge in Figue Excitation V = 5VDC with 0 Ω < R < 0 Ω Output Voltage Line Resistance Neglected Bottom Cuve : Line Resistance zeo ohms Middle Cuve : Line Resistance 5 ohms Top Cuve 3: Line Resistance 0 ohms

3 AN7 Datafoth Copoation Page 3 of 6 Figue and Equation eveal some impotant facts about Categoy bidges.. Bidge output is sensitive to excitation line esistance and will always be sensitive to excitation voltage, V.. The bidge output voltage is nonlinea fo nominal changes in Rx egadless of excitation line esistance and excitation voltage. 3. As ange of Rx deceases, the bidge output voltage begins to appoach zeo and appeas to become moe linea. See cicle in Figue. ange between -.3 and -9.6mV pe ohm with an aveage value of -0.5mV pe ohm at balance. Although these numbes ae inteesting, it is not pactical to use patial deivatives in calculating bidge outputs. Common pactice is to ecognize that bidge cicuits have nonlinea outputs, which ae influenced by excitation line esistance, and to accept manufactues specified tansfe function data and installation instuctions fo thei bidge sensos. Figue a Enlagement of Aea Cicled in Figue Figue a shows that the bidge output voltage still appeas to be linea fo vey small vaiations of Rx and emains sensitive to excitation line esistance. A question aises hee. Is the voltage output of the bidge topology in Figue eve linea? To answe this, Equation 3 is the patial deivative of the R-ohm bidge Vout in Equation a with espect to Rx (change in Vout fo a change in Rx) with all othe vaiables assumed constant and no excitation line esistance. Change in Vout Change in Rx = V* - R ( R+Rx) Eqn. 3 It is clea that Equation 3 is a nonlinea function and is not constant, which is the condition necessay fo Vout to be a linea function of Rx. Thus, Figue type bidge cicuits cannot have outputs that ae linea functions of Rx. See Figue 3. Fo the ange of Rx between 0 and 30 ohms, changes in Vout with changes in Rx (Equation 3 and Figue 3) Figue 3 Output of the 0Ω Bidge in Figue Black Cuve: 0Ω Bidge Output Voltage Blue Cuve: Deivative of Bidge Output vs. Rx Excitation 5VDC with No Line Resistance Output Voltage Line Resistance Neglected 0Ω < Rx < 30Ω Refeence Figues,, a, and Eqn. 3 Categoy R-ohm Bidge with Cuent Excitation Fo well ove a centuy, bidge topologies with voltage excitation have been used. Today, with moden semiconducto cicuit technology, cuent souce excitation is also an option. Equation 4 epesents the output of a cuent, Iexc, excited R-ohm bidge (Figue ) with output voltage line esistance neglected and no excitation line esistance. Vout = ( Iexc*R ) R-Rx * 3*R+Rx all line s = 0 Eqn. 4 Equation 4 becomes Equation 4a when the cuent excitation is adjusted to be Iexc = (V / R). R-Rx Vout = ( V )* 3*R+Rx V = R*Iexc Eqn. 4a Note the similaity between Equations a and 4a. Equation 5 is the patial deivative of the R-ohm bidge Vout in Equation 4a with espect to Rx (change in Vout

4 AN7 Datafoth Copoation Page 4 of 6 fo a change in Rx) with all othe vaiables assumed constant. Change in Vout 4*R = (V)* Change in Rx ( 3*R+Rx) Eqn. 5 Whee V = R*Iexc Figues 4 and 5 povide a visual compaison of the output voltages fo the Categoy R-ohm bidge with both voltage and cuent excitation. Figue 4 illustates the pefomance of a 0Ω bidge cicuit as shown in Figue with cuent souce excitation at teminals and whee line esistances ae zeo. The value of this cuent souce was selected to be 4.667mA, which is 5VDC / 0Ω. This value of cuent povides 5VDC excitation at the bidge teminals when Rx is 0Ω, the condition of no field paametic inputs. Figue 5 Output of the 0Ω Bidge in Figue Black Cuve: 0Ω Bidge Output Voltage Blue Cuve: Deivative of Bidge Output vs. Rx Cuent Excitation, 4.67mA (5V / 0Ω) Excitation Line Resistances of 0, 5, and 0Ω Output Voltage Line Resistance Neglected 0Ω < Rx < 30Ω Refeence Figues,, a, and Eqn. 5 Compaison of Categoy R-ohm Bidge Excitations The list of obsevations below ae based on the 0Ω bidge topology of Figue with eithe 5VDC voltage excitation o 4.67mA cuent excitation, with excitation line esistances of zeo, 5, and 0 ohms included and output voltage line esistance neglected.. Equations 4, 4a, and Figue 5 (Black Cuve) show that fo cuent excitation the output of the R-ohm bidge topology shown in Figue is independent of excitation line esistance. Figue 4 Output of the 0Ω Bidge in Figue Red Cuve: 5VDC Excitation, Eqn. a Blue Cuve: 4. 67mA (5V / 0Ω) Excitation, Eqn. 4a Black Cuve: Diffeence [Vout (Eexc) Vout (Iexc)] All line esistances neglected Y-axis not shown fo Red and Blue cuves Figue 5 shows that the output behavio fo the 0Ω bidge topology shown in Figue, with cuent excitation including diffeent line esistances of zeo, 5, and 0 ohms, is independent of excitation line esistances. In this case, the change in Vout fo a change in Rx vaies fom -0 to -0.8mV pe ohm with an aveage of -0.4mV pe ohm, which is appoximately the same as fo voltage excitation but clealy still not constant.. Figue 4 shows that when line esistance is neglected the R-ohm 4-wie bidge output is moe linea ove a lage ange of Rx fo cuent excitation (blue cuve) than fo voltage excitation (ed cuve). 3. Equation 6 and Figue 4 (black cuve) show that the bidge outputs as illustated by voltage excitation (Equation a) and cuent excitation (Equation 4a) ae essentially identical nea balance. Nea balance, one can assume that R >> R. Note that Rx = (R + R) and Iexc is defined as V / R. V R Vout ~ * 4 R Eqn. 6 Inteesting note: In Figue type stain gage applications whee changes in R, Rx ae positive equal and changes in R, R3 ae negative equal, Equation 6 becomes

5 AN7 Datafoth Copoation Page 5 of 6 R Vout ~ V* R Eqn. 6a Choosing Excitation Excitation line esistances have diffeent effects on bidge output voltages depending upon which bidge categoy (Categoy o ) and which excitation (cuent o voltage) ae used. Figues 6 and 7 illustate the output behavio of Categoy R-ohm bidges with a single bidge esisto located in the field connected to the emainde of the bidge with two and thee wies, espectively. equations fo the bidge shown in Figue ae evisited hee. Recall that voltage output line esistances ae neglected in Figue and that Rx = (R + R). Figue Equations (4-Wie Categoy ) Voltage excitation V: V Vout = * - R R R+ R + * 4+ ) R ( ) Cuent Excitation, with Iexc = V / R: Excitation R a b Vout = Vab R3 -pai (-wie) Connection Field Location b' V - R Vout = * Let V = R*Iexc R R+ Figue 6 Equations (-wie Categoy ) R Rx Voltage excitation V: V - R-) Vout = * R+ R+ Figue 6 Two-Wie Quate Bidge Cuent Excitation, with Iexc = V / R: Vout = ( V) R- * Let V = Iexc*R 4R+ R+ Excitation R a Vout = Vab b R3 3-wie Connection Field Location b' Figue 7 Equations (3-wie Categoy ) Voltage excitation V: V - R-) Vout = * R+ R+ Cuent Excitation, with Iexc = V / R: R Rx Vout = ( V) R- * 4R+ R+ Let V = Iexc*R Figue 7 Thee-Wie Quate Bidge Review In the following Figue bidge output voltage expessions, R = R = R3 = R and Rx = (R+ R). Voltage excitation is V and cuent excitation is Iexc flowing into teminal. Fo convenience, behavioal Conclusions The following obsevations ae made based on Figue 6 and Figue 7 topologies:. Bidge voltage outputs ae nonlinea egadless of whethe cuent o voltage excitation is used.

6 AN7 Datafoth Copoation Page 6 of 6. Categoy bidge topologies have output voltages that ae independent of line esistances when cuent excitation is used. 3. Categoy bidge topologies have output voltages that ae always dependent on line esistances egadless of whethe cuent o voltage excitation is used. 4. If ( << R << R), i.e., if line esistances can always be neglected and if changes in the sense esisto Rx ae vey small compaed to R, then bidge output is the same fo voltage o cuent excitation. - R) Vout = V* Voltage Excitation, o 4R - R) Vout = Iexc* Cuent Excitation = (V / R) 4R Output esponses fo R-bidge cicuits containing moe than one vaiable esistive element, with equal but opposite changes to pocess vaiables, ae common in stain gage bidge cicuits. These cicuits ae discussed in Datafoth s application note on stain gages. Figue 8 is a block diagam of Datafoth s Bidge Signal Conditioning Module Seies SCM5B38. These modules ae designed to inteface with Categoy full bidge cicuits with options fo Categoy half and quate bidge topologies. This module s pedominant application is in industial stain gage instumentation applications; howeve, it is well-suited fo any bidge type instumentation application. Datafoth s bidge SCMs SCM5B38 and DSCA38 have multiple (typically 5-7) pole filtes with anti-alias filteing on the field side. Moeove, these modules have 4-way isolation, which includes pecision isolated voltage fo field excitation, isolated field-side powe, isolated compute-side powe, and signal isolation. Datafoth s DIN ail DSCA38 seies of modules has both naow and wideband filte options to accommodate a wide ange of applications. In addition, the DSCA38 seies has +/-5% font-panel adjustments fo zeo and span. Zeo adjustments ae paticulaly useful fo balancing bidge cicuits. The eade is encouaged to visit Datafoth s website, Refeence, and examine all the options fo the SCM5B38 and DSCA38 bidge modules, as well as Datafoth s complete line of SCMs. Figue 8 Datafoth SCM5B38 Stain Gage Signal Conditioning Bidge Module Datafoth Refeences. Datafoth Cop.,