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1 AN03 Dataforth Corporation Pae of 5 DID YOU KNOW? James Prescott Joule (88-889) discovered that power (derivative of enery wrt time) dissipated in a resistor can e expressed as I 2 R and pulished his findins in 84 as Joule's Law. He was est known for estalishin the concept that heat is a form of enery. In his honor, the unit of enery was named Joule. Common Mode Voltae Preamle: Sinal conditionin modules typically have two types of front-ends; either sinle ended (SE) or differential ended (DE) inputs. Sinle ended sinals are referenced to the module's power supply common, which should e at the reference potential of the sinal ein measured. If this reference is not zero potential, then the actual input sinal includes an unwanted voltae, which is amplified alon with the desired differential sinal producin serious errors on the output. Differential ended inputs are simply two SE inputs referenced to a common potential where the "information" sinal is the difference etween these two SE inputs. Sinal conditionin modules must use differential input front-ends to amplify the difference etween two SE input sinals. Any non-zero potential on the reference is common to oth SE inputs. Fiure illustrates that nelectin all source resistors; is VcmVsinal2 and is VcmVsinal. Note, (-) is (Vsinal2- Vsinal). Vcm Rscm Vsinal Rs Fiure 2 is a simplified asic MOS differential pair, used in many instrumentation amplifiers. Vo I M VDD I2 M2 Iss VSS Vo2 Fiure 2 MOS Differential Input Pair Fiure 3 is a simplified dynamic model of the MOS differential pair shown in Fiure 2. Current sources I, I2, Iss are represented y Rd, Rd2, Rss respectively. Gm, Rds and Gm2, Rds2 model the MOS devices M, M2 respectively. Vsinal2 Rs2 Rds Rds2 Fi Typical Differential Input, (-) Gm Gm2 In theory, differential measurements eliminate the effects of common mode voltae (Vcm). Unfortunately, all differential amplifiers have two ains; a differential ain (Ad) and a common mode ain (Acm). Moreover, the value of these ains depend upon the output connection; either sinle ended (SE) or differential ended (DE) This application note discusses the internal oriin of IC differential amplifier common mode ain (Acm) and some of the external applications that create common mode voltaes. For the reader who is not particularly interested in the theory of Acm; he/she may skip to the section on Examples. Vo Rd Vss Rss Rd2 Vo2 Fiure 3 Simplified Model of Differential Pair

2 AN03 Dataforth Corporation Pae 2 of 5 The solution to a set of node equations written at Vss, Vo, and Vo2 will provide expressions for the individual output voltaes, Vo, Vo2. These symolic expressions are mathematically very messy. However, if one assumes M, M2 and I, I2 are identical, these expressions simplify sustantially. Moreover, if Rd=Rd2 Rd; Rds=Rds2 Rds; and if 2 Rss Gm Rds >>, then Rds Rd V02 =-Gm -... Rds Rd 2 Gm Rds Rd - 2 Rss Gm Rds Rds Rd V0 = Gm -... Rds Rd 2 Gm Rds Rd - 2 Rss Gm Rds Eqn Eqn 2 The assumptions made in developin Equations and 2 are not always completely possile; however, they provide the reader with an insiht into the parameters responsile for estalishin "ains". Equations and 2 are sinle ended (SE) output expressions with two terms; a) a ain term multiplyin the differential input, and ) another ain term multiplyin the SE input voltae. Note: This common SE term is the oriin of common mode voltae ain. Instrumentation amplifiers typically have several internal differential pairs, all of which contriute to developin the final SE output, which includes a net common mode ain term. Desiners and manufacturers of IC instrumentation amplifiers use two techniques to diminish this common mode term; a) ensure internal differential pairs have matched devices, and ) use topoloies that use lare dynamic values of Rss. Note: The SE term is diminished as Rss increases provided the stated conditions of "identity" are true. Therefore, differential input IC amplifiers have very lare dynamic values of Rss and differential pair cells with near identical devices. Unfortunately, such ideal conditions can not e completely achieved. Consequently, there will always e some common mode ain ( Acm). Model Analysis An exact numerical solution for the output voltaes Vo, Vo2 in the topoloy shown in Fiure 3 illustrates the validity of our assumptions. Tale illustrates matrix solutions for two different cases usin the device parameters shown in Fiure 3. Case : Identical devices with 0 volts of common mode voltae, two different Rss values of 5 MeΩ and 50 MeΩ show that; a) SE outputs do have a common mode ain, which decreases as Rss increases. ) There is no DE output, (no common mode ain). Case 2: Non-identical devices with 0 volts of common mode voltae, two different Rss values of 5 MeΩ and 50 MeΩ, comined with random % tolerance on device parameters show that; a) SE outputs do have a common mode ain that decreases as Rss increases. ) There are DE outputs; consequently, a common mode DE output ain exists. It is clear that in the practical real world, semiconductor amplifiers inherently have a common mode ain. The instrumentation enineer should e aware of this fact and use quality instrumentation modules and avoid application topoloies with lare common mode voltaes. Practical Examples of Common Mode Voltaes Fiure 4 illustrates a typical field sensor that enerates a net differential sinal and includes oth the sensor common mode voltae source (Vcm, Rscm) and a common mode voltae source (, ) contriution from the difference etween the field round and data acquisition system round. Vsinal Vsinal2 Rscm Vcm Rs Rs2 Module Field Gnd DAS Gnd Fiure 4 Field Sensor with Common Voltae Sources Vout The wirin etween a field sensor and its associated sinal-conditionin module is suject electro-manetic induced voltaes. These induced voltaes can add oth an additional common mode voltae source and a differential input error voltae. Analysis of this phenomenon is eyond the scope of this document.

3 AN03 Dataforth Corporation Pae 3 of 5 Fiure 5 illustrates two different topoloies for measurin load currents usin shunt resistors. Fiure 6 illustrates a standard ride sensor, which is often the asis for industrial measurements. Case A Case B R R3 Rshunt2 a Load Vexc Vsupply a R2 R4 Load2 Rshunt 0 Fiure 6 Typical Bride Sensor Fiure 5 Current Measurements; Case A & Case B Case A is a differential voltae (a/a) measurement across a shunt inserted in the supply line. In this case, the common mode voltae is equivalent to the supply voltae plus the voltae difference etween the field round and DAS round. Case B is, aain, a differential voltae (/field-round) measurement across a shunt inserted in the field round line. A differential measurement is recommended here to eliminate the error caused y the common mode voltae equivalent to the voltae difference etween the field round and DAS round. For the typical ride sensor shown aove, the differential output voltae (-) there has an inherent common mode voltae, which is typically /2 the excitation voltae with an additional common mode voltae component equivalent to the voltae difference etween the field round and DAS round. Avoidin Errors Due to Common Mode Voltaes Common mode voltaes are inevitale in practical industrial measurements. An instrument enineer should always use;! differential measurements and! sinal conditionin modules with hih CMR DATAFORTH MEASUREMENT DEVICES Dataforth has a unique patented Isochopper Amplifier front end, which employs a transformer isolation arrier with a unity ain amplifier resultin in CMR specifications independent of module ain. Many electronic amplifier manufactures typically specify common mode rejection (CMR) referred to the input (RTI), which means that common mode voltae errors are determined y; Verror = [Vcm (0 CMR/20 )] (Module Gain). Dataforth's specification for CMR is independent of ain; therefore, common mode voltae errors in Dataforth's modules are determined y; Verror = [Vcm (0 CMR/20 )]! The reader is encouraed to visit Dataforth's wesite for detail information on all Dataforth's product Fiure 7 is a lock diaram of Dataforth's SCM5B30/3 Analo Voltae, Narrow Bandwidth Input Module. This module has a 500 Vrms continuous common mode voltae ratin with a CMR of 60 db. Usin this module to measure a differential voltae with an associated common mode voltae (Vcm) will produce an output common mode error equal to Vcm 0E-9 volts. For example, a common mode voltae of 00 Volts would create an output error of µvolt. Usin Dataforth's SCM5B3 Narrow Bandwidth Analo Input Voltae Module Fiure 8 illustrates an Aluminum electrolytic reduction cell, which employs currents on the order of 50,000 to 50,000 amperes that eventually erodes these caron electrodes. The voltae etween electrodes is an indication of their condition and is used y plant maintenance personnel to determine when electrodes must e replaced.. A Dataforth SCM5B3 module is ideal for this electrode voltae measurement application.

4 AN03 Dataforth Corporation Pae 4 of 5 Fiure 7 Dataforth's SCM5B30/3 Analo Voltae Input Module, Narrow Bandwidth Module Cell Curent 50,000-50,000 Amps Differential Voltae 4-6 Volts Vcm ~200 Volts Al Reduction Cell Dataforth's SCM5B3 Sinal Conditionin Module has excellent specifications well suited for this application. For example;! 500 Vrms Common Mode! 60 db CMR! 4Hz Bandwidth. Factory customized to 0.5Hz for this application! 0-0 Volts input; 0-5 Volts output The output of Dataforth's SCM5B3 module is used oth as the sinal to a servo control packae, which controls the cell's electrode position and as a trend indicator for maintenance purposes. Electrode position controllers require sinals with errors less than mv. Hih frequency voltae enerated y the electrode arc and hih common mode voltae represent two lare sources of errors. Dataforth's 0.5 Hz Bandwidth eliminates the hih frequency arcin terms and 60dB CMR produces an error of only 200 (0 60/20 ), 2µV. Fiure 8 Measurin Al Reduction Cell Voltae

5 AN03 Dataforth Corporation Pae 5 of 5 Tale Simple Differential Pair Analysis of Topoloy in Fiure 3 An Excel tale similar to Tale is availale on spreadsheet # of an interactive Excel Workook from Dataforth's We site. The reader is encouraed to download this Excel file choose their own values, follow instructions, and examine the effects of their own selected values. Fiure 3 equation set. Vss Gm Gm2 -V0 - V02 = Gm Gm2 Rss Rds Rds2 Rds Rds2 F H G I K J F H G I K J F H G I K J F Vss Gm V V Gm V H G I Rds K J F H G I - 0 Rd Rds K J 02 0 = - F Vss Gm V V Gm V H G I Rds K J F H G I Rd Rds K J = CASE Identical devices; ==0; Different Rss Values 0 0 Rss Rd Rd2 Rds Rds2 Gm Gm2 Vo Vo2 (Vo2-Vo) 5.00E E E E E E E E E E E E E E E E E E E E00 CASE Non-identical devices; ==0; Different Rss Values Random run usin % tolerance on all parameters 0 0 Rss Rd Rd2 Rds Rds2 Gm Gm2 Vo Vo2 (Vo2-Vo) 5.02E06 2.0E05.99E E E E E E E-0.7E E E05 2.0E E E E E E E E-02

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