# slides electrical instrumentation lecture 4

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- 1.ET8.017Delft University of Technology El. Instr.Electronic Instrumentation Lecturer: Kofi MakinwaK.A.A.Makinwa@TUDelft.NL015-27 86466Room. HB13.270 EWI buildingAlso involved:Saleh Heidary(S.H.Shalmany@TUDelft.NL) ET8.017Delft University of TechnologyIntroduction El. Instr. Differential (as opposed to single-ended) measurements have many advantages:inherently reject common-mode interference and noiseallow a wider swing for a fixed power-supply voltageminimize offset and even order distortion(in some cases) lead to improved sensor linearity BUT most practical amplifiers also respond to some degree to common-mode signalsThe appropriate figure of merit is the common-mode rejection ratio (CMRR).Good amplifiers can achieve CMRRs > 120dB1

2. ET8.017Delft University of Technology Differential Amplifiers El. Instr.Widely used to amplify DCsignalsBalanced structure isNominally offset freeRejects common-mode andpower supply interferenceEasily realized in both CMOSand bipolar technologies ET8.017Delft University of TechnologyPractical Diff. Amps El. Instr. Component mismatch e.g. R1R2, M1M2 offset, finite CMRR & PSRR Mismatch is mainly due to Process variation Lithographic errors All things being equal: CMOS amplifiers are 10x worse than Bipolar amplifiers2 3. ET8.017Delft University of Technology Wheatstone bridgeEl. Instr. R + RR + R U1 = Ub =Ub( R + R ) + ( R R )2R R RR R U2 = Ub =Ub( R + R ) + ( R R )2RInformation is contained in the smalldifferential signal: R RU d = U1 U 2 =U b = 0.1 for V = 1%, U b = 10V RRWhich, however, is superimposed ona much larger common-mode signal: U1 + U 2 U bUc = == 5V at Ub = 10V22 Common-mode rejection in ET8.017Delft University of Technology differential measurementsEl. Instr. A differential measurement is characterized by a (small) differential signal of interest, which is superimposed on a (large) common-mode signal. The differential measurement should be sensitive to the differential signal only, regardless of the magnitude of the common-mode signal. The extent to which this is achieved by the read-out is by the common-mode rejection (CMRR or H).Uo Ad U id U ic H=== AC Uo U id Uo = constU icIdeally: Uo= AdUid, but practically: Uo= Ad(Uid+ Uic/H).The term Uic/H is an error signal, so H should be maximized.Note: Reader uses Gd rather than Ad 3 4. Reducing the effect of ET8.017Delft University of Technologycapacitive coupling El. Instr.Single-ended input:Differential readout:In a balanced systemUn results in Uic only high CMRR requiredET8.017Causes of finite CMRR (1) El. Instr.Delft University of TechnologyGeneralized input circuit with differential input resistance Rd1= Rd+Rd/2and Rd2= Rd- Rd/2, connected to isolation resistance Rc:.2Rc U icU cmi 2Rc + Rs + Rd U + -U RdRc 1- U ic Rs + RdRs + Rd Rc + 2 U + -U Rd U id Rs + RdU + -U U id R2R + Rs + RdHence, CMRR = H == d cU + -U RdRs + RdU ic 4 5. ET8.017Causes of finite CMRR (2)El. Instr.Delft University of TechnologyGeneralized input circuit with differential input resistance Rd1= Rd+Rd/2and Rd2= Rd- Rd/2, connected to isolation resistance Rc:. 2Rc U ic U cmi 2Rc + Rs + Rd U + -U RdRc 1- U ic Rs + RdRs + Rd Rc + 2 U + -U Rd U id Rs + Rd U + -U U id R2R + Rs + RdHence,CMRR = H == d c U + -U RdRs + Rd U icmatchingisolation Common-mode rejection ET8.017Delft University of Technology and discrimination factor El. Instr. A system with differential input AND differential output has differential AND common-mode signals at input AND output. Hence it is incompletely specified by differential gain and CMRR. U odAdd U id U ic H===Acd U od U id Uod = const U icU odUoc is not defined, thus:Add U idF== Acc U ocU icF = Discrimination factor, and it should be maximized.Alternatively, the common-mode gain Acc can be specified.5 6. Using an opamp as ET8.017Delft University of Technologydifferential amplifier (1)El. Instr.Transfer function via superposition: Using an opamp as aET8.017Delft University of Technologydifferential amplifier (2)El. Instr.R2 U o1 = -U1R1 6 7. Using an opamp as aET8.017Delft University of Technology differential amplifier (3)El. Instr.R4 R + R2 U o2 = . 1 U2R3 + R4 R1Using an opamp as aET8.017Delft University of Technology differential amplifier (4)El. Instr.R2 U o1 = -U1R1 R4 R + R2 U o2 =. 1 U2R 3 + R4 R1 R2R4 ( R1 + R2 )Superposition:Uo = Uo1 + U o 2 = U1 +U2 R1R1 ( R3 + R4 )R3 + R4 R4R U 2 = 4 (U 2 U 1 )R4For R1/R2= R3/R4:Uo = U1 +R3R3 R3 + R4R37 8. CMRR of the one-opamp ET8.017Delft University of Technology differential amplifier El. Instr. R2R4 ( R1 + R2 )Uo = U1 +U2 R1R1 ( R3 + R4 )But practical componentshave tolerances! Assume(R1+R2)/R2= (1+)(R3+R4)/R4 R2R 4 ( R 2 + R1 )R2R2 Uo = - U1 +U2 = -U1 +(1 + ) U 2 = R1( R 3 + R 4 ) R1R1R1R2 R2 (U1 + U 2 )(U + U2 )R 1 + ( U 2 U1 ) += Add ( U2 U1 ) + Acd 1 Add = 2R1 2 R12 2 R1 Add ( R2 / R1 ) ( 1 + / 2 ) 1 + / 2 1 ~ 1000 for resistors with H=== Acd( R2 / R1 ) 0.1% tolerance i.e. of no practical use ! Improving the CMRR of aET8.017Delft University of Technology1-opamp diff. amplifier El. Instr.1 HDue to component tolerances! CMRR is caused by resistor mismatch (in general, by component mismatch) CMRR can be improved by trimming e.g. one of the resistors Alternatively a better topology can be used the three-opamp instrumentation amplifier 8 9. The 3-opamp ET8.017Delft University of Technology instrumentation amplifier El. Instr. The 1-opamp differential amplifier is preceded by a differential-to- differential preamp with differential input voltage Ui1-Ui2 and differential output voltage Uo1-Uo2. Both input and output have the differential voltage superimposed on a common-mode level. The 3-opamp INA ET8.017Delft University of Technology transfer functionEl. Instr. Deriving the expression for transfer function (Uo1-Uo2)/(Ui1-Ui2). Can you identify the topologies of the inverting and non-inverting amplifier around OA1 and OA2 ? Use the virtual ground concept and superposition to derive Uo1/Ui1..9 10. ET8.017 Transfer function Uo1/Ui1 El. Instr.Delft University of Technology Differential-to-differentialpreamplifier Node R6/R7 is at virtual ground potential. OA1 is a non-inverting amplifier with: Uo1/Ui1= (R5+R6)/R6. Next transfer function Uo2/Ui1.. ET8.017 Transfer function Uo2/Ui1 El. Instr.Delft University of Technology Differential-to-differentialpreamplifier10 11. ET8.017 Transfer function Uo2/Ui1El. Instr.Delft University of TechnologyDifferential-to- differential preamplifierUi1 virtually available at node R5/R6.With respect to this node OA2 is an inverting amplifier:Uo2/Ui1= -R7/R6.Calculation of transfer function Uo2/Ui2 is similar to that of Uo1/Ui1..ET8.017 Transfer function Uo2/Ui2El. Instr.Delft University of TechnologyDifferential-to- differential preamplifier 11 12. ET8.017Transfer function Uo2/Ui2El. Instr.Delft University of TechnologyDifferential-to- differential preamplifier Node R5/R6 is at virtual ground potential. OA2 is a non-inverting amplifier with: Uo2/Ui2= (R6+R7)/R6. Finally, the transfer function Uo1/Ui2 .. ET8.017Transfer function Uo1/Ui2El. Instr.Delft University of TechnologyDifferential-to- differential preamplifier12 13. ET8.017Transfer function Uo1/Ui2 El. Instr.Delft University of TechnologyDifferential-to- differential preamplifierUi2 is virtually available at node R7/R6.With respect to this node, OA1 is an inverting amplifier:Uo1/Ui2= -R5/R6.Superposition: The overall transfer function (Uo1-Uo2)/(Ui1-Ui2)follows by summation of these four components ...ET8.017 Preamp transfer function (1) El. Instr.Delft University of TechnologyR 5 + R6 R5Transfer function follows as:U o1 = U i1 -U i2 R6R6R7R6 + R7 U o2 = -U i1 +U i2R6R6 13 14. ET8.017 Preamp transfer function (2) El. Instr.Delft University of TechnologyR 5 + R6 R5 U o1 = U i1 -U i2 R6R6R7R6 + R7 U o2 = -U i1 +U i2R6R6 R 5 + R6 + R7R 5 + R6 + R7R5 + R6 + R7 U o1 - U o2 = U i1 - U i2 = UdDiff. output:R6 R6 R6 R5 + R6 + R7 U o1 - U o2 = AddU d + AcdU c Add = , Acd = 0Generally:R6 U o1 + U o2 R 5 + R 6 - R 7 R6 + R7 - R5R5 - R7 U d=U i1 + U i2 = U c +Also: 22R62R6 R6 2 U o1 + U o2= AccU c + AdcU d Acc = 12So, what is the advantage ?Preamp boosts only the differential signal increased CMRRPreamp transfer function: ET8.017Delft University of Technology the easy way!El. Instr.Set Ud = 0 then by inspection: U01 + Uo2 = 2UcSet Uc = 0 then by inspection Ud appears across R6So U01 Uo2 = Ud + Ud(R5+R7)/R6 = Ud(R5+R6+R7)/R6 14 15. ET8.017Commercial ProductsEl. Instr.Delft University of Technology You dont have to make one yourself! Instrumentation amplifiers based on laser trimmed resistors can be purchased from several manufacturers (including Texas Instruments, Analog Devices, Linear Technology and Maxim Integrated Products) Common-mode rejection vs. ET8.017Delft University of Technologydiscrimination factorEl. Instr. The common-mode rejection (CMRR, H) specifies the extent to which a common-mode signal at the input results in a differential signal at the output (Acd non-zero results in signal mixing) and is normalized by the differential gain, Add. This signal mixing directly limits the amplifiers detectivity. The discrimination factor (F) specifies to what extent a common- mode signal at the input of a fully differential amplifier results in a common-mode signal at the output (Acc non-zero does not remove common-mode signal) and is normalized by the differential gain, Add. Attenuating the input common-mode signal reduces the required CMRR of the subsequent stage.15 16. ET8.017Limits on Pre-amp CMRR H1El. Instr.Delft University of TechnologyAdd R 5 + R 6 + R 7 H1 = = Acd0.R 6 Non-realistic due to assumptions implicitly made:1 Opamp common-mode impedance is finite2 The CMRR of each of the opamps in the differential-to-differentialpre-amplifier is finite and frequency dependent3 The open-loop gain of the opamps in the differential-to-differentialpre-amplifier is finite and frequency dependent Effect of finite opampET8.017Delft Universi

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