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Operational AmplifierElectronic CircuitsCHO, Yong Heui

Electronic CircuitsEM Wave Lab

* OP amp terminal ground . 3 signal terminals and 2 power terminals (Not displayed) Differential input voltage, single-ended output voltage Infinite input impedance ii = 0 Zero output impedance Zero common-mode gain (v2=v1 vo=0) Infinite open-loop gain A Infinite bandwidth : A is constant at any frequencies.*Differential input voltage, single-ended output voltageIdeal OP Amp1. Ideal OP amp OP amp


*vId = v2 v1vIcm = (v1 + v2)v1 = vIcm - vId /2v2 = vIcm + vId /2v3 = mvd vd = (Gm v2 Gm v1) Rv3 = mGmR (v2 v1)Gain A = mGmR = 1001010 = 10 4 = 80 dB1. Ideal OP amp Differential and common mode


*R2 negative feedback (positive feedback if connected between 2 and 3)Closed-loop gain stable and predictable, but gain loss is inevitable For ideal OP amp, finite vo means v2-v1=0v2 v1 = vo /A = 0 v2 v1 : Virtual short circuitif v2 is grounded, v1 is a virtual ground terminal.i1 = (vI v1) /R1 = vI /R1 vo = v1 i2 R2 = v1 i1 R2 = 0 vI R2 / R1 infinite input impedance of ideal OP amp vo / vI = - R2 / R1 Closed-loop gain G vo / vI = - R2 / R1 2. Inverter Closed loop gain


*2. Inverter Equivalent circuit


*2. Inverter Finite open loop gain


*R1 should be large as a input impedance, but large R1 causes low voltage gain2. Inverter Example


*Output is a weighted sum of input signals Different summing coefficients are possiblevo = v1(Ra/R1)(Rc/Rb) + v2(Ra/R2)(Rc/Rb) v3(Rc/R3) v4(Rc/R4)2. Inverter Summer


* 3. Noninverter Closed loop gain


*vo = A ( vI - vx )i1 = - vx / R1i2 = ( vx vo )/ R2vI vx (finite gain) vx = R1 / (R1+ R2) vovo = A ( vI - vx ) Op amp . A 1 + (R2 / R1 ) infinite gain Inverting 3. Noninverter Finite open loop gain


*Non-inverting closed-loop R1=, R2=0 Buffer Amp Voltage Source Load impedance Ideal Op amp infinite input impedance source inpedance source , ideal Op amp zero output impedance load inpedance load 3. Noninverter Voltage follower


*For practical circuits,Common-mode voltage gain Acm 0vo = AdvId + AcmvIcm input voltage . , Acm gain .4. Difference Common mode rejection ratio


* inverting/noninverting input GND, difference amp input . (why dont you use Op amp itself ?)Output port Common-mode signal , inverting gain noninverting gain magnitude . (vI1 = vI2 v0 =0 )Inverting Noninverting vO1 / vI 1 = - R2 / R1 i = 04. Difference Difference amplifier


*inverting gain = noninverting gain R2 / R1 = []R1 + R2 R2 ==vO2 = []vI 2 vI 2 =By superposition, vO = vO1 + vO2 = ( vI 2 - vI 1 ) =vIdR1 R2 Ad=4. Difference Difference amplifier


*i1 = [vIcm -vIcm]=vIcmvO = vIcm i2R2=vIcm- vIcm=vIcm[1 -R4 R3 ]Acm vOvIcm=[1 -R4 R3 ]For R1 = R3 , R2 = R4Rid vIdiIvId = R1iI + 0 + R1iI vertual shortRid = 2R1 : low input resistance for high differential gain4. Difference Difference amplifier


*High input impedance and high differential gainR3 R4 []( vI 2 - vI 1 ) =[]vIdvO =R3 R4 vId=][vIdAd=Ad =[] Acm is equal to 1+R2/R1 at the first stage. Issues of imperfect match at the first two Op amps. Two R1 resistors should be simultaneously varied : Not easy jobIssues4. Difference Instrumentation amplifier


*(vO2 vO1) 2R1 + 2R2 2R1 =vIdvO2 vO1 =2R1 1 + 2R2 []vIdvO = R3 R4 (vO2 vO1) = R1 1 + R2 ]vId[R3 R4 Ad vOvId=R1 1 + R2 ][R3 R4 4. Difference Instrumentation amplifier


* Noninfinite CMRR, noninfinite input resistance, nonzero output resistance : Closed-loop circuits Not critical Differential open-loop gainA(jw) =A01+ jw/wbFor w = 0For w wb5. Nonideal OP amp Nonideal OP amp


*Vo(s)/Vi(s) For A0 1+R2/R1 - R2 / R1 1 + wT / (1 + R2 / R1 ) s---------wTw3dB =1 + R2 / R1 For noninverting closed-loop case, only DC gain (1 + R2/R1) is different5. Nonideal OP amp Frequency response


*Closed-loop gain R2/R1 f3dB=ft/(1+R2/R1)+1000 999 1kHz+100 99 10kHz+10 9 100kHz+1 0 1MHz-1 1 0.5MHz-10 10 90.9kHz-100 100 9.9kHz-1000 1000 0.99kHz1 + R2 / R1 - R2 / R1 wT = A0 wbConstant gain-BW product5. Nonideal OP amp Frequency response


*6. Large signal Output voltage saturation


*6. Large signal Slew rate


*6. Large signal Slew rate


*Unity-gain voltage follower input sine wave , slew 6. Large signal Full power bandwidth


*7. DC effect Offset voltage


*DC biasing issueDC signal issueInvertingNoninverting7. DC effect Equivalent model


*Only for DCA 1 + R2/R1Only for ACSTC HPF7. DC effect Capacitive coupling


* IB1, IB2 OP amp mismatch Only for DC7. DC effect Input bias current


*VO = IB1 R2 IB R2 limits on R2VO = -IB2R3 + R2 (IB1 IB2R3/R1) (for IB1 = IB2 = IB3) input .7. DC effect Input bias current


*For R3 = ( R1R2 ) and IB1 IB2 IB3IB1 = IB + IOS/2IB2 = IB - IOS/2VO = IOS R2 (compare with VO = IB1 R2 in case of without R3 )AC coupled inverting ampAC coupled non-inverting amp7. DC effect Input bias current


*8. Integrator Impedance characteristics


*8. Integrator Example


*Integrator Frequency : wint = 1/RCInfinite DC gain : weak at DC imperfection8. Integrator Miller integrator


*8. Integrator DC imperfection


*HPF with infinite corner frequency.Noise magnifier at High Frequency8. Integrator Differentiator