= 20 Log P IN VIN V P OUT V OUT NOISE GAIN = V I Noise for GAIN FROM db = 10 Log PPOUT = 20 Log VVOUT 4kTR2 Op Amp Single-Pole System Closed-Loop Frequency Response R2 I = B OUT GAIN R1 “A” TO OUTPUT db = = 1020 LogLog ININ(dB) = 20 Log Voltages IN R2 IN (Gain) Sinusoidal andAmplifiers Currents P V NG = 1 + for Voltage Feedback IN I IN R1 = NOISE GAIN IN RMS = Root Mean Square = Effective Transformers V I 4kTR2 V IOUT 4kTR1 R1 Op Amp Noise CLOSEDfor Single-Pole System R2 Closed-Loop Frequency Response OUT Decibel (dB) Formulas (Equal Impedances) Decibel (dB) Formulas (Equal Impedances) LOOP BW (Step-Up or Step-Down Ratios) IOUT = 20 Log (Gain) NG = 1 + V VVoltage VPEAK =Amplifiers VEFF RMS = 0.707 = 20 (Gain) for Feedback R1 = fV V I A(S),Log LOOP IN IN GAIN, V 6dB/OCTAVE I A 4kTR1 CLOSEDGAIN FROM = V = 0.637 V R2 R3 IN I OPEN-LOOP AVE PEAK R2 A𝛃GAIN VOUT GAIN FROM =“A” LOOP BW V OUTPUT N ROLL-OFF – TO EP IS VOUT V1.11 GAINZPPOUT P OUT “B” TO OUTPUT OUT VAVE R1 (dB) TOTAL VEFF = =f = = = V A(S), Transformers db = 10 Log = 20 Log db = 10 Log = 20 Log LOOP GAIN, NOISE GAIN = V V I 6dB/OCTAVE 4kTR2 NS ES IP(Step-Up Zor OPEN-LOOP Transformers R2 FROM B 4kTR3 R3 S PIN VPEAK V=INV1.57 VROLL-OFF A𝛃 R2 IN IN R1 I GAIN FROM = – GAIN AVE Step-Down Ratios) R2 = GAIN R2 Voltage Follower Noninverting Op Amp Inverting Op Amp Design Equations—Commonly Used Amplifier Configurations RG VIN N, R2 N, R1 RF B db = 10 Log GAIN FROM = “A” TO OUTPUT IN GAIN (dB) OUT OUT N– N, R1 N– N OUT VOUT VoltageVoltage Follower Follower VIN Voltage Follower Voltage Follower Voltage Follower Voltage Follower Voltage Follower Voltage Follower Voltage Follower VoltageVoltage Follower Follower Voltage Follower Voltage Follower Voltage Follower VOUT = VIN VOUT VOUT Noninverting Op Amp Noninverting Op Amp Noninverting OpAmp Amp Noninverting Op Op Amp Noninverting Noninverting Amp Noninverting Op Amp Noninverting OpOp Amp Noninverting Op Amp Op Amp Noninverting Noninverting Op Op Amp Op Amp Noninverting VIN Noninverting Amp Noninverting Op Amp RG VIN Inverting Op Amp Inverting Op Amp Inverting Op Amp Inverting OpAmp Amp Inverting Inverting Op Amp Inverting Op Inverting OpR Amp RF Amp R N+ Amp G Inverting F Inverting Inverting Op Op Amp Op Amp Inverting Op Amp RF RG R G Op Amp RF Inverting R RF RFF RG RG Op Amp RF V RR G GInverting A N, R3 N, R1 N+ N OUT N– CL N, R2 GAIN TO “B” TO OUTPUT “A”NG R1=OUTPUT 1+ R1 2 R2 NOISE GAIN = V I CLOSED4kTR2 N N– + 4kTR1 F VIN VN + 4kTR3 R1 VOUT VOUT LOOP BW VOUT R1 + R2 R2 VOUT VOUT NG = 1 + × = fCL 2 VOUT VOUT VOUT VOUT RTI NOISE = VN,BW R1 R3 R2 VOUT 2 A 2 2 R3 I + 4kTR1 AMPLIFY AND INVERT INPUT VN R2 4kTR1 V R1 N + 4kTR3N+ GAIN FROM R1CLOSED× R2 VVVOUT VOUT VOUT = – V R1 + R2 OUT 2 R32 + I 2 + 4kTR2 + IN+TOTAL LOOP BW VOUT OUT N– “B” TO OUTPUT R1OUT RTI NOISE = BW × R1 + R2 R1 + R2 = fCL V4kTR3 N, R3 2 2 A R3 R IN+ R1 × R2 R2 1 FROM +BW 4kTR2 = GAIN 1.57 fCL IN+2 R32 + IN–2 RTO NOISE = NG × RTI+NOISE = – “B” TO 2OUTPUT R1 + R2 R1 + R2 R1 TOTAL RTI = REFER TO INPUT R2 AMPLIFY INVERT INPUT AMPLIFY ANDAND INVERT INPUT AMPLIFY AND INVERT INPUT 4kTR3 AMPLIFY AND INVERT INPUT 2 + 4kTR3 + 4kTR1 RTO = REFER TO OUTPUT V AMPLIFY AND INVERT INPUT N AMPLIFY AND AND INVERT INPUT AMPLIFY INVERT INPUT R1 += R21.57 fCL BW AMPLIFY AMPLIFY AND INVERT INPUT RTO NOISE = NG × RTI NOISE AND INVERT INPUT RTI NOISE = BW × RTI = REFER TO INPUT 2 AMPLIFY AND INVERT INPUT 2 R2 2 AMPLIFY AMPLIFY AND INVERT ANDAMPLIFY INVERT INPUT AMPLIFY INVERT INPUT INPUT RTO = REFER TO OUTPUT AND INVERT INPUT R1 R1 × R2 + 4kTR1 VN2 + 4kTR3 AMPLIFY AND AND INVERT INPUT 2 2 2 + + IN+ R3 + IN– R1 + R2 4kTR2 R1 + R2 R1 + R2 RTI NOISE = BW × VIN IN R G VINVR IN RG RGGVIN VIN VIN R G RG VIN VIN VVIN IN VIN VOUT VOUT VOUT VOUT VVOUT VOUTOUT CLN, R2 N, R3 R R R F RFFF RRG RF (Step-Up or Step-Down AVE = 0.9 VEFF IIOUT (dB) VRatios) = 20 Log OUT (Gain) EP NOISE IS(Gain) ZP N=P 20 Log CLOSEDIIIN GAIN, = Transformers = = TOTAL RF 4kTR3 V4kTR1 N, R1 B 2 V XL = 2π fL POUTV (Tuned SCircuit) XLL Figure FigureVof of Merit OUTMerit R. R. R = RLog 20Figure QXL= Q = of PCoil ofofaa1Merit Coil V 1 = SR. 1B.W. 1 I2R PINQ = R L of=Ra Coil =2 2 2 L 2=V12 IN 2 Q2C=.159 B.W. 2C Circuit) (Tuned (Tuned S =4π SR 4π C Sor(Tuned 4π Hz SCircuit) L Circuit) R 4π SR L R C√LC IOUT R 2π√LC =VI20 Log 1 √P .159 P Formulas Q S(Gain) & Frequency Formulas Impedance Formulas (Series) Reactance Formulas Q &PIResonant I RR Resonant =1Frequency or Hz IN 1 R.159 1 db = 10 Log √PR SR = or Hz 2π√LC √LC L =2π√LC √LC CSR.= XofL4π S X 2 (Series RL) XL1 Figure Figure of Merit √R 2 + Z =4π Merit 2S 2C V Q = Q = Q = Q =2 SR2R.L L R XC = V of aRCoil of a Coil R fC R B.W. 2π CCircuit) =1 2 12 B.W. L = 1 2 1 2 (Tuned I 22 L X 2 (Series RC) L= (Tuned Circuit) 2 SR2 CC = Formulas 4π 4π√2RSRR+ Z= Reactance C 2 2 4π2 SR2 Formulas L P X = 2π fL 4π SR C VR2 Reactance 1 .159 L 1 .159 I SR = SP = or P1X = orHz Z = X1LHz – XC (Series LC) R C √LC IR 2π√LC Q= I R of a Coil Q= B.W. (Tuned Circuit) 1 .159 S = or Hz VoltageR and2π√LC Impedance Formulas (Parallel) √LC V RXL 1 (RL) Z = 1A Z= C = L =√R2 + 2 I 2 4π2 SRX2L C 4π2LINE SR L Z= RXC √R2 + XC2 (RC) VA = VL = VC = VR EEPS A(S),IN𝛃1 IIPS LOOP GAIN,ZZS P NLOOP I2 2π√LC 2πXCfC=√LC NP SCurrents 6dB/OCTAVE GAIN = = = OPEN-LOOP Reactance Formulas Sinusoidal Voltages and 2π fC (Step-Up or Step-Down Ratios) A𝛃 1 1 XL XC Transformers ROLL-OFF NOISE GAIN, CLOSED-Transformers GAIN Z = √R12 + (XL – XC)2 (Series RLC) L= N E I Z VIN 1CX= = 2π Z = Reactance (LC) Formulas VA = ILINEZ S S P S Ohm’s Law (DC Circuits) N N Transformers 2S 2C 2 SfL2 L RMS = Root Mean Square = Effective 1 LOOP VIN OUT IN OUT OUT L X IN IN 4π 4π (Step-Up or Step-Down Ratios) C = L = L – XC R(Series) 1R A(S), Reactance Formulas VOUTV=VOUT VIN=V =VOUT VIN= VIN GAIN, (Step-Up Step-Down Ratios) Impedance Formulas 𝛃LOOP GAIN or 2 2 2 2 Reactance Formulas 6dB/OCTAVE VOUT = V (Step-Up or Step-Down Ratios) IN E I Z N X = 4π S C 4π S L OUT IN VRMS = 0.707 VPEAK =PVEFF OPEN-LOOP fL R XL =Z 2π P RC CLOSED-LOOP ROLL-OFF = P GAIN = S =A𝛃BANDWITH = VA 1 2π1 fC VVOUT VIN = VVV OUT = VVOUT = VVININ 2 +E 2 (Series IN OUT = OUT = IN RX XC =(RLC) V = 0.637 V 1 I Z N LOG FREQUENCY (HZ) N E I Z √ R X RL) Z = V = V AVE PEAK P PSeries/Capacitors S Pin OUT IN Resistors in Parallel S S P S L 2 Z = E I Z N I X = P P S P C Sinusoidal Voltages Currents V EPP ISand ZPP V N BUFFER IMPEDANCE SOURCE BUFFER HIGHHIGH IMPEDANCE SOURCE BUFFER HIGH IMPEDANCE SOURCE = = =XC = C PP BUFFER HIGH IMPEDANCE SOURCE S BUFFER HIGH IMPEDANCE SOURCE √R2 + X2 2π fC BUFFER HIGH IMPEDANCE SOURCE BUFFER HIGH IMPEDANCE SOURCE VEFF = 1.11 VAVE ==CLOSED== CLOSED-LOOP = GAIN, BANDWITH fC NOISE fC TOHIGH LOW RESISTANCE LOAD TO LOW RESISTANCE LOAD C2π C3 + … RTOTAL = RN1S+ R2 +ERS3 + … I/PCTOTAL = ZC2π BUFFER HIGH IMPEDANCE SOURCE TO LOW LOAD BUFFER IMPEDANCE SOURCE TORESISTANCE LOW RESISTANCE LOAD = 2π fL 1 L+ 2+ SX R R RMS = Root Mean Square = Effective TO LOW RESISTANCE LOAD N E I Z S S P S N E I Z TO LOW RESISTANCE LOADLOAD TO LOW RESISTANCE 1 LOOP SS SS PPandLOG SS Sinusoidal Voltages Currents FREQUENCY (HZ) TOLOW LOW RESISTANCE VPEAK = 1.57 VAVE P TO RESISTANCE LOAD Formulas (Series) Z = √R2 + XC2 (Series Impedance RC) Transformers BUFFER HIGH IMPEDANCELOAD SOURCE GAIN R𝛃 VRoot 0.707Square VPEAK = = VI2EFF XL = 2π fL FER BUFFER HIGH HIGHBUFFER IMPEDANCE SOURCE SOURCE FFER HIGH IMPEDANCE IMPEDANCE SOURCE HIGHRESISTANCE IMPEDANCE SOURCE RMS =Mean TO LOW LOAD = 2π fL X Reactance Formulas = 2π fL X L RMS = Effective BUFFER HIGH IMPEDANCE SOURCE V V = 0.9 V (Step-Up or Step-Down Ratios) L Lin Series AVE EFF Resistors in Parallel/Capacitors Transformers 2Impedance 2 (Series TO TORESISTANCE LOW RESISTANCE LOAD LOAD TO LOW LOW RESISTANCE LOAD TO LOWLOAD RESISTANCE LOAD VAVECLOSED=LOOP 0.637 VPEAK NOISE1GAIN, Formulas (Series) √ R + X RL) Z = TO LOW RESISTANCE L Common Resistor Sinusoidal Voltages VRMS =GAIN 0.707 V and=Currents V𝛃EFF Z = XL –11% XC (Series LC) Values Reactance Formulas 1 (Step-Up Step-Down Ratios) 2 1 √P 2 PR VP EFF = or 1.11 VAVEPEAK E I Z N X = VI R1 Voltage Impedance Formulas (Parallel) R1 × R2 P S P C CLOSED-LOOP BANDWITH / = C = BW = 1.57 f P I 2+ 2 and RTO NOISE = NG × RTI NOISE RMS = Root Mean Square = Effective TOTAL TOTAL 1%Sinusoidal CL + 4kTR2 V = 0.637 V + IN+2 R32 + IN–2 Voltages and Currents = = = standard values decade multiples are available from 10.0 Ω RL) through 1.00 MΩ (also 1.10 MΩ, 1.20 MΩ, 1.30 MΩ, 1.50 MΩ, 1.60 MΩ, 1.80 MΩ, √ R X Z = Sinusoidal Voltages and Currents R 2π fC Sinusoidal Voltages and Currents AVE PEAK 2 + X1 2 (Series 1 1 1 1 L (Series 1(Series) VS PEAK =E1.57 VAVEIP R1 + R2 R1 + R2 Impedance Formulas √ Z = R RC) RTI = REFER TO INPUT LOG FREQUENCY (HZ) N Z C S S + + + … + + + … V = 0.707 V = V VA RX 2 2 2.00 MΩ, and 2.20 MΩ). E I Z N X = RMS = Root Mean Square = Effective RMS PEAK EFF L V = 1.11 V RMS = Root Mean Square Effective RMS = Root Mean Square = Effective P P S P C ZR=1 √RR2 + R(X3L – XC) (Series RLC) C1 C2Z = C3 RTO = REFER TO OUTPUT EFF AVE Ohm’s Law (DC Circuits) VAVE 0.9 V= (RL) Z = ====0.637 = EFF V Impedance Formulas (Series) Impedance Formulas (Series) 2π fC2 RL) Impedance Formulas (Series) 22π 2 (Series CLOSED-LOOP BANDWITH = fL X V R BW = 1.57 fCL V V RTI NOISE Voltage Subtractor/ Low-Pass Filter/Integrator RTO NOISE = NG ×Resistor √PR √ R + X Z = Voltage Adder L 2 2 2 V 0.707 V V = 0.707 V V AVE PEAK V = 0.707 V = V I Standard base resistor values are given in the following table for the most commonly used Johnson Noise Formula NVSPEAK IP EFF 1.57 RMS= E PEAK RMS PEAK EFF RMS PEAK EFF ZS √R + RC) XL LINE tolerance (1%), along with typically available resistance ranges. Z–=XC√(Series RL + XLC) S AVE RMS PEAK EFF C (Series Z = X I RTI = REFER TO INPUT LOG FREQUENCY (HZ) L 1.11 VVAVE 2 RL)the base value by 10, 100, 1000, or 10,000. R1 RF VEFF 0.637 VPEAK To determine values other than the Difference Amplifier ===0.637 0.637 22L2+ √ZR=2 in + Xbase, (Series ZV=PEAK Z = VVAVE AVE= PEAK Z = √R2 + XL2 (Series RL) Two Resistors AVE PEAK RTO = REFER TO OUTPUT A = VVVAVE 0.9 VEFF √RParallel Xmultiply L2 (Series C AVE 2 2π fL RL) RX VA 2 + XXLL = 2 (Series V R2 2 V = 1.57 V P V = 1.11 V Z = √ R RC) V = 1.11 V V = 1.11 V PEAK AVEand Currents EFF AVE C I V VSinusoidal C10.7 Resistor Johnson Noise Formula Voltages EFF AVE 10.0EFF 10.2 AVE 10.5 12.1 12.4 12.7 13.0 EFF AVE Voltage Subtractor/ Voltage Subtractor/ Low-Pass Filter/Integrator Low-Pass Filter/Integrator Voltage Adder Voltage R2 Adder (RC) VA =11.5 = 11.0LC) VL = VC = 11.8 VR 222= L22L––X Voltage Subtractor/ P =R+1√RXRZ +X(X XCC(Series )Z2 (Series RLC) 11.3 Low-Pass Filter/Integrator Voltage Adder Voltage Subtractor/ Voltage Subtractor/ I VAVE 1.57 VAVE Low-Pass Filter/Integrator Low-Pass Filter/Integrator Voltage Adder Voltage Adder VOhm’s ===0.9 VEFF 2 + X 2 (Series RC) Law (DC R=214.0 RC) ZVAVE = =√ZZ V 1.57 V 22C+(Series R PEAK AVE Circuits) 2 + X 2 15.0 V = 1.57 RMS = Root Mean Square = Effective R R Voltage Subtractor/ Voltage Subtractor/ PEAK P Voltage Subtractor/ Z = √ R Low-Pass Filter/Integrator TOTAL Low-Pass Filter/Integrator Voltage Adder Voltage Adder V 13.3 13.7 14.3 14.7 15.4 15.8 16.2 16.5 16.9 17.4 Low-Pass Filter/Integrator PEAK Voltage Adder √ R X (Series RC) C √ R PEAK AVE R R R R R C B Difference Amplifier Difference Amplifier C (Series) 1 C F F 1 10,000 VA Difference Impedance Formulas Voltage Subtractor/ R111 Voltage P =0.9 R=1X+R C Filter/Integrator C Difference Amplifier VOUT IR Low-Pass Adder R1 R RF R R FF 2R Amplifier VRMS 0.9 VEFF Difference Amplifier 2 X (Series VA VA 2 VOUT AVE== EFF V V V 0.707 V = V C R1C Voltage Subtractor/ Z – LC) I R1 Voltage R2 R2 R Low-Pass Filter/Integrator RF V = 0.9 V Adder C Difference Amplifier I Sinusoidal Voltages and Currents R AVE PEAK EFF R V 17.8 18.2 18.7 19.1 19.6 20.0 20.5 21.0 21.5 22.1 22.6 23.2 Difference Amplifier R L C R F R Difference Amplifier AVE EFF 1 V V F A AVE EFF 1 3 F AV A C C C R2 R R2 V = 0.637 V 2 + (X – X )2 (Series RLC) =XXC2V(Series RF Difference Amplifier VA RR1 A VA VIN AZ = √R R2 2 –24.9 (Series LC) Z√=R2XZZ VC RRR21 R VRoot R2 X X RF RL) Z = L+ VB R2 C Difference Amplifier R222 AVE PEAK L C 23.7 24.3 25.5 26.1 26.7 27.4 28.0 28.7 29.4 30.1 30.9 L C RMS = Mean Square = Effective L Ohm’s Law (DC Circuits) V Z = X – X (Series LC) – X (Series LC) = X Equal Resistors in Parallel L C 2 C VVB VBA L L C R VCM R1 RR R2 Z2 = (Series) (LC) VA = ILINEZ 1 VA Voltage VASubtractor/ VOUT VOUT Voltage Voltage Subtractor/ I 2 C 34.0 R2 Adder V2 VAVE V R2 2 1000 Low-Pass Low-Pass Filter/Integrator Filter/Integrator Impedance Formulas Voltage Adder 2A VV VR R1 Low-Pass Filter/Integrator VOUT 10,000 VEFF = 1.11 RA1 1 R1 Subtractor/ B BB Voltage RN Voltage Adder Resistor Johnson Noise Formula V VOUT VOUT VOUT –X X Voltage √P 31.6 32.4 33.2 34.8 35.7 36.5 37.4 38.3 39.2 40.2 41.2 Low-Pass Filter/Integrator VA Subtractor/ V VA V Voltage Adder V R R R R R R L C V = 0.707 V = V P R B OUT OUT 2 Z = √ R + (X – X ) (Series RLC) R R 1 1 2 VOUT 1 is the value(Parallel) of one RMS PEAK EFF VB VI R Where RFormulas VOUTVB L2 of the C VOUT VOUT R Voltage and Impedance Ohm’s Law Circuits) R1VA 2 R3 R R RR1 R1 V R3R3R P I VA VOUT VOUT 2 X+2 (X R V(DC R VA R1 Amplifier R3 VIN VIN R VOhm’s 1.57 R11VVC VVCR Difference Difference Amplifier Z =Z√=R2√Z+ (Series RC) RVFOUT R = R Amplifier R R11 B 1N PEAK = R AVE Circuits) R – X ) (Series RLC) VBV VAmplifier 22L+ 2 (Series t = RC = RFC CR 42.2 43.2 44.2 45.3 46.4 47.5 48.7 49.9 51.1 52.3 53.6 R3RFF 3RF RF1 VOUT VOUT 1 V 2 Z = V TOTAL BDifference C R V 2 2 R B Law (DC Difference R V V C C IN C 2 2 R V V = 0.637 V √ (X – X ) RLC) = R A A R OUT 1 1 C P equal resistors, and N is the number V IN 1 VR RL) = √R + XLLL (Series VV VCM VCMVB VVAB VA VOUT C PEAK B1 VOUT VOUT CV3 VCC RV3A Z = √R + (XL – XC) (Series RLC) 54.9 R VOUT V IN1 AA CFR1 R F C Ohm’s (DC Circuits) RF R R2 R1 R1 R I2VAVE RAVE = Law VOUT Ohm’s (DC Z Circuits) 0.92 VEFF V2B2 R2 C VOUT VA RXNL Law V VCM VCM RRN RR VIN R1 VOUT VOUT 1000 VIN RR RX N3 en at 25°C VCVA VC 56.2 57.6 59.0 60.4 61.9 63.4 64.9 66.5 68.1 69.8 71.5 73.2 100 R2 IN 1 2 RRR 12 VB 3 R Resistor Johnson Noise Formula VBCM VCM R V I Resistors in Series/Capacitors in Parallel of equal resistors V V Z = V V R Z = (RLC) V V = 1.11 V N OUT R2 1 Z= R N R22VVN VVNR IN A VIN EFF AVE R R2 V VCM RN N 2 R R2 R1 RV1BVB C 2 + X2 84.5 R VC 2 V R t == RC =OUT RFC VOUT –RF t = RC RFCV Z(RL) =ZX=L –VZXA = (Series LC) 80.6 1 VR √PR 2 C78.7 2 + X 276.8 VCM 75.0 82.5 86.6 88.7 90.9 93.1 95.3 97.6 √ R I NVN 2VNN R VOUT R VR 2 t = RC = R C nV V V V V 2 2 R Z = V √ R LINE 1 CM R2 V = V V t = RC = R C N t RC = R C F R = R + R + R + … / C = C + C + C + … R R OUT B B B R 1 I VPEAK = 1.57 N R1 VV F OUT IN VR1 B R L RN 2 ZI = √AAR + XC (Series RC) 2 3 TOTAL 1 2 3 VB V Z = VA VA 11 10,000 IVRVTOTAL t = RC = RFCF VNOUT 2 VAVEV R11 VA ROUT A OUT V VOUT N V R1 RFCS + 1 R √P VA 22 N P V V V V 2 P OUT t = RC =tR R C = RFC OUT R Hz 100 OUT R R R1 VII2RVAVE2= 0.9 R11 =R OUT RF1 2PV and en at 25°C FFRC I Impedance Formulas (Parallel) N R R33 VN VR VR VOUT OUT R3 1 R–R 10 IVRR AMPLIFY THE DIFFERENCE RFFF t = RC R =–R RC CFt F 1= RFC I R3 3 V2Z Voltage R =FFV =OUT V= VVIN VIN 1 R EFF V VINVVOUT=V = √R2V+ (XL – XC)2 (Series RLC) –R 1 IN –RF1 1 IN–R IN VVCC VC P Common Capacitor Values P RX F VC VB Ohm’s Law (DC Circuits) V V 2 V V C 1 –R B R R R CS + 1 R CS + 1 V = V V = V BETWEEN TWO VOLTAGES, OUT IN B IN V F 1 F 1 F P OUT IN OUT IN I R nV R R VB R Resistors in Parallel/Capacitors in Series C 2 V RX VOUT = VIN RR11 RR CS + 1 V V Z = X – X (Series LC) V (RC) V Z = = V = V = V R R R11 VCM R1 M V CS + 1 R R CS + 1 F 10,000 L A R I R OUT R P F1 OUT AMPLIFY DIFFERENCE AMPLIFY THE DIFFERENCE OUT 1F CS –RF BANDWIDTH 1 THE 1000 1F OFOUT I PV R1 –RR + 1–R CM R R SUM MULTIPLE VOLTAGES RNN COMMON-MODE VOLTAGE LIMIT SIGNAL RN 1 F V1OUT –R Z= Z = A LLP CC (RL) AMPLIFY THE DIFFERENCE 1 VOUT = VV R RBETWEEN = V R22 RREJECT AMPLIFY THE DIFFERENCE AMPLIFY THE DIFFERENCE P I22R F R IN Hz RN N OUT IN F = √pF RI22R+ XC2 ZpF 2DIFFERENCE VOUT =V V R 1VV V√P 1 BETWEEN TWO VOLTAGES, VV TWO VOLTAGES, 10 1 THE R22 AMPLIFY √PR IN RIN1 RVROUT pF CS +VR 1+FCS = VA √R2pF+ X 2 +1R CS + 1 I Formulas µF µF µF µF µF µF µF VN FR IR BETWEEN TWO VOLTAGES, NN V VN P 1 FCS R 1 BETWEEN TWO VOLTAGES, BETWEEN TWO VOLTAGES, R 2 1 VI tt == RC tR RC =SIGNAL RFC 1 t = RC RC ==OF R=FFC C R C / = = L Impedance LINE F Voltage and (Parallel) = R C V N SUM MULTIPLE VOLTAGES SUM MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGE REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH OF LIMIT BANDWIDTH SIGNAL I I TOTAL TOTAL BETWEEN TWO VOLTAGES, AMPLIFY THE DIFFERENCE F P I AMPLIFY THE DIFFERENCE 2 √P t = RC =OF RFSIGNAL C AMPLIFY THE DIFFERENCE SUM MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH PR 2Impedance 2 (Series 0.01 AMPLIFY THE DIFFERENCE I Z Impedance √P VP V 1 SUMSUM MULTIPLE VOLTAGES MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH OF SIGNAL REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH OF SIGNAL VI P 1 1 1 1 1 Voltage and Formulas (Parallel) = √ R + (X – X ) RLC) 1.0 10 100 1000 0.1 1.0 10 100 1000 10,000 VI SUM MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGE 1000 LIMIT BANDWIDTH OF SIGNAL Voltage and Formulas (Parallel) I L C BETWEEN TWO VOLTAGES, Ohm’s Law BETWEEN BETWEEN TWO VOLTAGES, en at 25°C 100 XL XC P (DCIRCircuits) BETWEEN TWO + + +… TWO VOLTAGES, VOLTAGES, R … V2R√P RP+ V RXL1100 VI P RX Impedance Formulas (Parallel) PR IR1+ R2P+ VAand = I110 Z √P C1 C2 CZ3=VI X1.1– X (LC)PVoltage SUM MULTIPLE VOLTAGES 11 REJECT COMMON-MODE VOLTAGE LIMIT LIMIT BANDWIDTH OF SIGNAL 1 0 SUM SUM MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGEVOLTAGE LIMITBANDWIDTH BANDWIDTH OF 1OF 1 –R –R 1F SIGNAL –R LINE MULTIPLE VOLTAGES REJECTCOMMON-MODE COMMON-MODE OF SIGNAL 1 –RF 3R Voltage and Impedance Formulas (Parallel) FF SIGNAL SUM MULTIPLE VOLTAGES REJECT VOLTAGE LIMIT BANDWIDTH 2 VVA(RL) Z V=C = VRA = LC PR (RC) 1 –R ZI =RX VVOUT = V V = V nV = V L C 10 100 1k 10k 100k 1M 10M 100M V = V V LZ RX F I R OUT IN OUT = V IN IN A = VV L A= P OUT IN I VOUT V R (RL) Z = Z = IN R √PR 1.2 12 120 1200 R1 ++ 11 RFCS + 1 R1 RFCS + 1 2A+ (RL) Z = Z = R11 R RFFCS CS 2 2 Z = V V I V P V V RX RESISTANCE (𝛀) L A √ R X LINE R1 RFCS + 1 √PR en at Hz 25°C 100 √PR 2 L√RC2 + XL IZ VA RXL IA AMPLIFY AMPLIFY THE THE AMPLIFY DIFFERENCE AMPLIFY THE DIFFERENCE DIFFERENCE 10 IRV RRVI2 √R=2 +√RX22130 THE DIFFERENCE Two VIResistors in Parallel L + XL (RL) 1.3 RX 13 Z 1300LINE= I LINE VR = 4kTRB AMPLIFY THE DIFFERENCE II VV2 (RL) Z = Z= √PR 2 I+ XL22V LINE 0 √P BETWEEN BETWEEN TWO VOLTAGES, TWO VOLTAGES, BETWEEN TWO VOLTAGES, √ R LINE V R BETWEEN TWO VOLTAGES, Resistors in Series/Capacitors in Parallel P nV 10 Z√PR = 1.5 Voltage (RLC) 2 2 VI P where: 1k BETWEEN TWO VOLTAGES, and Impedance (Parallel) 100 10k 100k 1M 10M 100M 0.15 1.5 15 √R2 + X150 1500 ILINE P I R XC LFormulas L V2V2 I R R SUM MULTIPLE SUM MULTIPLE VOLTAGES VOLTAGES SUMSUM MULTIPLE VOLTAGES JECT REJECT COMMON-MODE COMMON-MODE VOLTAGE VOLTAGE LIMIT BANDWIDTH LIMIT BANDWIDTH OF SIGNAL OF SIGNAL OF SIGNAL I RXC1500 V = I 0.015 JECT COMMON-MODE VOLTAGE LIMIT OF SIGNAL √R2 + X2 15 Z =RXCXL150 SUM MULTIPLE VOLTAGES REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH PP C1 + CR2 + C3 + RX RESISTANCE (𝛀) VR = resistor Johnson Noise spectral density Hz MULTIPLE VOLTAGES (LC) Z REJECT COMMON-MODE VOLTAGE LIMIT BANDWIDTH BANDWIDTH OF SIGNAL … VVP22 RRTOTAL = 1 2 RTOTAL = R1 + R2 + R3 + … / CTOTAL 2= C(RC) A LINE 101 (RC) V Z = = V = V = V 1.6 16 160 1600 V Z = = V = V = V – X2CC A = VL C R A VA LVA =C VL =R V (RC) ZRX=L X RX PPP IIPRI I VR k== 4kTRB Boltzmann’s constant (1.38 × 10–23 J/K) 2V C Z R1+R2 PPP Z =18 Z √R=2 +√2RXL2180 RXC √XRC222 =+ XC2 VAA = VLL = VCCC= VRRR (RC) C(RL) PV V 1.8P 1800 + V R √PR I 2+ IR T = absolute temperature in Kelvin where: I 2 IR 2 LINE √ R X (RC) VA = VL = VC = VR Z= IR L R2 + PIII22 P XCC2 √ I I Resistors in Parallel/Capacitors in Series IR 2.0 20 200 2000 2 R = resistance in Ohms V = resistor Johnson Noise spectral density P=X RX Equal Resistors in Parallel √R + XC2 10 R √P I22 Resistors in Series/Capacitors in Parallel X P Z (RLC) L C 2 VI IR –23 Voltage and Impedance Formulas (Parallel) X X bandwidth inconstant Hz V (1.38 ×100k 10 J/K) P 1I 2X+ 10k B= =Boltzmann’s 100 1k 10k 1M 10M 100M 2.2 0.022 0.22 2.2 22 220 2200 L220 C 2L CVA2200 1 P = ILINE Z Z22= XRX= Differential Amplifier Instrumentation High-Pass Filter/Differentiator IC2 √XXZ Differential Amplifier Instrumentation Amplifier Amplifier Differential Amplifier Instrumentation Amplifier RLL(LC) High-Pass Filter/Differentiator High-Pass Filter/Differentiator RC2 +R Cis3the Where value of one of the X(RC) =XCC XX(LC) + R2I=+ R3 + … / CTOTAL =R +… RTOTAL =/ RC Differential Amplifier Instrumentation Amplifier –20 W/Hz, High-Pass Filter/Differentiator Z =24 Z V–AX= V2400 = VVC A==VRILINEVZA = ILINEZ RESISTANCE L – XCX Differential Amplifier Instrumentation Amplifier Differential Amplifier Instrumentation Amplifier 1 TOTAL = absolute temperature in KelvinVR(𝛀) High-Pass Filter/Differentiator therefore, =RTOTAL 1.65 × = 10 –20RB High-Pass Filter/Differentiator At 25°C,T4kT = 1.65 × 10 L(LC) P C1 + –RX = R 2.4 240 Differential Amplifier Instrumentation Amplifier High-Pass Filter/Differentiator (LC) V = I Z Z = A LINE X X L C 2 2 RF RFRF V TOTAL L C A LINEA 1 1 1 1 IR 1 P1 √R + XXC L –– XCL R F R F RF VR = 4kTRB in Ohms N equal resistors, and N is the number RF R R 0 R = resistance Z = L– C (LC) VA = ILINEZ + +–V 100M + –V+ … –V RF F F RF R RFF Differential Amplifier Instrumentation Amplifier Op Amp Noise for Single-Pole System Frequency Response 2.7 27 Z =RX L 2270C 2 (RL) 2700Z = 10k𝛀 10k𝛀 + –VIN+R High-Pass Filter/Differentiator R2' R3' I2C + … ofV10k𝛀 X L XC 10BClosed-Loop 100 1kHz 10k 100k 1M 10M + RF where: –V = bandwidth in –V 10k𝛀 √PR10k𝛀 10k𝛀C V C equal resistors I R R R A1 A1 Differential Amplifier Instrumentation Amplifier √ R + X LINE 1 2 3 1 2 3 Resistors in Series/Capacitors in Parallel Differential Amplifier Instrumentation Amplifier High-Pass Filter/Differentiator Differential Amplifier Instrumentation A1 Amplifier Z = (RLC) –V High-Pass Filter/Differentiator High-Pass Filter/Differentiator Resistors in Parallel/Capacitors in Series L 10k𝛀 A1 RESISTANCE (𝛀) V ~ ~ R RX I 10k𝛀 10k𝛀 A1 ~ A1 for Voltage Amplifiers C 3.0 30X √ZXRC= 300 3000 2 2RX F V Johnson Noise spectral density–20RB Resistors inSeries/Capacitors ininParallel Parallel CININ CCIN CIN RF therefore, V At 25°C, 4kT = 1.65 10–20Feedback W/Hz, R =×resistor (RLC) A1 RG R G ~ ~ ~ R = 1.65 × 10 10k𝛀 10k𝛀 2 CIN Resistors Parallel10k𝛀 RF IN R Z = LZ (LC) = ILINEZ (RLC) Resistors Series/Capacitors VOUT VOUT ZX22330 =+ X22 2VRX RF R =+ = R110k𝛀 + 10k𝛀 R12in + RSeries/Capacitors RTOTAL OpR Amp VNoise for Single-Pole System Closed-Loop Frequency Response –V VIN V ~ VR 4kTRB A(RLC) in 10k𝛀 IN C 3 + … / CTOTAL = C1in F VOUT VIN– VIN–RGR RR RGF G G 2 + C2 + C31+ … k= = Boltzmann’s constant (1.38 × 10–23 J/K) – XC √R2 X RF 3.3 33 0.033 0.33 3.3 33 OUT VOUT VVOUT V R V F OUT+VOUT+ VVININ VIN R VIN L IN R RX 330(RLC) 3300 + + R R V 2 + G A1 V V = R + R + R + … / C = C + C + C + … √ R + X Two Resistors in Parallel V V 24.7k𝛀 VOUT + 3300 X2 P2+10k𝛀 –V –VR RXin VIN– VIN–IN– IN– V IN CTOTAL VOUT+OUT+ V R2' VIN RIN Resistors in Series/Capacitors Parallel R2'R3' R3' OUT+ TOTAL 1+ TOTAL IN = =–V R2' R3' where: Z= OUT R V CM 10k𝛀 C√R + R1IN11+ R V3+ … R/10k𝛀 CTOTAL =OUT C222C+ C333C +3 + …… + RR TOTAL TOTAL RIN + ~ R= 24.7k𝛀 R24.7k𝛀 R1IN210k𝛀 =C=11C1+ RRV24.7k𝛀 for Voltage Amplifiers VIN– 24.7k𝛀 RINCIN T = Feedback absolute temperature in Kelvin V V VOUT+ OUT+ TOTAL TOTAL 24.7k𝛀 V OUT… / C TOTAL TOTAL 11+ 21+ IN RIN 22 + 133 + OUT 2 + X2 R1' V OUT OUT R 3.6 36 Z = 360 3600 VA = VL = VC = VR A1 (RC) VN, R2VA1 V A1 RG V OCMVVOCM A3 A3 RIN 1 1 24.7k𝛀 V V P OCM √ R V V OUT V = resistor Johnson Noise spectral density I OCM OCM OCM VIN C ~ ~ R A3 OUT 10k𝛀 ~ R = resistance in Ohms C √R= C +2C + C3 + … RTOTAL = R1 + R2 + R3 + … / RX A3 2+ CIN V A3 R V VIN–VIN+ GAIN FROM CIN + in +… + + +… Resistors in Parallel/Capacitors Series IN R+1 R210k𝛀 2R2 P10k𝛀 10k𝛀in in 2 VVOUT+ OUT–VOUT– 2 ~ = A3 V A3R1 RG V IN+ ~ R RVG VVIN+RG RRGGOCM GAIN VOUT– 3.9 3901 XC 2 3900 Resistors Series/Capacitors Parallel RIN Z =39 TOTAL (RLC) “A” TO OUTPUT 24.7k𝛀10k𝛀 VOUT– V V k (1.38 × 10–23 J/K) VOUT VOUT VOUT– IN+ R10k𝛀 C110k𝛀 R10k𝛀 C 2 C3 VIN VIN High-Pass ~ ~ IR OUT 10k𝛀 RTOTAL =Resistors IN+ VINFilter/Differentiator ~ B == Boltzmann’s bandwidth inconstant Hz 1 R10k𝛀 2 1in 3Parallel/Capacitors VIN+VIN+ Differential Differential Amplifier Amplifier Instrumentation Instrumentation Amplifier Amplifier VOUT– OUT– R + Resistors in in Series 2 2 2 High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier V ~ VIN– OUT (dB) R R G V High-Pass Filter/Differentiator V V OCM V IN– V 1 Parallel/Capacitors in Series G G R V OUT+ ~ √ R + X I OUT+ IN– Differential Amplifier CM OUT+ R10k𝛀 CM +V V A3 R+V High-Pass G RG Amplifier CM Resistors RIN RIN T = absolute temperature in Kelvin 10k𝛀 R11+R + R224.7k𝛀 + R24.7k𝛀 + … / C C = C=OUT + Cin +Series COUT R R24.7k𝛀 VIN, R2Instrumentation 4.3 43 430 4300 RINFilter/Differentiator NOISE GAIN =V in Parallel/Capacitors VN, R1 –20RB 2OUT 3+ … R1' V +VRTOTAL +VTOTAL = =R10k𝛀 V ~R1' ~ 4kTR2 At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10+V V V +R1' 10k𝛀 N– V VOUT– TOTAL 1 VOCM R R 10k𝛀 RFF VVOCM IN+ B VOCM RF +V 1210k𝛀1 3 +VIN/ TOTAL GAINA2FROMA3 XL470 XC in Series V RA2 R R2 ~ ~ R ~ R1 ~ 10k𝛀1 11 1 Resistors in Parallel/Capacitors A3 R2 R3 10k𝛀 1 R = resistance in Ohms RFF = RF RG R RFF A2 ~ A2 R2A3 1 1 1 R R R GAIN 4.7 47 0.047 0.47 4.7 47 470 4700 A2 ~ F + + Two Resistors in Parallel F F + TO OUTPUT R1 = + 10k𝛀 V V 2 + R1 “A” Z= (LC) 4700 VA = ILINE Z 1 +R3' 1–V+ RS –RF –RFRINCIN VIN+V = RF= RVR –V –V VOUT– ++ ROUT– A2 R1 R2' A2 FF V R RRTOTAL CCTOTAL //10k𝛀 == 24.7k𝛀 + Parallel + 1+… TOTAL= TOTAL –VIN R2' R3' + R2' R2' NG = R3' INCINS VIN+ VIN+ IN 10k𝛀+ … 10k𝛀 10k𝛀 INin V 10k𝛀 FF + VOUT R3' +V VIN TOTAL TOTAL + ~ + F VR B = bandwidth in Hz + R2' RFR= RRFIN –R R1 = VFIN VOUT V =OUT VIN –R –RR + F V IN R Equal Resistors V V 10k𝛀 (dB) 21× 24.7k𝛀 –V+IN=2 × ~ – XC XL 510 10k𝛀 diff diff CIN SINCRININSCINS FR ~+ VOUT RFOUT– 1 1 1 1 1 1 F IN R R3'A1 R C C R C F / = R C 124.7k𝛀 +21 +in V 3Parallel/Capacitors V =V 1= VV11R + 2VV 10k𝛀 R R V = V Resistors in Series V = V G R OUTdiff IN R = V A1 A1 A1 2 × 24.7k𝛀 5.1 51 5100 ~ G 1 1 1 1 R V G G OUT IN 1 1 2 3 OUT IN R –R C S R C S R C S F G R RIN VOUT =VOUT VIN =VOUT V IN TOTAL TOTAL 2 × × 24.7k𝛀 2R1 V RININ –RFF REF VV diff V = diff IN IN 4kTR1 I IN IN +C 1INCS+S1 CLOSEDVOUT = 1RB + V 2= VR VNOISE GAIN RV + V+ NV A2 A1 = + V = V + +… … 10k𝛀2R×110k𝛀 + + + 10k𝛀 +… … RTOTAL = + =RVGGIN F VN, VIN 1+V + V= 1+ + RG R R1 RININ VOUT VRIN / CTOTAL = 1+ R ×V24.7k𝛀 4kTR2 R3 10k𝛀 At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 ×V 10V–20 ~ R2 10k𝛀 + +VIN V++1V + diff OUT + ~ SININ N– RIN V + ~~ C CIN VOUT = =VIN CR CIN 24.7k𝛀 C V BW diff IN RRIN = 1 + R Where V1 V+ +C1ININS +IN1 + 1 R IN RF IN RR LOOP R 1 ~V 2 V22 R2 R3 R3R2 IN IN 2 is+V the value of of the 10k𝛀 G RININ R2 R V10k𝛀 ==1 + VC R1 RG R R VOUT VOUT CIN V RGG R2 R3 VOUT 110k𝛀 C1+11+VREF =VR 5.6 1 56 560 1 RB IN OUT IN RC ~ F =V CINCINSINS+S+1 1 RR33one C1C2221 + CC333 1 + … R+R+ R R–R RTOTAL 2 ~ OCM 1 1 156001 R2 3+ G F R IN 2 VOUT ~ =OUT VOCM … + IN cm cm 11 RR222+ RG G VVOUT VOUT 2 RG = VIN V =V A2 = f OUT OUTdiff IN 2 OUT V VOUT = VV VVIN = R 2 × 24.7k𝛀 1 1 =V V =V A2 OCM CL R C / = A2 V IN A(S), 2R1 IN NG = 1 + OCM OUT=V OCM TOTAL V = 1 + equal VIN– + 6.2+ + …62 Z = +(RLC) + +… R3 TOTAL VIN VVOUT+ VN, Resistors Parallel LOOP GAIN, VR + VV Rand N Rcm RX Vcm cm VOUT+ IF R2 = R3, G = 1 + VOUT IN– V VIN– VVCM RinTOTAL resistors, is31Series/Capacitors the G R OUT+ OUT+ CINS +V IN– RIN ROUT Vnumber C R C C 6dB/OCTAVE CM 2 AVRF CM ROCM R RTwo R R1 INR 1 2 R Resistors in in Parallel CM N R 620 6200 V+R R 1 cmVOUT R RIN R RIN R3 1 1 2 3 F =V I 24.7k𝛀 24.7k𝛀 2R1 24.7k𝛀 –R C S R OPEN-LOOP R IN– F REF F 1 1 1 1 1 V V R3 + R2 24.7k𝛀 OUT+ R V IN N+ R C R R C C3 OCM 2R1 BLOCK DC, AMPLIFY AC BLOCK DC, AMPLIFY AC RVINFIN –RF CIN=SR F IN IN F DRIVE REF A𝛃 CM R +LOW V = R1' V 2R1 DIFFERENTIAL INPUT FROM AMPLIFY LEVEL DIFFERENTIAL INPUT ADCADC FROM A V VVA LEVEL SIGNAL, OUT OUT –R OUT VDIFFERENTIAL = cm VIN F AV REF R1' R1' V R1'LOW 1+ R OUT 1 2 3 2 VV SIGNAL, VAMPLIFY V = V DIFFERENTIAL 24.7k𝛀 INCINS OUT VA VIN VFROM = V VV+ GAIN ROLL-OFF 2 + X2 1 2 × 24.7k𝛀 1 +=R VDRIVE =DRIVE R3 1+ V VDIFFERENTIAL + + + … + + … VDRIVE BLOCK DC, AMPLIFY ACVOUTdiff = diff IN – R3 4kTR1 OUT VOUTR=INVVIN IN A DIFFERENTIAL INPUT ADC FROM A AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, CLOSED2resistors × 24.7k𝛀 V OUT INOCMR OUT + NA V DC, R1' BLOCK AMPLIFY AC 2 × 24.7k𝛀 GAIN BLOCK DC, AMPLIFY AC OCM OCM OCM V =V R2 RA3V R2 A INPUT ADC FROM A AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, DRIVE A DIFFERENTIAL INPUT ADC FROM AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, of equal √ R R R V = 1 + V + V R R2 diff OCM OUT = V “B” TO OUTPUT Two Resistors in Parallel OUT R R1 Two Resistors in Parallel OUT IN REF V A3 G TOTAL VOUT = 1V+OUT +V A3SIGNAL R RINCINSAC R R RINAMPLIFY cm =RR 1 ++ RVIN+ VIN +V 6.8 68 680 6800 0.068 0.68 6.8 68 680 6800 RGDIFFERENTIAL A3 DIFFERENTIAL OR SINGLE-ENDED SOURCE REJECT COMMON-MODE SIGNAL DIFFERENTIAL OR SINGLE-ENDED SOURCE REJECT COMMON-MODE BLOCK DC, REF = R + … / C = C + C + C + … R OCM G DRIVE A INPUT ADC FROM A AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, C R C S RIN RIN REF 1 2 + 1 R R C S R RC LOOP BW V IN TOTAL 1 2 3 TOTAL 1 2 3 1 2 3 1 2 A3SIGNAL G Resistors in Parallel +IN1DC, IN AMPLIFY IN RG +1 OUT R1 R1 R1 DIFFERENTIAL OR SINGLE-ENDED SINGLE-ENDED SOURCE REJECT COMMON-MODE 2R1 R Equal R1 DIFFERENTIAL SINGLE-ENDED SOURCE REJECT COMMON-MODE SIGNAL DIFFERENTIAL OR SOURCE REJECT COMMON-MODE SIGNAL BLOCK AC G RTOTAL10k𝛀 = VVIN+ VIN+ 2R1LEVEL VVOUT– V DRIVE DIFFERENTIAL INPUT ADC FROM A AMPLIFY LOW DIFFERENTIAL SIGNAL, IF R2 = R3, G= 1+ V V AOR 2R1 VOUT– 4kTR3 IN+ OUT– OUT– R1 IF R2 = R3, G 10k𝛀 1+ 10k𝛀 in ++SIGNAL + R IF=R2 = R3, = 1+ DIFFERENTIAL SINGLE-ENDED SOURCE 10k𝛀 = fCL REJECT ~ AMPLIFY + =V VADC Two Resistors Parallel ~LEVEL DIFFERENTIAL R +G BLOCK DC, AMPLIFY AC VIN+VR 7.5 75 750 7500 OUTcmOR OCM VINPUT DRIVE AIN+ DIFFERENTIAL LOWCOMMON-MODE SIGNAL, A(S), R OUT– FROM A ~~ ~ ROCM R Two Resistors in Parallel 10k𝛀 VOUT =V R R +R N, R3 OUT LOOP GAIN, G G cm G cmR=V R R R R OCM G 11 DIFFERENTIAL OR SINGLE-ENDED REJECT COMMON-MODE SIGNAL 11value 6dB/OCTAVE A 2222 of one of the GDIFFERENTIAL Where R==is+Vthe R3 SOURCE IN+ SOURCE ++ +REJECT COMMON-MODE R Two OPEN-LOOP R2 + OR SINGLE-ENDED SIGNAL in Parallel +V RResistors +VIN A𝛃 GAIN FROM IN IN RParallel/Capacitors TOTAL 8.2 82 820 8200 VV V TOTAL 2= R2 + IN10k𝛀 10k𝛀 10k𝛀 V ROLL-OFF R2 R3 R3 R2 R3 TOTAL 10k𝛀 –LEVEL +VIN RTOTAL = +V10k𝛀 R2 BLOCK AMPLIFY AC Resistors in equal in Series DRIVE AINPUT DIFFERENTIAL INPUT A LOW DIFFERENTIAL SIGNAL, R3 GAIN V ~ ~ AMPLIFY R2 ~ BLOCKBLOCK DC, AMPLIFY ACDC, AC R R R2 R1 R3 ~DIFFERENTIAL DRIVE DRIVE A DIFFERENTIAL ADC FROM A ADC AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, “B” TOA2 OUTPUT DC, AMPLIFY R 1 R2 R +R A DIFFERENTIAL INPUT ADC FROM A FROM AMPLIFY LOW LEVEL SIGNAL, 222 2 resistors, and TOTAL 1 2 R +R 1 2222 N is the number Equal Resistors in Parallel A2 1 A2 ~ N A2 + 4kTR3 + 4kTR1 V 1 2 N 9.1 91 910 9100 DIFFERENTIAL OR SINGLE-ENDED REJECT COMMON-MODE SIGNAL A2 RTOTAL = VVRREF RTOTAL = R1 + R2 R R 1 R2 V RFFSINGLE-ENDED NOISE GAIN, CLOSEDDIFFERENTIAL OR SOURCE COMMON-MODE SIGNAL RF SOURCE REJECT DIFFERENTIAL SOURCE REJECT COMMON-MODE SIGNAL 1 of 1 VREF R RSINGLE-ENDED R 2R1 R –R –R R –RFF CIN S RINCINS –RF F OR equal REF RF= FRF4kTR3 REF R×VTOTAL =resistors R3 ++ R3= V 2R1 2R1 RINCINSVVOUT BW × R3 + R3 1 + 2R1 RTI NOISE = IN INFC INS VV + == VV V ==VOUTFF = VV VVIN RIN R +R Where R is the value of one of the 1 LOOP V = V 11 ++2R1 V R +R R 1 + R –R C S F REF OUT IN R3 VVOUT = V V = V + / = R C = = V 1 2 2 × 24.7k𝛀 2 24.7k𝛀 2 × 24.7k𝛀 OUT IN R R R V = V 1 2 2 × 24.7k𝛀 F IN IN R2 R2 diff diff R2 diff Equal Resistors in Parallel R IN V = V OUT IN VOUT R TOTAL VVOUT R2 diff Parallel OUT IN 1+ R ++OUT = 1 + Resistors VVIN VVREF +in VREF R VIN = 11V + RGG= VOUT = VINR S R 2 =1 VEqual 2R ×TOTAL VOUT =VRIN1+R +TOTAL VREF RG 2 2 𝛃 GAIN R2 IN + REF diff OUT RIN CIN R RC RIN IN + 1 IN INS IN IN VOUT = 1 + OUT RG G ++IN 11CINS + 1RIN RINCINS + 1 1=24.7k𝛀 1 Vnumber 1 RG resistors, R equal and N IN REF RGis the R12× R2 RIN NRR+GGV1Where 2R1 2R1 2R1 IN RINCINS + 1 2R1 2 RG+ +==4kTR2 + IN+2 R32 + IN– IF R3, R3, G = 1 + 11 ++=2R1 + + … + + +… IF R2 R2 R3, G GIF==R2 R is the value of one of the IF R2 = R3, G = 1 + R2 Where R is the value of one of the Where R is the value of one of the R R R R Equal Resistors in Parallel R VVOUT =V VOUT =VOCM VOUT =VOCM R =V R1 + R2 IF R2 = R3, G = 1 + R1 + R2 of equal resistors OCM OUTcm OCM Equal Resistors in Parallel 2 Equal Resistors in Parallel R C R R C C R cm = R cm + 4kTR3 + 4kTR1 V VOUTcm =VOCM cm 1 = 2 3 1 number 2 3 N RTOTAL TOTAL TOTAL equal resistors, and N is the R1 + R2 NOISE GAIN, CLOSEDequal resistors, and N is the number equal resistors, and N is the number N NR Where RR isisthe R Where R is the value of one of the BW × RTI NOISE = RTO of one of theof the 1 CLOSED-LOOP BANDWITH LOOP BLOCK DC, DC, AMPLIFY AC AC AMPLIFY BW =DIFFERENTIAL 1.57 fCL LEVEL BLOCKBLOCK DC, AMPLIFY AMPLIFY AC AC thevalue value of one NOISE =A NGADC × RTI NOISEAMPLIFY DRIVE A DRIVE A DIFFERENTIAL INPUT ADC INPUT FROM ADC A FROM AMPLIFY LEVEL LOWAMPLIFY LEVEL DIFFERENTIAL SIGNAL, SIGNAL, DRIVE A DIFFERENTIAL DIFFERENTIAL INPUT ADC FROM A AMPLIFY LOW DIFFERENTIAL SIGNAL, BLOCK DC, ACDRIVE DRIVE A DIFFERENTIAL INPUT FROM ALOW LOW DIFFERENTIAL SIGNAL, of equal resistors RTOTAL = ofof equal resistors BLOCK DC, AMPLIFY =R TwoWhere RTOTAL equal resistors A DIFFERENTIAL INPUT ADC FROM A AMPLIFY LOWLEVEL LEVEL DIFFERENTIAL SIGNAL, 2 2 𝛃 GAIN = R RTI SOURCE = REFER TO INPUT Resistors in Parallel LOG FREQUENCY (HZ) equal resistors, and N is the number TOTAL N equal resistors, and N is the number DIFFERENTIAL DIFFERENTIAL OR SINGLE-ENDED OR SINGLE-ENDED SOURCE REJECT REJECT COMMON-MODE COMMON-MODE SIGNAL SIGNAL DIFFERENTIAL OR SINGLE-ENDED SOURCE REJECT COMMON-MODE SIGNAL N R DIFFERENTIAL ORSOURCE SINGLE-ENDED SOURCE REJECT COMMON-MODE SIGNAL R1 × R2 resistors, and N is the number 1 DIFFERENTIAL OR SINGLE-ENDED SIGNAL N equal RTO = REFER + 4kTR2 + TO IN+2OUTPUT R32 + IN–2 REJECT COMMON-MODE of equal resistors of equal resistors R1 + R2 R1 + R2 R1 R2 of equal resistors RTOTAL = CLOSED-LOOP BANDWITH BW = 1.57 fCL R1+R2 RTO NOISE = NG × RTI NOISE VIN VIN VIN VIN V V VIN IN VV INININ HIGH VVOUT VOUT BUFFER SOURCE VOUT OUT IMPEDANCE VOUT VOUT LOW RESISTANCE LOAD VIN IN VOUT = VVINVTO =V V V =V =V F F F F F F F SIG V SIG V CM V2 V CM V CM CM V CM V CMSIG + RG G RGRSIG RG SIG SIG SIG SIG CM CM CM + R+ V SIG + V SIG G + + 2 CM 2V +SIG V SIG CMV SIG V SIG 2 G 2 2 G 2 + V SIG 2 SIG CM GG G R2' R1' R1' R1' R1'R1 R1 R1 R1 R1' G SIG R3' R3' IN ++ + R2 R2 + + + + OUT CM R2 R2 R2 R2 2R1 IF R2OUT = R3, G =SIG 1 + OUT SIG GRG SIG G G CM V OUT V OUT V OUT V OUT V OUT V OUT OUT G SIG SIG OUT SIG SIG OUT G GG G 1 GG G G G OUT G OUT OUT G OUT SIG G G G G G G IN OUT CM G CM G IN IN IN SIG OUT OUT OUT IN CM CM IN OUT G G G CM V OUT OUT OUT OUT CM IN IN IN IN IN R3' R1' R1' R1G R1 G SIG SIG SIG R3' R3' R3' R3' R3 R3 R3 OUT R3 OUT R3 SIG G R3 2R1 2R1 R3 R3 + V + V = V = V + R 1+ R OUT OUT SIG R3 SIG1 2R1 R2G R2 2R1 2R1G R3 ++ R3 + VV OUT == R2 SIG = R3 VVSIG V 11+2R1 + RRG 1 + R OUT OUT R3R2 + R21SIG R2 G G + 2R1 SIG V OUT = VSIG R OUT SIG 2R1 IF R2 = R3, G =G 1 + IF R2 = R3, GR2 1+ 2R1 RG RG 2R1 R2 R3, G= =R3 ++ 2R1 + IFIFR2 G IF R2 =11R3, G2R1 = 1+ V OUT = ==VR3, R 1+ 2R1 SIG RGGR RG IF R2 = R3, G = 1R2 + G RG R1 SIG SIG RG CM RG R2' R2' R2' R2' R2' R2' SIG V CM CM + + + ++ + + + + +V + V SIG SIG + V SIG2V SIG V SIG 2 V SIG 2 2 2 2 + OUT OUT G G IN IN OUT OUT IN G G G G G REF REF G IN G IN IN REF REF GIN REF IN REF G REF IN REF G G G REF REF REF REF REF REF G