P I V P I V P == = V Design Equations—Commonly …...Op Amp Noise for Single-Pole System...
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Op Amp Noise for Single-Pole System CLOSED- LOOP BW = f CL B A V N, R1 R1 R3 4kTR3 4kTR1 V N, R3 I N+ I N– V N 4kTR2 V N, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 V OUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW × V N 2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + I N+ 2 R3 2 + I N– 2 R1 × R2 R1 + R2 2 + 4kTR2 R 1 R1 + R2 2 RTO NOISE = NG × RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 f CL Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 Log P OUT P IN V OUT V IN = 20 Log (Gain) I OUT I IN Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective V = 0.707 V = V V RMS = 0.707 V PEAK = V EFF V AVE = 0.637 V PEAK V EFF = 1.11 V AVE V PEAK = 1.57 V AVE V AVE = 0.9 V EFF Ohm’s Law (DC Circuits) √P VI IR √PR I P I 2 P P V 2 I V R P V P R V R V 2 I 2 R P I V R RESISTANCE () 10,000 1000 10 1 0 10 1k 100k 10M 100 10k 1M 100M 100 e n at 25°C nV Hz where: V R = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 × 10 –23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRB V R At 25°C, 4kT = 1.65 × 10 –20 W/Hz, therefore, V R = 1.65 × 10 –20 RB Resistor Johnson Noise Formula GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A A(S), OPEN-LOOP GAIN CLOSED- LOOP GAIN 1 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel 1 + 1 + 1 + … R 1 R 2 R 3 1 R TOTAL = 1 + 1 + 1 + … C 1 C 2 C 3 1 C TOTAL = / R 1 +R 2 R 1 R 2 R TOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N R R TOTAL = Impedance Formulas (Series) Z = √R 2 + X L 2 (Series RL) Z = √R 2 + X C 2 (Series RC) Z = X L – X C (Series LC) Z = √R 2 + (X L – X C ) 2 (Series RLC) Z = V A I Voltage and Impedance Formulas (Parallel) Z = RX L (RL) Z = V A √R 2 + X L 2 I LINE Z = RX C (RC) V A = V L = V C = V R √R 2 + X C 2 Z = X L X C (LC) V A = I LINE Z X L – X C Z = RX (RLC) √R 2 + X 2 Reactance Formulas X C = X L = 2π fL 2π fC 1 Transformers (Step-Up or Step-Down Ratios) = = = N P N S E P E S I S I P Z P Z S Common Capacitor Values pF pF pF pF µF µF µF µF µF µF µF 1.0 10 100 1000 0.01 0.1 1.0 10 100 1000 10,000 1.1 11 110 1100 1.2 12 120 1200 1.3 13 130 1300 1.5 15 150 1500 0.015 0.15 1.5 15 150 1500 1.6 16 160 1600 1.8 18 180 1800 2.0 20 200 2000 2.2 22 220 2200 0.022 0.22 2.2 22 220 2200 2.4 24 240 2400 2.7 27 270 2700 3.0 30 300 3000 3.3 33 330 3300 0.033 0.33 3.3 33 330 3300 3.6 36 360 3600 3.9 39 390 3900 4.3 43 430 4300 4.7 47 470 4700 0.047 0.47 4.7 47 470 4700 5.1 51 510 5100 5.6 56 560 5600 6.2 62 620 6200 6.8 68 680 6800 0.068 0.68 6.8 68 680 6800 7.5 75 750 7500 8.2 82 820 8200 9.1 91 910 9100 Common 1% Resistor Values 10.0 10.2 10.5 10.7 11.0 11.3 11.5 11.8 12.1 12.4 12.7 13.0 13.3 13.7 14.0 14.3 14.7 15.0 15.4 15.8 16.2 16.5 16.9 17.4 17.8 18.2 18.7 19.1 19.6 20.0 20.5 21.0 21.5 22.1 22.6 23.2 23.7 24.3 24.9 25.5 26.1 26.7 27.4 28.0 28.7 29.4 30.1 30.9 31.6 32.4 33.2 34.0 34.8 35.7 36.5 37.4 38.3 39.2 40.2 41.2 42.2 43.2 44.2 45.3 46.4 47.5 48.7 49.9 51.1 52.3 53.6 54.9 56.2 57.6 59.0 60.4 61.9 63.4 64.9 66.5 68.1 69.8 71.5 73.2 75.0 76.8 78.7 80.6 82.5 84.5 86.6 88.7 90.9 93.1 95.3 97.6 Design Equations—Commonly Used Amplifier Configurations V OUT = V IN V OUT V IN BUFFER HIGH IMPEDANCE SOURCE TO LOW RESISTANCE LOAD Voltage Follower Noninverting Op Amp Inverting Op Amp AMPLIFY AND INVERT INPUT V IN R G R F V OUT V A V B R 1 R 1 R 2 V OUT R 2 V CM Voltage Subtractor/ Difference Amplifier R AMPLIFY THE DIFFERENCE BETWEEN TWO VOLTAGES, REJECT COMMON-MODE VOLTAGE SUM MULTIPLE VOLTAGES Voltage Adder V A V C V B V OUT R 1 R 2 R 3 R F V N R N Low-Pass Filter/Integrator LIMIT BANDWIDTH OF SIGNAL V IN V OUT R 1 C R F t = RC = R F C V OUT = V IN –R F 1 R 1 R F CS + 1 High-Pass Filter/Differentiator BLOCK DC, AMPLIFY AC C IN R IN V OUT V IN R F V OUT = V IN –R F R IN C IN S R IN R IN C IN S + 1 Differential Amplifier R F R F R G R G V OUT+ V OUT diff = R F V IN R G V OUT– V OCM V IN– V IN+ V OUT cm =V OCM DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL, REJECT COMMON-MODE SIGNAL Instrumentation Amplifier V OUT R G R1' R1 R2' R2 R3 R3' + + + V OUT =V SIG 1 + 2R1 R G R3 R2 IF R2 = R3, G = 1 + 2R1 R G ~ ~ ~ ~ ~ ~ V CM + + V SIG 2 V SIG 2 A1 A2 A3 Resistors in Series/Capacitors in Parallel R TOTAL = R 1 + R 2 + R 3 + … / C TOTAL = C 1 + C 2 + C 3 + … 1% standard values decade multiples are available from 10.0 Ω through 1.00 MΩ (also 1.10 MΩ, 1.20 MΩ, 1.30 MΩ, 1.50 MΩ, 1.60 MΩ, 1.80 MΩ, 2.00 MΩ, and 2.20 MΩ). Standard base resistor values are given in the following table for the most commonly used tolerance (1%), along with typically available resistance ranges. To determine values other than the base, multiply the base value by 10, 100, 1000, or 10,000.
Transcript of P I V P I V P == = V Design Equations—Commonly …...Op Amp Noise for Single-Pole System...
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R √P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Responsefor Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
CLOSED-LOOP BW
= fCL
B
A
VN, R1R1
R3
4kTR3
4kTR1
VN, R3IN+
IN–
VN
4kTR2
VN, R2R2
NOISE GAIN =
GAIN FROM“A” TO OUTPUT
=
NG = 1 +R2
R1
VOUT
GAIN FROM“B” TO OUTPUT
= –R2
R1
RTI NOISE =
TOTAL
BW ×
VN2 + 4kTR3 + 4kTR1
R2
R1 + R2
2
+ IN+2 R32 + IN–
2 R1 × R2R1 + R2
2
+ 4kTR2R1
R1 + R2
2
RTO NOISE = NG × RTI NOISERTI = REFER TO INPUTRTO = REFER TO OUTPUT
BW = 1.57 fCL
GAIN(dB)
6dB/OCTAVEROLL-OFF
LOOP GAIN,A
A(S),OPEN-LOOP
GAIN
CLOSED-LOOP GAIN
1
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE ()
10,000
1000
10
1
010 1k 100k 10M100 10k 1M 100M
100en at 25°C
nV
Hz
where:
VR = resistor Johnson Noise spectral density
k = Boltzmann’s constant (1.38 × 10–23 J/K)
T = absolute temperature in Kelvin
R = resistance in Ohms
B = bandwidth in Hz
= 4kTRBVR
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10–20RB
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
Common Capacitor Values
pF pF pF pF µF µF µF µF µF µF µF1.0 10 100 1000 0.01 0.1 1.0 10 100 1000 10,0001.1 11 110 11001.2 12 120 12001.3 13 130 13001.5 15 150 1500 0.015 0.15 1.5 15 150 15001.6 16 160 16001.8 18 180 18002.0 20 200 20002.2 22 220 2200 0.022 0.22 2.2 22 220 22002.4 24 240 24002.7 27 270 27003.0 30 300 30003.3 33 330 3300 0.033 0.33 3.3 33 330 33003.6 36 360 36003.9 39 390 39004.3 43 430 43004.7 47 470 4700 0.047 0.47 4.7 47 470 47005.1 51 510 51005.6 56 560 56006.2 62 620 62006.8 68 680 6800 0.068 0.68 6.8 68 680 68007.5 75 750 75008.2 82 820 82009.1 91 910 9100
Common 1% Resistor Values
10.0 10.2 10.5 10.7 11.0 11.3 11.5 11.8 12.1 12.4 12.7 13.013.3 13.7 14.0 14.3 14.7 15.0 15.4 15.8 16.2 16.5 16.9 17.417.8 18.2 18.7 19.1 19.6 20.0 20.5 21.0 21.5 22.1 22.6 23.223.7 24.3 24.9 25.5 26.1 26.7 27.4 28.0 28.7 29.4 30.1 30.931.6 32.4 33.2 34.0 34.8 35.7 36.5 37.4 38.3 39.2 40.2 41.242.2 43.2 44.2 45.3 46.4 47.5 48.7 49.9 51.1 52.3 53.6 54.956.2 57.6 59.0 60.4 61.9 63.4 64.9 66.5 68.1 69.8 71.5 73.275.0 76.8 78.7 80.6 82.5 84.5 86.6 88.7 90.9 93.1 95.3 97.6
Design Equations—Commonly Used Amplifier Configurations
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
VOUT = VIN
VOUTVIN
BUFFER HIGH IMPEDANCE SOURCETO LOW RESISTANCE LOAD
Voltage Follower
VIN
RG RF
VOUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCEBETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/Difference Amplifier
VA
VBR1
R1
R2
VOUT
R2
VCM
SUM MULTIPLE VOLTAGES
Voltage Adder Low-Pass Filter/Integrator
LIMIT BANDWIDTH OF SIGNAL
High-Pass Filter/Differentiator Differential Amplifier Instrumentation Amplifier
DRIVE A DIFFERENTIAL INPUT ADC FROM A DIFFERENTIAL OR SINGLE-ENDED SOURCE
AMPLIFY LOW LEVEL DIFFERENTIAL SIGNAL,REJECT COMMON-MODE SIGNAL
RF
RF
RG
RG
VOUT+
VOUTdiff = RF VIN
RG
VOUT–
VOCM
–VIN
+VIN
VREF
OUT
10k
10k
24.7k
10k
10k
RGVCM
VOUT = 1 + 2 × 24.7k VIN + VREF RG
BLOCK DC, AMPLIFY AC
VIN
VOUT
R1
C
RF
t = RC = RFC
VOUT = VIN
–RF 1
R1 RFCS + 1
CIN
RIN
VOUTVIN VIN–
VIN+
RF
VOUT = VIN
–RF RINCINS
RIN
VA
VC
VBVOUT
R1
R2
R3
RF
VN
RN
VOUTRG
R1'
R1
R2'
R2 R3
R3'+
+
+
VOUT = VSIG 1 +2R1RG
R3R2
IF R2 = R3, G = 1 +2R1RG
~~
~~
~~
VCM
+
+
VSIG2
VSIG2
A1
A2
A3
RINCINS + 1
VOUTcm =VOCM
√P
Decibel (dB) Formulas (Equal Impedances)
db = 10 Log = 20 LogPOUT
PIN
VOUT
VIN
= 20 Log (Gain) IOUT
IIN
Transformers(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and CurrentsRMS = Root Mean Square = Effective
VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF
Ohm’s Law (DC Circuits)
Resistors in Series/Capacitors in ParallelRTOTAL = R1 + R2 + R3 + … / CTOTAL = C1 + C2 + C3 + …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
= = =NP
NS
EP
ES
ISIP
ZP
ZS
1 + 1 + 1 + …R1 R2 R3
1RTOTAL =
1 + 1 + 1 + …C1 C2 C3
1CTOTAL =/
R1+R2
R1 R2RTOTAL =
Where R is the value of one of the equal resistors, and N is the number of equal resistors
NRRTOTAL =
VI
IR
√PR
IP
I2P P
V2
IV
RP
VP
RV
RV2
I2R
B.W.SR.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
RXL Figure of Merit
of a CoilQ =
SR = or Hz2π√LC
1
√LC
.159
L =4π2 SR
2 C
1C =
4π2 SR2 L
1
XC =
XL = 2π fL
2π fC
1
Impedance Formulas (Series)
Z = √R2 + XL2 (Series RL)
Z = √R2 + XC2 (Series RC)
Z = XL – XC (Series LC)
Z = √R2 + (XL – XC)2 (Series RLC)
Z = VA I
Voltage and Impedance Formulas (Parallel)
Z = RXL (RL) Z =
VA √R2 + XL
2 ILINE
Z = RXC (RC) VA = VL = VC = VR √R2 + XC
2
Z = XL XC (LC) VA = ILINEZ XL – XC
Z = RX (RLC) √R2 + X2
P I
V R
1% standard values decade multiples are available from 10.0 Ω through 1.00 MΩ (also 1.10 MΩ, 1.20 MΩ, 1.30 MΩ, 1.50 MΩ, 1.60 MΩ, 1.80 MΩ, 2.00 MΩ, and 2.20 MΩ).
Standard base resistor values are given in the following table for the most commonly used tolerance (1%), along with typically available resistance ranges. To determine values other than the base, multiply the base value by 10, 100, 1000, or 10,000.
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