Op Amp Noise for Single-Pole System
Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
Op Amp Noise for Single-Pole System Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
Op Amp Noise for Single-Pole System Closed-Loop Frequency Response
for Voltage Feedback Amplifiers
Resistor Johnson Noise Formula
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
GAIN
(dB)
6dB/OCTAVE
ROLL-OFF
LOOP GAIN,
A𝛃
A(S),
OPEN-LOOP
GAIN
CLOSED-
LOOP
GAIN
1
𝛃
NOISE GAIN,
CLOSED-LOOP BANDWITH
LOG FREQUENCY (HZ)
RESISTANCE (𝛀)
10,000
1000
10
1
0
10 1k 100k 10M100 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
= 4kTRBV
R
At 25°C, 4kT = 1.65 × 10
–20
W/Hz,
therefore, V
R
= 1.65 × 10
–20
RB
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
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
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
V
OUT
= V
IN
V
OUT
V
IN
BUFFER HIGH IMPEDANCE SOURCE
TO LOW RESISTANCE LOAD
Voltage Follower
V
IN
R
G
R
F
V
OUT
AMPLIFY AND INVERT INPUT
Inverting Op AmpNoninverting Op Amp
AMPLIFY THE DIFFERENCE
BETWEEN TWO VOLTAGES,
REJECT COMMON-MODE VOLTAGE
Voltage Subtractor/
Difference Amplifier
V
A
V
B
R
1
R
1
R
2
V
OUT
R
2
V
CM
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
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
REF
OUT
10k𝛀
10k𝛀
24.7k𝛀
10k𝛀
10k𝛀
R
G
V
CM
V
OUT
= 1 +
2 × 24.7k𝛀
V
IN
+ V
REF
R
G
BLOCK DC, AMPLIFY AC
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
C
IN
R
IN
V
OUT
V
IN
V
IN–
V
IN+
R
F
V
OUT
=
V
IN
–R
F
R
IN
C
IN
S
R
IN
V
A
V
C
V
B
V
OUT
R
1
R
2
R
3
R
F
V
N
R
N
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
R
IN
C
IN
S
+ 1
V
OUT
cm
=V
OCM
√P
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
Transformers
(Step-Up or Step-Down Ratios)
Sinusoidal Voltages and Currents
RMS = Root Mean Square = Effective
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)
Resistors in Series/Capacitors in Parallel
R
TOTAL
= R
1
+
R
2
+
R
3
+ … / C
TOTAL
= C
1
+
C
2
+
C
3
+ …
Resistors in Parallel/Capacitors in Series
Two Resistors in Parallel
Equal Resistors in Parallel
===
N
P
N
S
E
P
E
S
I
S
I
P
Z
P
Z
S
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
=
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
B.W.
S
R.
(Tuned Circuit)
Q =
Q & Resonant Frequency Formulas
Reactance Formulas
R
X
L
Figure of Merit
of a Coil
Q =
S
R
=orHz
2π√LC
1
√LC
.159
L =
4π
2
S
R
2
C
1
C =
4π
2
S
R
2
L
1
X
C
=
X
L
= 2π
fL
2π
fC
1
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
PI
VR
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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