Design Equations—Commonly Used Amplifier Configurations

= 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
AGAIN
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
A
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),IN1 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)
A
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
LOOP
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 =ABANDWITH
= 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
R
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
VEFF
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
()
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
()
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()
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 =
10k 10k + –VIN+R
High-Pass Filter/Differentiator
R2'
R3'
I2C + … ofV10k
X L XC
10BClosed-Loop
100
1kHz
10k
100k
1M
10M
+
RF
where:
–V
= bandwidth
in
–V 10k √PR10k 10kC 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
10k
A1
RESISTANCE
()
V
~
~
R
RX
I
10k
10k
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
10k 10k
2
CIN
Resistors
Parallel10k
RF IN R
Z = LZ
(LC)
= ILINEZ (RLC)
Resistors
Series/Capacitors
VOUT VOUT
ZX22330
=+ X22 2VRX
RF
R
=+
=
R110k
+ 10k
R12in
+
RSeries/Capacitors
RTOTAL
OpR Amp VNoise
for Single-Pole
System
Closed-Loop
Frequency
Response
–V
VIN V
~
VR
4kTRB
A(RLC)
in
10k
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
24.7k
VOUT
+ 3300
X2
P2+10k
–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 10k
C√R
+
R1IN11+
R V3+
… R/10k
CTOTAL
=OUT
C222C+
C333C
+3 +
……
+
RR TOTAL
TOTAL
RIN
+ ~
R= 24.7k
R24.7k
R1IN210k
=C=11C1+
RRV24.7k
for Voltage
Amplifiers
VIN–
24.7k
RINCIN
T = Feedback
absolute temperature
in Kelvin
V
V
VOUT+ OUT+
TOTAL
TOTAL
24.7k
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
24.7k
V
V
P
OCM
√
R
V
V
OUT
V
=
resistor
Johnson
Noise
spectral
density
I
OCM
OCM
OCM
VIN C
~
~
R
A3
OUT
10k
~
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 R210k
2R2
P10k 10kin 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
24.7k10k
VOUT–
V
V
k
(1.38 × 10–23 J/K)
VOUT VOUT
VOUT–
IN+
R10k
C110k
R10k
C 2 C3
VIN
VIN High-Pass
~ ~
IR
OUT
10k
RTOTAL
=Resistors
IN+
VINFilter/Differentiator
~
B == Boltzmann’s
bandwidth inconstant
Hz
1 R10k
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+
R10k
CM +V V
A3
R+V
High-Pass
G
RG Amplifier
CM Resistors
RIN
RIN
T = absolute temperature in Kelvin
10k
R11+R
+
R224.7k
+
R24.7k
+ … / C C = C=OUT
+ Cin
+Series
COUT
R
R24.7k
VIN, R2Instrumentation
4.3
43
430
4300
RINFilter/Differentiator
NOISE
GAIN =V
in
Parallel/Capacitors
VN, R1
–20RB
2OUT
3+ …
R1'
V
+VRTOTAL
+VTOTAL
= =R10k
V
~R1'
~ 4kTR2
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 × 10+V
V
V
+R1'
10k
N– V
VOUT–
TOTAL 1
VOCM
R
R
10k
RFF
VVOCM
IN+
B
VOCM
RF
+V
1210k1 3 +VIN/ TOTAL
GAINA2FROMA3
XL470
XC in Series
V RA2
R
R2 ~ ~ R ~
R1
~
10k1 11 1
Resistors
in
Parallel/Capacitors
A3
R2
R3
10k
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
= + 10k
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
//10k
== 24.7k
+ Parallel
+ 1+…
TOTAL=
TOTAL
–VIN
R2'
R3' + R2'
R2' NG =
R3'
INCINS VIN+
VIN+
IN 10k+ …
10k
10k
INin
V
10k
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 10k
(dB)
21×
24.7k
–V+IN=2 ×
~
– XC
XL 510
10k
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
124.7k
+21
+in
V 3Parallel/Capacitors
V
=V 1=
VV11R
+ 2VV 10k
R
R
V
=
V
Resistors
in
Series
V
=
V
G
R
OUTdiff
IN
R
=
V
A1
A1
A1
2
×
24.7k
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
×
×
24.7k
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
+
+…
… 10k2R×110k
+ +
+ 10k
+…
… RTOTAL =
+
=RVGGIN F VN,
VIN
1+V
+ V= 1+ +
RG R
R1
RININ
VOUT
VRIN
/ CTOTAL =
1+ R
×V24.7k
4kTR2
R3
10k
At 25°C, 4kT = 1.65 × 10–20 W/Hz, therefore, VR = 1.65 ×V 10V–20
~
R2 10k
+
+VIN V++1V +
diff OUT
+ ~
SININ
N–
RIN
V + ~~
C
CIN
VOUT
= =VIN
CR
CIN
24.7k
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
10k
G
RININ
R2
R
V10k
==1 +
VC
R1
RG
R
R VOUT VOUT
CIN
V
RGG
R2 R3 VOUT
110k
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
×
24.7k
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
24.7k
24.7k
2R1
24.7k
–R
C
S
R
OPEN-LOOP
R
IN–
F
REF
F
1
1
1
1
1
V
V
R3
+
R2
24.7k
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
A
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
24.7k
INCINS
OUT
VA
VIN
VFROM
= V
VV+ GAIN
ROLL-OFF
2 + X2 1
2 × 24.7k
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
× 24.7k
V
OUT
INOCMR
OUT +
NA V
DC,
R1'
BLOCK
AMPLIFY
AC
2
×
24.7k
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
RTOTAL10k
=
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
10k
1+
10k in
++SIGNAL
+
R
IF=R2
= R3,
= 1+
DIFFERENTIAL
SINGLE-ENDED
SOURCE
10k
= 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
10k
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
A
GAIN FROM
IN
IN
RParallel/Capacitors
TOTAL
8.2
82
820
8200
VV
V
TOTAL
2= R2
+
IN10k
10k
10k
V
ROLL-OFF
R2 R3
R3
R2
R3
TOTAL
10k
–LEVEL
+VIN RTOTAL
= +V10k
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
×
24.7k
2
24.7k
2
×
24.7k
OUT
IN
R
R
R
V
=
V
1
2
2
×
24.7k
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

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=24.7k
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

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