operational amplifier stability - texas instruments · 2012. 2. 22. · 1.95m 2.23m 2.50m vg1 0.00...
TRANSCRIPT
1
Operational Amplifier Stability
Collin Wells
Texas Instruments
HPA Linear Applications
2/22/2012
2
The CulpritsCapacitive Loads!
High Feedback Network Impedance!
Transimpedance Amplifiers!
Reference Buffers! Cable/Shield Drive! MOSFET Gate Drive!
High-Source Impedance or
Low-Power Circuits!
-
+
IOP2
R3 499kR4 499k
+
VG2
Cin 25p Vout
-
+
OPA
Cin 1u
C1 1u
C2 1u
VIN 5
Vin
Temp
GND
Vout
Trim
U1 REF5025
C3 10u
ADC_VREF
C4 100n
-
+
OPA
RL 250
Rf 20kRg 1k
+
Vin
-
+
OPA
C_Cable 10nVout
VREF 2.5
VREF
Shielded Cable
-
+
OPA
VRef 2.5
R1 20k
R2 20k
Vin 10
VReg
Q1
RL 200
Vo
Rf 1M
Rd 4.99G Cd 10p-
+
OPA
Id
Photodiode
Model
Attenuators!
V+
-
+
OPA
Rf 49kRg 4.99M
Cd 200p Vout
+Vin
D1
D2TVS
3
Just Plain Trouble!
Inverting Input Filter??
Output Filter??
-
+
OPA
VoutV1 5
R1 10k
R2 49kC1 10u C5 100n
-
+
OPA
Rf 100kRg 10k
Cin 1u
Vout
+
Vin
Oscillator
Oscillator
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
4
Recognize Amplifier Stability Issues on the Bench
• Required Tools:
– Oscilloscope
– Step Generator
• Other Useful Tools:
– Gain / Phase Analyzer
– Network / Spectrum Analyzer
5
Recognize Amplifier Stability Issues
• Oscilloscope - Transient Domain Analysis:
– Oscillations or Ringing
– Overshoots
– Unstable DC Voltages
– High Distortion
Time (s)
1.75m 2.25m 2.75m
Vo
lta
ge
(V
)
0.00
18.53m
Time (s)
1.75m 50.88m 100.00m
Ou
tpu
t
-14.83
0.00
15.00
Time (s)
1.75m 2.25m 2.75m
Vo
lta
ge
(V
)
0.00
21.88m
6
Recognize Amplifier Stability Issues
• Gain / Phase Analyzer - Frequency Domain: Peaking, Unexpected
Gains, Rapid Phase Shifts
Ga
in (
dB
)
-60.00
-40.00
-20.00
0.00
20.00
40.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
-360.00
-180.00
0.00
7
Quick Op-Amp Theory and Bode Plot Review
8
Poles and Bode Plots
+90
-90
+45
+-45
10 100 1k 10k 100k 1M 10M
Frequency
(Hz)0
(d
eg
ree
s)
-45o @ fP
-45o/Decade
-90o
0o
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB
)
-20dB/Decade
-6dB/Octave
fPG
0.707G = -3dB
Actual
FunctionStraight-Line Approximation
R
CV
IN
VOUT
A = VOUT
/VIN
Single Pole Circuit Equivalent
X100,000
Pole Location = fP
Magnitude = -20dB/Decade Slope
Slope begins at fP and continues down as frequency increases
Actual Function = -3dB down @ fP
Phase = -45°/Decade Slope through fP
Decade Above fP Phase = -84.3°
Decade Below fP Phase = -5.7°
9
Zeros and Bode Plots
+90
-90
+45
+-45
10 100 1k 10k 100k 1M 10M
Frequency
(Hz)0
(d
eg
ree
s)
+90o
0o
+45o/Decade
+45o @ fZ
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB
)
fZ
+20dB/Decade
+6dB/Octave
Straight-Line Approximation
G
1.414G = +3dB
(1/0.707)G = +3dBActual
Function
R
C
VOUT
A = VOUT
/VIN
Single Zero Circuit Equivalent
X100,000
Zero Location = fZ
Magnitude = +20dB/Decade Slope
Slope begins at fZ and continues up as frequency increases
Actual Function = +3dB up @ fZ
Phase = +45°/Decade Slope through fZ
Decade Above fZ Phase = +84.3°
Decade Below fZ Phase = 5.7°
10
Capacitor Intuitive Model
frequency
controlled
resistor
OPEN SHORT
DC XC
Hi-f XCDC < X
C < Hi-f
XC = 1/(2fC)
11
Inductor Intuitive Model
frequency
controlled
resistor
SHORT OPEN
DC XL
Hi-f XLDC < X
L < Hi-f
XL = 2fL
12
Op-Amp Intuitive Model
K(f)Ro
Rin
Vo
Vout
Vdiff
+
-
IN+
IN-
x1
13
Op-Amp Loop Gain Model
+
-
RF
RI
VIN
+
-
network
Aol+
-
VOUT
VIN
VFB
VOUT
VFB
RF
RI
=VFB
/VOUT
VOUT
network
VOUT/VIN = Acl = Aol/(1+Aolβ)
If Aol >> 1 then Acl ≈ 1/β
Aol: Open Loop Gain
β: Feedback Factor
Acl: Closed Loop Gain
14
Amplifier Stability CriteriaVOUT/VIN = Aol / (1+ Aolβ)
If: Aolβ = -1
Then: VOUT/VIN = Aol / 0 ∞
If VOUT/VIN = ∞ Unbounded Gain
Any small changes in VIN will result in large changes in VOUT which will feed
back to VIN and result in even larger changes in VOUT OSCILLATIONS
INSTABILITY !!
Aolβ: Loop Gain
Aolβ = -1 Phase shift of +180°, Magnitude of 1 (0dB)
fcl: frequency where Aolβ = 1 (0dB)
Stability Criteria:
At fcl, where Aolβ = 1 (0dB), Phase Shift < +180°
Desired Phase Margin (distance from +180° Phase Shift) > 45°
15
What causes amplifier stability issues???
16
Fundamental Cause of Amplifier Stability Issues
• Too much delay in the feedback network
-
+
BUF
BUF BUF
R1 100kR2 100k+ VG1
Vfb
Vo
DELAY
DELAY
17Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
Cause of Amplifier Stability Issues
• Example circuit with too much delay in the feedback network
-
+
BUF
BUF BUF
R1 100kR2 100k+
VG1
Vfb
Vo
R3 10
C1 10uC2 20p
DELAY DELAY
18
Cause of Amplifier Stability Issues
• Real circuit translation of too much delay in the feedback network
-
+
BUF
BUF BUF
R1 100kR2 100k
+
VG1
Vfb
Vo
R3 10
C1 10uC2 20p
-
+
BUF
BUF BUF
R1 100kR2 100k
+
VG1
Vfb
Vo
Ro 10
Cin 4pCstray 16p
Cload 10u
19
Cause of Amplifier Stability Issues
• Same results as the example circuit
-
+
BUF
BUF BUF
R1 100kR2 100k
+
VG1
Vfb
Vo
Ro 10
Cin 4pCstray 16p
Cload 10u
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
20
How do we determine if our system has too
much delay??
21
Phase Margin
• Phase Margin is a measure of the “delay” in the loop
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[de
g]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se (
de
gre
es)
Frequency (Hz)
100
Phase Margin
AOL
AOL
Phase
1/Beta
(Unity-Gain)fcl
V+
V-
+
VG1 353.901124n+
-
+
U2 OPA627E
VF1
Open-Loop
22
Damping Ratio vs. Phase Margin
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley
Publishing Company. Reading, Massachusetts. Third Edition, 1981.
23
Small-Signal Overshoot vs. Damping Ratio
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley
Publishing Company. Reading, Massachusetts. Third Edition, 1981.
Phase Margin Overshoot
90° 0
80° 2%
70° 5%
60° 10%
50° 16%
40° 25%
30° 37%
20° 53%
10° 73%
24
AC Peaking vs. Damping Ratio
From: Dorf, Richard C. Modern Control Systems. Addison-
Wesley Publishing Company. Reading, Massachusetts. Third
Edition, 1981.
Phase Margin AC Peaking
@Wn
90° -7dB
80° -5dB
70° -4dB
60° -1dB
50° +1dB
40° +3dB
30° +6dB
20° +9dB
10° +14dB
25
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
AOL*B
1/Beta
Rate of Closure
= 20dB/decade
fcl
Rate of ClosureRate of Closure: Rate at which 1/Beta and AOL intersect
ROC = Slope(1/Beta) – Slope(AOL)
ROC = 0dB/decade – (-20dB/decade) = 20dB/decade
26
Rate of Closure and Phase MarginRelationship between the AOL and 1/Beta rate of closure and Loop-
Gain (AOL*B) phase margin
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se (
de
gre
es)
Frequency (Hz)
100
Phase Margin
≥ 45 degrees!
Rate of Closure
= 20dB/decadeAOL
1/B
AOL*B
Phase
AOL*B
27
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
1/Beta
Rate of Closure and Phase MarginSo a pole in AOL or a zero in 1/Beta inside the loop will decrease AOL*B Phase!!
40dB/decade
40dB/decade
AOL pole
1/B zero
28
Rate of Closure and Phase Margin
AOL Pole
1/Beta Zero
Gain
(dB)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Phas
e [d
eg]
0.00
45.00
90.00
135.00
180.00
120
80
40
0
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (
degr
ees)
Frequency (Hz)
Phase Margin
≈ 0degrees!
Rate of Closure
= 40dB/decade!
Zero in 1/B
Gain
(dB)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Phas
e [d
eg]
0.00
45.00
90.00
135.00
180.00
120
80
40
0
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (
degr
ees)
Frequency (Hz)
Phase Margin
≈ 0degrees!
Rate of Closure
= 40dB/decade!
Pole in AOL
29
Testing for Rate of Closure in SPICE
V+
V-
+
VG1 0
+
-
+
U2 OPA627E
VF1
R1 1k R2 1k
V+
V-
+
-
+
U1 OPA627E
Vo
R3 1k R4 1k
L1 1T
C1 1T
+
VG2
Vfb
VinShort out the input source
Break the loop with L1 at
the inverting input
Inject an AC stimulus
through C1
• Break the feedback loop and inject a small AC signal
30
Breaking the Loop
DC AC
V-
V+
+
-
+
U1 OPA627E
Vo
Rf 1k
Rg 1k
+
VG2Vfb
Vin
L1
C1V-
V+
+
-
+
U1 OPA627E
Vo
Rf 1kRg 1k+
VG1
Vfb
VinL1
C1
31
Plotting AOL, 1/Beta, and Loop Gain
AOL = Vo/Vin
1/Beta = Vo/Vfb
AOL*B = Vfb/Vin
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 14.14k 200.00M
Ph
ase
[de
g]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (
degr
ees)
Frequency (Hz)
100
Phase Margin
= 80degrees
AOL*B
1/B
AOL*B
Phase
AOLV+
V-
+
-
+
U1 OPA627E
Vo
+
VG1 0
L1 1T
C1 1T
Vin
Rg 1k Rf 1k
Vfb
32
Noise Gain
• Understanding Noise Gain vs. Signal Gain
Signal Gain, G = -1 Signal Gain, G = 2
Both circuits have a NOISE GAIN (NG) of 2.
NG = 1 + ΙSGΙ = 2 NG = SG = 2
V+
V-
V+
V-
+
VG1
+
-
+
U1 OPA627E
Vo
R1 1k R2 1k
+
VG1
+
-
+
U1 OPA627E
Vo
R1 1k R2 1k
33
Noise Gain
• Noise Gain vs. Signal Gain
Gain of -0.1V/V, Is it Stable?
Signal Gain, G = -0.1
If it’s unity-gain stable then it’s stable as an inverting
attenuator!!!
V+
V-
+
VG1
+
-
+
U1 OPA627E
Vo
R1 10k R2 1k
V+
V-
+
VG1
+
-
+
U1 OPA627E
Vo
R1 10k R2 1k
Noise Gain, NG = 1.1
34
Capacitive Loads
35
Capacitive LoadsUnity Gain Buffer Circuits Circuits with Gain
V+
V-
+
Vin
+
-
+
U1 OPA627E
Vo
CLoad 1uF
0 150u 300u
Time (seconds)
80m
0
Vo (V)
Time (s)
0.00 150.00u 300.00u
VF1
-40.00m
-10.00m
20.00m
50.00m
80.00m
VG1
0.00
20.00m
Vin (V)
20m
-40m20m
10m
Time (s)
0.00 150.00u 300.00u
V1
0.00
20.00m
40.00m
VG1
0.00
1.00m
0 150u 300u
Time (seconds)
40m
0
Vo (V)
Vin (V)
20m
0
1m
V+
V-
+
-
+
U1 OPA627E
Vo
R2 100kR3 4.99k
+
VinCLoad 1u
36
Capacitive Loads – Unity Gain Buffers - Results
Determine the issue:
Pole in AOL!!
ROC = 40dB/decade!!
Phase Margin 0!!
NG = 1V/V = 0dB120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
Vo
lta
ge
(V
)
-40
-20
0
20
40
60
80
100
120
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Vo
lta
ge
(V
)
0.00
45.00
90.00
135.00
180.00
Phase Margin
= 0.2degrees!
Rate of Closure
= 40dB/decade!
AOL + AOL*B
1/B
AOL*B
Phase
Pole in AOL
V+
V-
+
-
+
U1 OPA627E
Vo
CLoad 1u+
Vin
L1 1T
C4 1
T
Vin
37
Capacitive Loads – Unity Gain Buffers - Theory
+
AOL
Ro 54
CLoad 1u
Loaded AOL
V+
V-
+
-
+
U1 OPA627E
Vo
CLoad 1u+
Vin
L1 1T
C4 1
T
Vin
Loaded AOL
Ro 54
CLoad 1u
L1
+
Vin
-
+
-
+
AOL 1M
C1
38
Capacitive Loads – Unity Gain Buffers - Theory
Transfer function:
W(s)=1
1+Ro
Cload
s
Ga
in (
dB
)
-80.00
-60.00
-40.00
-20.00
0.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
-90.00
-45.00
0.00
0
-20
-40
-60
-80
0
-45
-901 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
Loaded AOL
Pole
+
Vin
Ro 54
CLoad 1u
Loaded AOL
f(pole)=1
2 pi Ro CLoad s
39
Capacitive Loads – Unity Gain Buffers - Theory
X
=G
ain
(dB
)
-80.00
-60.00
-40.00
-20.00
0.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Pha
se [d
eg]
-90.00
-45.00
0.00
0
-20
-40
-60
-80
0
-45
-901 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (d
egre
es)
Frequency (Hz)
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Pha
se [d
eg]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (
degr
ees)
Frequency (Hz)
100
Volta
ge (V
)
-40
-20
0
20
40
60
80
100
120
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Volta
ge (V
)
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)Ph
ase
(deg
rees
)
Frequency (Hz)
100
AOL AOL Load
Loaded AOL
40
Stabilize Capacitive Loads –Unity Gain Buffers
41
Unity-Gain circuits can only be stabilized by modifying the AOL load
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
Stability Options
42
Method 1: Riso
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 6+
VG1
Vo
VLoad
43
Method 1: Riso - ResultsTheory: Adds a zero to the Loaded AOL response to cancel the pole
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
Phase Margin
= 87.5degrees!
Rate of Closure
= 20dB/decade
AOL + AOL*B
Pole in AOL1/B
AOL*B
Phase
Zero in AOL
V+
V-
+
-
+
U1 OPA627E CLoad 1u
L1 1T
C1 1T
Vin
Riso 5
+
VG1
Vo
Ro 54
CLoad 1u
+
VG1
-
+
-
+
AOL 1M
Riso 5
Loaded AOL
C1
Ro 54
Riso 5
Loaded AOL
CLoad 1u
+
AOL
44
Method 1: Riso - ResultsWhen to use: Works well when DC accuracy is not important, or when
loads are very light
Vo (V)
Vload (V)
Vin (V)
Time (s)
0.00 125.00u 250.00u
V1
0.00
20.37m
V2
0.00
20.00m
VG1
0.00
20.00m
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 6
+
VG1
Vo
VLoad
45
Method 1: Riso - Theory
V+
V-
+
-
+
U1 OPA627E CLoad 1u
L1 1T
C1 1T
Vin
Riso 5
+
VG1
Vo
Ro 54
CLoad 1u
+
VG1
-
+
-
+
AOL 1M
Riso 5
Loaded AOL
C1
Ro 54
Riso 5
Loaded AOL
CLoad 1u
+
AOL
46
Method 1: Riso - Theory
Zero Equation:
f(zero)=1
2 pi Riso CLoad s
Pole Equation:
f(pole)=1
2 pi (Ro+Riso) CLoad s
Transfer function:
Loaded AOL(s)=1+CLoad Riso s
1+(Ro+Riso) CLoad s
Ro 54Ohm
Riso 5Ohm
Loaded AOL
CLoad 1uF
+
Vin
Ga
in (
dB
)
-40.00
-20.00
0.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
-90.00
-45.00
0.00
0
-20
-40
0
-45
-901 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
47
Method 1: Riso - Theory
X
=
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Pha
se [d
eg]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (
degr
ees)
Frequency (Hz)
100
Gai
n (d
B)
-40.00
-20.00
0.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Pha
se [d
eg]
-90.00
-45.00
0.00
0
-20
-40
0
-45
-901 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (d
egre
es)
Frequency (Hz)
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Phas
e [d
eg]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)Ph
ase
(deg
rees
)
Frequency (Hz)
100
48
Method 1: Riso - DesignEnsure Good Phase Margin:
1.) Find: fcl and f(AOL = 20dB)
2.) Set Riso to create AOL zero:
Good: f(zero) = Fcl for PM ≈ 45 degrees.
Better: f(zero) = F(AOL = 20dB) will yield slightly less than 90 degrees phase margin
fcl = 222.74kHz
f(AOL = 20dB) = 70.41kHz
Zero Equation:
f(zero)=1
2 pi Riso CLoad s
Pole Equation:
f(pole)=1
2 pi (Ro+Riso) CLoad s
Transfer function:
Loaded AOL(s)=1+CLoad Riso s
1+(Ro+Riso) CLoad s
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
f(AOL = 20dB)
fcl
120
80
60
40
20
0
-20
-40
Ga
in (
dB
)100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
49
Method 1: Riso - DesignG
ain
(d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
F(zero) =
70.41kHz
PM = 84°
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
F(zero) =
222.74kHz
PM = 52°
f(AOL = 20dB) = 70.41kHz
→ Riso = 2.26Ohms
fcl = 222.74kHz
→ Riso = 0.715Ohms
Zero Equation:
f(zero)=1
2 pi Riso CLoad s
Pole Equation:
f(pole)=1
2 pi (Ro+Riso) CLoad s
Transfer function:
Loaded AOL(s)=1+CLoad Riso s
1+(Ro+Riso) CLoad s
2.26R
V+
V-
+
-
+
U1 OPA627E
CLoad 1u
L1 1T
C1 1T
Vin
Riso 714m
+
VG1
Vo
1uF
0.715R
V+
V-
+
-
+
U1 OPA627E
CLoad 1u
L1 1T
C1 1T
Vin
Riso 714m
+
VG1
Vo
1uF
Ensure Good Phase Margin: Test
50
Method 1: Riso - DesignG
ain
(d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM_min = 35°
F(zero) =
26.5kHzF(pole) =
2.65kHz
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM_min = 20°
F(zero) =
100.2kHz
F(pole) =
2.86kHz
Riso = Ro/9 Riso = Ro/34
Prevent Phase Dip:
Place the zero less than 1 decade from the pole, no more than 1.5 decades away
Good: 1.5 Decades: F(zero) ≤ 35*F(pole) → Riso ≥ Ro/34 → 70° Phase Shift
Better: 1 Decade: F(zero) ≤ 10*F(pole) → Riso ≥ Ro/9 → 55° Phase Shift
51
Method 1: Riso - DesignPrevent Phase Dip: Ratio of Riso to Ro
If Riso ≥ 2*Ro → F(zero) = 1.5*F(pole) → ~10° Phase Shift
**Almost completely cancels the pole.
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
Riso = Ro*2
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM_min = 80°
Riso = Ro*2 Phase Shift vs. Riso/Ro
108R
V+
V-
+
-
+
U1 OPA627E
CLoad 1u
L1 1T
C1 1T
Vin
Riso 714m
+
VG1
Vo
1uF
52
Method 1: Riso – Design Summary
6R
V+
V-
+
-
+
U1 OPA627E
CLoad 1u
L1 1T
C1 1T
Vin
Riso 714m
+
VG1
Vo
1uF
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM_min = 35°
PM = 87.5°
Final Circuit
Summary:
1.) Ensure stability by placing Fzero ≤ F(AOL=20dB)
2.) If Fzero is > 1.5 decades from F(pole) then increase Riso up to at least Ro/34
3.) If loads are very light consider increasing Riso > Ro for stability across all loads
53
Method 1: Riso - Disadvantage
6R
1uFV+
V-
+
-
+U1 OPA627E
CLoad 1u
Riso 6
+
VG1
Vo
Vload
RLoad 25
25R
+ -
Time (s)
0.00 125.00u 250.00u
Vo
lta
ge
(V
)
0.00
20.09m20.19m
0
0 125u 250u
Vo
lta
ge
(V
)
Time (seconds)
Riso Voltage Drop
Vo
VLoad
Disadvantage:
Voltage drop across Riso may not be acceptable
54
Method 2: Riso + Dual Feedback
V+
V-
+
-
+
U1 OPA627ECLoad 1u
Riso 6
+
VG1
VLoad
Rf 49k
Cf 100n
Vo
55
Method 2: Riso + Dual FeedbackTheory: Features a low-frequency feedback to cancel the Riso drop
and a high-frequency feedback to create the AOL pole and zero.
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
Phase Margin
= 87.5degrees!
Rate of Closure
= 20dB/decade
AOL + AOL*B
Pole in AOL1/B
AOL*B
Phase
Zero in AOL
V+
V-
+
-
+
U1 OPA627ECLoad 1u
+
VG1
Rf 49k
Cf 100n
VoL1 1T
C1 1T
Vfb
Vin
Riso 6
56
Method 2: Riso + Dual FeedbackWhen to Use: Only practical solution for very large capacitive loads ≥
10uF
When DC accuracy must be preserved across different
current loads
Time (s)
0.00 150.00u 300.00u
V1
0.00
20.27m
V2
0.00
20.00m
VG1
0.00
20.00m
0 150u 300u
Time (seconds)
20.3m
0
VLoad(V)
020m
20m
0
Vo(V)
Vin(V)
V+
V-
+
-
+
U1 OPA627ECLoad 1u
Riso 5
+
VG1
Vload
R2 49k
C1 100n
Vo
57
Method 2: Riso + Dual Feedback - DesignEnsure Good Phase Margin:
1.) Find: fcl and f(AOL = 20dB)
2.) Set Riso to create AOL zero:
Good: f(zero) = Fcl for PM ≈ 45 degrees.
Better: f(zero) = F(AOL = 20dB) will yield slightly less than 90 degrees phase margin
3.) Set Rf so Rf >>Riso
Rf ≥ (Riso * 100)
4.) Set Cf ≥ (200*Riso*Cload)/Rf
fcl = 222.74kHz
f(AOL = 20dB) = 70.41kHz
Zero Equation:
f(zero)=1
2 pi Riso CLoad s
Pole Equation:
f(pole)=1
2 pi (Ro+Riso) CLoad s
Transfer function:
Loaded AOL(s)=1+CLoad Riso s
1+(Ro+Riso) CLoad s
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
f(AOL = 20dB)
fcl
120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
58
Method 2: Riso + Dual Feedback - SummaryEnsure Good Phase Margin (Same as “Riso” Method):
1.) Set Riso so f(zero) = F(AOL = 20dB)
2.) Set Rf: Rf ≥ (Riso * 100)
3.) Set Cf: Cf ≥ (200*Riso*Cload)/Rf
V+
V-
+
-
+
U1 OPA627ECLoad 1u
Riso 5
+
VG1
Vload
R2 49k
C1 100n
Vo
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
Phase Margin
= 87.5degrees!
59
Capacitive Loads – Circuits with Gain
60
Capacitive Loads – Circuits with Gain
V+
V-
+
-
+
U1 OPA627E
Vo
Rf 100kRg 4.99k
+
VG1 0CLoad 100n
0 150u 300u
Time (seconds)
40m
0
Vol
tage
(V
)
30m
20m
10m
Time (s)
0.00 150.00u 300.00u
Vol
tage
(V)
0.00
10.00m
20.00m
30.00m
40.00m
61
Capacitive Loads – Circuits With Gain - Results
Same Issues as Unity Gain Circuit
Pole in AOL!!
ROC = 40dB/decade!!
Phase Margin = 10°!!
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 10.5°
AOL
1/B
AOL*B
Phase
Pole in AOL
AOL*B
ROC =
40dB/decade
V+
V-
+
-
+
U1 OPA627E
Vo
Rg 100kRf 4.99k
CLoad 100n
+
VG1
L1 1T
C1 1T
Vin
Vfb
62
Stabilize Capacitive Loads –Circuits with Gain
63
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
1/Beta
Stability Options – Circuits with GainCircuits with gain can be stabilized by modifying the AOL load and by
modifying 1/Beta
64
Method 1 + Method 2
Method 1: Riso
Method 2: Riso+Dual Feedback
Methods 1 and 2 work on circuits with gain as well!
V+
V-
+
-
+U1 OPA627E
Rf 100kRg 4.99k
+
VG1CLoad 100n
Riso 10
VLoad
Vo
0 150u 300u
Time (seconds)
25m
0
VLoad(V)
0
25m
1m
0
Time (s)
0.00 150.00u 300.00u
V1
0.00
12.50m
25.00m
V2
0.00
12.50m
25.00m
VG1
0.00
1.00m
Vo(V)
Vin(V)
V+
V-
+
-
+
U1 OPA627ECLoad 100n
Riso 10
VLoad
Rf 100k
Cf 100p
Vo
Rg 4.99k
+
VG1
Time (s)
0.00 150.00u 300.00u
V1
0.00
10.00m
20.00m
V2
0.00
10.00m
20.00m
VG1
0.00
1.00m
0 150u 300u
Time (seconds)
25m
0
VLoad(V)
0
25m
1m
0
Vo(V)
Vin(V)
65
Method 3: Cf
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
C1 27p
+
VG1
66
Method 3: Cf - ResultsTheory: 1/Beta compensation. Cf feedback capacitor causes 1/Beta to
decrease at -20dB/decade and if placed correctly will cause the ROC to be
20dB/decade.
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 68°
AOL
1/B
AOL*B
Phase
AOL*B
ROC =
20dB/decade
1/B Pole
1/B Zero
AOL Pole
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cf 27p
+
VG2
L1 1T
C1 1T
Vin
Vfb
67
Method 3: Cf - ResultsWhen to use: Especially effective when NG is high, ≥ 30dB.
Systems where a bandwidth limitation is not an issue
- Limits closed-loop bandwidth at 1/(2*pi*Rf*Cf)
Time (s)
0.00 150.00u 300.00u
Vo
lta
ge
(V
)
0.00
5.00m
10.00m
15.00m
20.00m
25.00m
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
C1 27p
+
VG1
68
Method 3: Cf - DesignEnsure Good Phase Margin:
For 20dB/decade ROC, 1/Beta must intersect AOL while its slope is -20dB/decade.
Therefore: f(1/B pole) < f(cl_unmodified)
f(1/B zero) > f(AOL = 0dB)
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(cl_unmodified)
f(AOL = 0dB)
f(cl_unmodified) = 152.13kHz
f(AOL = 0dB) = 704.06kHz
1/B Pole Equation:
f(1/B pole)=1
2 pi Rf Cf
1/B Zero Equation:
f(1/B zero)=1
2 pi (Rg Rf) Cf
69Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(cl_unmodified)
f(AOL = 0dB)
Method 3: Cf - DesignEnsure Good Phase Margin:
1.) Find f(AOL=0dB)
2.) Set f(1/B zero) by choosing Cf:
Good: Set f(1/B zero) = f(AOL = 0dB) for PM ≈ 45 degrees.
Better: Set f(1/B zero) so AOL @ f(cl) = ½ Low-Frequency NG in dB
f(cl) @
f(AOL = ½ DC NG)
f(AOL = 0dB) = 704.06kHz
1/B Zero Equation:
f(1/B zero)=1
2 pi (Rg Rf) Cf
70
Method 3: Cf – Design - SummarySummary:
1.) Ensure stability by placing:
a) f(1/B zero) ≥ f(AOL = 0dB
b) f(1/B pole) ≤ f(cl_unmodified)
2.) Try to adjust the zero location so the 1/B curve crosses the AOL curve in the middle of the
1/B span allowing for shifts in AOL
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
C1 27p
+
VG1
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 68°
Final Circuit
71
Method 4: Noise-Gain
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
72
Method 4: Noise Gain - ResultsTheory: 1/Beta compensation. Raise high-frequency 1/Beta so the
ROC occurs before the AOL pole causes the AOL slope to change
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 56°
AOL
1/B
AOL*B
Phase
AOL*B
ROC =
20dB/decade
1/B Pole1/B ZeroAOL Pole
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.9k
+
VG1
L1 1T
C4 1T
Vin
Vfb
Cn 820n Rn 75
73
Method 4: Noise Gain - ResultsWhen to use: Better for lighter capacitive loading
When AOL @ f(AOL pole) < (Closed loop gain + 20dB)
Due to the increase in noise gain, this approach may not be practical
when required noise gain is greater than the low-frequency signal
gain by more than ~25-30dB.
Time (s)
0.00 150.00u 300.00u
Vo
lta
ge
(V
)
0.00
5.00m
10.00m
15.00m
20.00m
25.00m
0 150u 300u
Time (seconds)
0
25m
10m
20m
15m
5m
Vo
lta
ge
(V
)
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
74
Method 4: Noise Gain - DesignEnsure Good Phase Margin:
For 20dB/decade ROC, 1/Beta must intersect AOL above the AOL pole.
Therefore: |High-Freq NG| > |AOL| @ f(AOL pole)
f(1/B zero) < f(AOL = High-Freq NG)
1/B Zero Equation:
f(1/B zero)=1
2 pi Rn Cn
1/B Pole Equation:
f(1/B pole)=1
2 pi (Rn+(Rg Rf) Cf
High-Freq Noise-Gain Equation:
HF NG = Rf
(Rg Rn)
|AOL| @ f(AOL pole) = 52.11dB
f(AOL pole) = 29.49kHz
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
ltag
e (
V)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(AOL pole)
|AOL| @
f(AOL pole)
75
Method 4: Noise Gain - DesignEnsure Good Phase Margin:
1.) Find f(AOL pole) and |AOL| @ f(AOL pole)
2.) Set High-Freq Noise-Gain by choosing Rn:
Good: |HF NG| ≥ |AOL| @ f(AOL pole)
Better: |HF NG| ≥ |AOL| @ f(AOL pole) + 10dB
High-Freq Noise-Gain Equation:
HF NG = Rf
(Rg Rn)
|AOL| @ f(AOL pole) = 52.11dB
f(AOL pole) = 29.49kHz
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
ltag
e (
V)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(AOL pole)
|AOL| @
f(AOL pole)
76
Method 4: Noise Gain - DesignEnsure Good Phase Margin:
3.) Find f(cl_modified) = f(AOL @ |HF NG|)
4.) Set f(1/B zero) by choosing Cn:
Good: f(1/B zero) ≤ f(cl_modified)
Better: f(1/B zero) ≤ f(cl_modified) / 3.5 (~ ½ decade)
High-Freq Noise-Gain Equation:
HF NG = Rf
(Rg Rn)
f(cl_modified) = 29.49kHz
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
ltag
e (
V)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(AOL pole)
|AOL| @
f(AOL pole)
f(cl_modified)
77
Method 4: Noise Gain - SummarySummary:
1.) Ensure stability by setting:
a) |HF NG| ≥ (|AOL| @ f(AOL pole) + 10dB)
b) f(1/B zero) ≤ f(cl_modified) / 3.5
Final Circuit
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 56°
78
Method 4: Noise GainQuick reminder that inverting and non-inverting noise gain circuits are different!
Time (s)
0.00 150.00u 300.00u
Volta
ge (V
)
0.00
5.00m
10.00m
15.00m
20.00m
25.00m
0 150u 300u
Time (seconds)
0
25m
10m
20m
15m
5m
Volta
ge (V
)
0 150u 300u
Time (seconds)
-24m
1m
-14m
-4m
-9m
-19m
Volta
ge (V
)
Time (s)
0.00 150.00u 300.00u
Volta
ge (V
)
-24.00m
-19.00m
-14.00m
-9.00m
-4.00m
1.00m
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
V-
V+
+
-
+
U1 OPA627ECLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
Rn 75
+
VG1
79
Circuits with High Feedback Network Impedance
80
Circuits with High Feedback Network Impedance
0 150u 300u
Time (seconds)
1
0
Vo (V)
Vin (V)
0
-1
10m
Time (s)
0.00 150.00u 300.00u
Vout (V)
-1.00
0.00
1.00
VG1
0.00
10.00m
V-
V+
+
-
+
U1 OPA627E
Vo
Rf 499kRg 499k
+Vin
Cstray 20p
81
Circuits with High Feedback Network Impedance
Determine the issue:
Zero in 1/Beta!!
ROC = 40dB/decade!!
Phase Margin 2!!
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 2°
AOL
1/B
AOL*B
Phase
AOL*B
ROC =
40dB/decade!
1/B Zero
V-
V+
+
-
+
U1 OPA627E
Vo
Rf 499kRg 499k
+
VG1
L1 1T
C1 1T
Vin
Vfb
Cin 27p
82
Circuits with High Feedback Network Impedance - Theory
V-
V+
+
-
+
U1 OPA627E
Vo
Rf 499kRg 499k
+
VG1
L1 1T
C1 1T
Vin
Vfb
Cin 27p
Loaded AOL
Ro 54
+
VG1
-
+
-
+
AOL 1M
Rf 499k
Rg 499k Cin 27p
Beta
C1
Loaded AOL
Ro 54
Rf 499k
Rg 499k Cin 27p
Beta
+
AOL
83
Beta Pole & 1/Beta Zero Equation:
f(B pole)=f(1/B zero)=1
2 pi (Rg Rf) Cin
Circuits with High Feedback Network Impedance - Theory
Ga
in (
dB
)-80.00
-60.00
-40.00
-20.00
0.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
-90.00
-45.00
0.00
0
-20
-40
-60
-80
0
-45
-901 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
Pole in Beta =
Zero in 1/Beta
AOL
UnaffectedBeta
AOL
Load
Ro 54
Rf 499k
Rg 499k Cin 27p
+
VG1 Beta
AOL Load
84
Stabilize Circuits With High Feedback Network Impedance
85
Stability Options – Zero in 1/BetaThe only practical option is to add a pole to cancel the 1/Beta Zero
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Gai
n (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
86
Method 1: Cf
V-
V+
+
-
+
U1 OPA627E
Rf 499kRg 499k
+
VG1
Cstray 20p
Cf 21p
Vo
87
Method 1: Cf - ResultsTheory: 1/Beta compensation. Cf feedback places a pole in 1/Beta to
cancel the zero from the input capacitance.
V-
V+
+
-
+
U1 OPA627E
Vo
Rf 499kRg 499k
Cf 21p
+
VG1
L1 1T
C1 1T
Vin
Vfb
Cin 27p
Vo
lta
ge
(V
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Vo
lta
ge
(V
)
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 81°
AOL
1/B
AOL*B
Phase
AOL*BROC =
20dB/decade!
1/B Zero 1/B Pole
88
Method 1: Cf - Results
Time (s)
0.00 150.00u 300.00u
V1
0.00
12.50m
25.00m
VG1
0.00
10.00m
0 150u 300u
Time (seconds)
25m
0
Vo (V)
Vin (V)
0
10m
When to use: Almost always a safe design practice.
Limits gain at 1/(2*pi*Rf*Cf)
V-
V+
+
-
+
U1 OPA627E
Rf 499kRg 499k
+
VG1
Cstray 20p
Cf 21p
Vo
89
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ga
in (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(cl)
Method 1: Cf - DesignEnsure Good Phase Margin:
For 20dB/decade ROC, the 1/Beta pole must flatten the 1/Beta Zero before f(cl)
Therefore f(1/Beta pole) ≤ f(cl)
f(cl) = 445.6kHz
1/B Pole Equation:
f(1/B pole)=1
2 pi Rf Cf
1/B Zero Equation:
f(1/B zero)=1
2 pi (Rg Rf) Cin
90Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ga
in (d
B)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00120
80
60
40
20
0
-20
-40
Ga
in (
dB
)100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
f(cl)
Method 1: Cf - DesignEnsure Good Phase Margin:
1.) Find f(cl)
2.) Set f(1/B pole) by setting Cf:
Good: f(1/B pole) ≤ f(cl)
Better: f(1/B pole) ≤ f(cl)/ 3.5 (~ ½ decade)
1/B Pole Equation:
f(1/B pole)=1
2 pi Rf Cf
1/B Zero Equation:
f(1/B zero)=1
2 pi (Rg Rf) Cin
91
Method 1: Cf - SummarySummary:
1.) Ensure stability by setting f(1/B pole) ≤ f(cl)/ 3.5 (~ ½ decade)
V-
V+
+
-
+
U1 OPA627E
Rf 499kRg 499k
+
VG1
Cstray 20p
Cf 21p
Vo
Vo
lta
ge
(V
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Vo
lta
ge
(V
)
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = 81°
92
Ro vs. Zo
93
When Ro is really Zo!!
V+
V-
+
-
+
U1 OPA627E
VoVos 80.0432u
IG1V+
V-
-
++
4
3
5
1
2
U1 OPA2376
Vo
Vos -25.3845uV
IG1
94
With Complex Zo, Accurate Models are Key!
Ga
in (
dB
)
-60.00
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ph
ase
[d
eg
]
-90.00
-45.00
0.00
45.00
90.00
135.00
180.00
120
80
60
40
20
0
-20
140
180
135
90
-901 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
ha
se
(d
eg
ree
s)
Frequency (Hz)
100
PM = -77°!!
1/B
AOL +
AOL*B
ROC =
60dB/decade!
AOL*B
Phase
-40
-60
45
0
-45
V+
V-
-
++
4
3
5
1
2
U1 OPA2376
Vo
CLoad 1uF+
Vin
Time (s)
0.00 150.00u 300.00u
V1
-40.00m
10.00m
60.00m
VG1
0.00
20.00m
0 150u 300u
Time (seconds)
60m
0
Vo (V)
Vin (V)
-40m
20m
95
With Complex Zo, Accurate Models are Key!
V+
V-
-
++
4
3
5
1
2
U1 OPA2376
Vo
Vos -25.3845uV
IG1
1 10 100 1k 10k 100k 1M 10M 100M
Frequency (Hz)
100m
1k
10
1
10k
100
Imp
ed
an
ce
(O
hm
s)
Frequency (Hz)
100.00m 1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ga
in (
dB
)
1.00
10.00
100.00
1.00k
10.00k
96
Questions/Comments?
Thank you!!Special Thanks to:
Art Kay
Bruce Trump
Marek Lis
Tim Green
PA Apps Team