operational amplifier stability collin wells texas instruments hpa linear applications 2/22/2012
TRANSCRIPT
Operational Amplifier Stability
Collin Wells
Texas Instruments
HPA Linear Applications
2/22/2012
The Culprits!!!Capacitive 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 5Vin
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
Just Plain Trouble!!Inverting Input Filter??
Output Filter??
-
+
OPA
VoutV1 5R1 10k
R2 49kC1 10u C5 100n
-
+
OPA
Rf 100kRg 10k
Cin 1u
Vout
+
Vin
Oscillator
OscillatorT
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
T
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
Recognize Amplifier Stability Issues on the Bench
• Required Tools:– Oscilloscope
– Step Generator
• Other Useful Tools:– Gain / Phase Analyzer
– Network / Spectrum Analyzer
Recognize Amplifier Stability Issues• Oscilloscope - Transient Domain Analysis:
– Oscillations or Ringing
– Overshoots
– Unstable DC Voltages
– High Distortion
T
Time (s)
1.75m 2.25m 2.75m
Vo
ltag
e (
V)
0.00
18.53m
T
Time (s)
1.75m 50.88m 100.00m
Ou
tpu
t
-14.83
0.00
15.00T
Time (s)
1.75m 2.25m 2.75m
Vo
ltag
e (
V)
0.00
21.88m
Recognize Amplifier Stability Issues• Gain / Phase Analyzer - Frequency Domain: Peaking, Unexpected
Gains, Rapid Phase Shifts
T
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
[de
g]
-360.00
-180.00
0.00
What causes amplifier stability issues???
T
Time (s)
1.95m 2.08m 2.20m
Vo
-15.00
0.00
15.00
Vfb
-2.25
0.00
2.25
VG1
0.00
10.00m
ab
Cause of Amplifier Stability Issues• Too much delay in the feedback network
-
+BUF
BUF BUF
R1 100kR2 100k+ VG1
Vfb
Vo
DELAY
DELAY
T
Time (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
Cause of Amplifier Stability Issues• Real circuit translation of too much delay in the feedback network
-
+BUF
BUF BUF
R1 100kR2 100k
+
VG1
Vfb
VoRo 10
Cin 4pCstray 16p
Cload 10u
Cause of Amplifier Stability Issues• Same results as the example circuit
-
+BUF
BUF BUF
R1 100kR2 100k
+
VG1
Vfb
VoRo 10
Cin 4pCstray 16p
Cload 10u
T
Time (s)
1.95m 2.23m 2.50m
VG1
0.00
10.00m
Vfb
-37.08m
62.12m
Vo
-1.00
1.16
How do we determine if our system has too
much delay??
Phase Margin• Phase Margin is a measure of the “delay” in the loop
T
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
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (d
egre
es)
Frequency (Hz)
100
Phase Margin
AOL
AOLPhase
Unity-Gain
V+
V-
+
VG1 353.901124n+
-
+
U2 OPA627E
VF1
Open-Loop
Damping Ratio vs. Phase Margin
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley Publishing Company. Reading, Massachusetts. Third Edition, 1981.
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%
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
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
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
Gai
n (d
B)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
AOL*B
1/Beta
Rate of Closure= 20dB/decade
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
Rate of Closure and Phase MarginRelationship between the AOL and 1/Beta rate of closure and Loop-Gain (AOL*B) phase margin
T
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
a120
80
60
40
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (d
egre
es)
Frequency (Hz)
100
Phase Margin≥ 45 degrees!
Rate of Closure= 20dB/decade
AOL
1/B
AOL*BPhase
AOL*B
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
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
Gai
n (d
B)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
1/Beta
Understanding Amplifier Stability IssuesSo 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
Understanding Amplifier Stability Issues
AOL Pole
1/Beta Zero
Noise Gain• Understanding Noise Gain vs. Signal Gain
Inverting Gain, G = -1 Non-Inverting Gain, G = 2
Both circuits have a NOISE GAIN (NG) of 2.
NG = 1 + ΙGΙ = 2 NG = G = 2
V+
V-
V+
V-
+
VG1
+
-
+
U1 OPA627E
Vo
R1 1k R2 1k
+
VG1
+
-
+
U1 OPA627E
Vo
R1 1k R2 1k
Noise Gain• Noise Gain vs. Signal Gain
Gain of -0.1V/V, Is it Stable?
Inverting 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
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
Breaking the Loop
DC AC
V-
V+
+
-
+U1 OPA627E
Vo
Rf 1k
Rg 1k
+
VG2 Vfb
Vin
L1
C1V-
V+
+
-
+U1 OPA627E
Vo
Rf 1kRg 1k+
VG1
Vfb
VinL1
C1
Plotting AOL, 1/Beta, and Loop GainAOL = Vo/Vin
1/Beta = Vo/Vfb
AOL*B = Vfb/Vin
T
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
[d
eg
]
0.00
45.00
90.00
135.00
180.00
120
80
60
40
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (d
B)
Pha
se (d
egre
es)
Frequency (Hz)
100
Phase Margin= 82degrees
AOL*B
1/B
AOL*BPhase
AOLV+
V-
+
-
+
U1 OPA627E
Vo
+
VG1 0
L1 1T
C1 1T
Vin
Rg 1k Rf 1k
Vfb
Capacitive Loads
Capacitive LoadsUnity Gain Buffer Circuits Circuits with Gain
V+
V-
+
-
+
U1 OPA627E
VF1
R2 100kR3 249
+
VG1 0 CLoad 1uV+
V-
+
Vin
+
-
+
U1 OPA627E
Vo
CLoad 1uF
0 150u 300uTime (seconds)
80m
0
Vo (V)
T
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
T
Time (s)
0.00 150.00u 300.00u
V1
0.00
20.00m
40.00m
VG1
0.00
1.00m
0 150u 300uTime (seconds)
40m
0
Vo (V)
Vin (V)
20m
01m
Capacitive Loads – Unity Gain Buffers - ResultsDetermine the issue:
Pole in AOL!!
ROC = 40dB/decade!!
Phase Margin 0!!
NG = 1V/V = 0dB
V+
V-
+
-
+
U1 OPA627E
Vo
CLoad 1u+
VG1 0
L1 1T
C1
1T
Vin
120
80
60
40
200
-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
T
Vo
ltag
e (
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
ltag
e (
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*BPhase
Pole in AOL
Capacitive Loads – Unity Gain Buffers - Theory
V+
V-
+
-
+
U1 OPA627E
Vo
CLoad 1u+
VG1
L1 1T
C4
1T
Vin
Loaded AOLRo 54
CLoad 1u
L1
+
VG1
-
+
-
+
AOL 1M
C1
+
AOL
Ro 54
CLoad 1u
Loaded AOL
Capacitive Loads – Unity Gain Buffers - Theory
Transfer function:
W(s)=1
1+RoCload
s
T
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
[de
g]
-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 (
degr
ees)
Frequency (Hz)
Loaded AOLPole
CLoadRoFPOLE
2
1
+
Vin
Ro 54
CLoad 1u
Loaded AOL
Capacitive Loads – Unity Gain Buffers - Theory
X
=
T
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
Gai
n (d
B)Ph
ase
(deg
rees
)
Frequency (Hz)
T
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
200
-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
T
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
120
80
60
40
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gain
(dB)
Phas
e (de
gree
s)
Frequency (Hz)
100
AOL AOL Load
Loaded AOL
Stabilize Capacitive Loads – Unity Gain Buffers
Unity-Gain circuits can only be stabilized by modifying the AOL load
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
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
Gai
n (d
B)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
Stability Options
Method 1: Riso
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 6+
VG1
Vo
VLoad
Method 1: Riso - ResultsTheory: Adds a zero to the Loaded AOL response to cancel the pole
T
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
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (
dB)
Pha
se (
degr
ees)
Frequency (Hz)
100
Phase Margin = 87.5degrees!
Rate of Closure = 20dB/decade
AOL + AOL*B
Pole in AOL1/B
AOL*BPhase
Zero in AOL
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 6
+
VG1
Vo
VLoad
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)
T
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
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
Method 1: Riso - Theory
Zero Equation:
f(zero)=1
2piRisoCLoad
s
Pole Equation:
f(pole)=1
2pi(Ro+Riso)CLoad
s
Transfer function:
Loaded AOL(s)=1+CLoad
Risos
1+(Ro+Riso)CLoad
s
Ro 54Ohm
Riso 5Ohm
Loaded AOL
CLoad 1uF
+
Vin
T
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
[de
g]
-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 (
degr
ees)
Frequency (Hz)
Method 1: Riso - Theory
X
=
T
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
200
-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)
100T
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
Gai
n (d
B)Ph
ase
(deg
rees
)
Frequency (Hz)
T
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
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gain
(dB)
Phas
e (d
egre
es)
Frequency (Hz)
100
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
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ga
in (
dB
)
-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
Gai
n (
dB)100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
Method 1: Riso - Design
T
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
200
-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
F(zero) = 70.41kHz
PM = 84°
T
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
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Gai
n (
dB)
Pha
se (
degr
ees)
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
2piRisoCLoad
s
Pole Equation:
f(pole)=1
2pi(Ro+Riso)CLoad
s
Transfer function:
Loaded AOL(s)=1+CLoad
Risos
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
Method 1: Riso - Design
T
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
200
-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
PM_min = 35°
F(zero) = 26.5kHzF(pole) =
2.65kHz
T
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
200
-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
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
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.
Riso = Ro*2 Phase Shift vs. Riso/Ro
Method 1: Riso – Design Summary
6R
V+
V-
+
-
+
U1 OPA627E
CLoad 1u
L1 1T
C1 1T
Vin
Riso 714m
+
VG1
Vo
1uF
T
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
200
-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
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/343.) If loads are very light consider increasing Riso > Ro for stability across all loads
Method 1: Riso - Disadvantage
6R
1uFV+
V-
+
-
+U1 OPA627E
CLoad 1u
Riso 6
+
VG1
Vo
Vload
RLoad 25
25R
+ -
T
Time (s)
0.00 125.00u 250.00u
Vol
tage
(V)
0.00
20.09m20.19m
0
0 125u 250u
Vo
ltag
e (
V)
Time (seconds)
Riso Voltage Drop
Vo
VLoad
Disadvantage:
Voltage drop across Riso may not be acceptable
Method 2: Riso + Dual Feedback
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 6
+
VG1
VLoad
Rf 49k
Cf 100n
Vo
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.
T
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
200
-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 = 87.5degrees!
Rate of Closure = 20dB/decade
AOL + AOL*B
Pole in AOL1/B
AOL*BPhase
Zero in AOL
V+
V-
+
-
+
U1 OPA627E CLoad 1u
+
VG1
Rf 49k
Cf 100n
VoL1 1T
C1 1T
Vfb
Vin
Riso 6
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
T
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 300uTime (seconds)
20.3m
0
VLoad(V)
020m
20m0
Vo(V)
Vin(V)
V+
V-
+
-
+
U1 OPA627E CLoad 1u
Riso 5
+
VG1
Vload
R2 49k
C1 100n
Vo
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 margin3.) Set Rf so Rf >>Riso Rf ≥ (Riso * 1004.) Set Cf ≥ (200*Riso*Cload)/Rf
fcl = 222.74kHz
f(AOL = 20dB) = 70.41kHz
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
Ga
in (
dB
)
-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
Gai
n (d
B)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
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 OPA627E CLoad 1u
Riso 5
+
VG1
Vload
R2 49k
C1 100n
Vo
T
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
200
-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 = 87.5degrees!
Capacitive Loads – Circuits with Gain
Capacitive Loads – Circuits with Gain
V+
V-
+
-
+
U1 OPA627E
Vo
Rf 100kRg 4.99k
+
VG1 0 CLoad 100n
0 150u 300uTime (seconds)
40m
0
Vol
tage
(V
)
30m
20m
10m
T
Time (s)
0.00 150.00u 300.00u
Vo
ltag
e (
V)
0.00
10.00m
20.00m
30.00m
40.00m
Capacitive Loads – Circuits With Gain - ResultsSame Issues as Unity Gain Circuit
Pole in AOL!!
ROC = 40dB/decade!!
Phase Margin = 10°!!T
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
200
-20
-40
180
135
90
45
01 10 100 1k 10k 100k 1M 10M 100M
Ga
in (
dB
)P
has
e (
deg
rees
)
Frequency (Hz)
100
PM = 10.5°
AOL
1/B
AOL*BPhase
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
Stabilize Capacitive Loads – Circuits with Gain
T
Frequency (Hz)
1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M
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
Gai
n (d
B)
100
1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)
AOL
1/Beta
Stability OptionsCircuits with gain can be stabilized by modifying the AOL load and by modifying 1/Beta
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 10VLoad
Vo
0 150u 300uTime (seconds)
25m
0
VLoad(V)
025m
1m
0
T
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 OPA627E CLoad 100n
Riso 10VLoad
Rf 100k
Cf 100p
Vo
Rg 4.99k
+
VG1
T
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 300uTime (seconds)
25m
0
VLoad(V)
025m
1m
0
Vo(V)
Vin(V)
Method 3: Cf
V-
V+
+
-
+U1 OPA627E CLoad 100n
Vo
Rf 100kRg 4.99k
C1 27p
+
VG1
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.
T
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
200
-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
PM = 68°
AOL
1/B
AOL*BPhase
AOL*B
ROC = 20dB/decade
1/B Pole
1/B Zero
AOL Pole
V-
V+
+
-
+U1 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cf 27p
+
VG2
L1 1T
C1 1T
Vin
Vfb
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)
V-
V+
+
-
+U1 OPA627E CLoad 100n
Vo
Rf 100kRg 4.99k
C1 30p
+
VG1
T
Time (s)
0.00 150.00u 300.00u
Vo
ltag
e (
V)
0.00
5.00m
10.00m
15.00m
20.00m
25.00m
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)T
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
2piRfCf
1/B Zero Equation:
f(1/B zero)=1
2pi(Rg Rf)Cf
T
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)
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
2pi(Rg Rf)Cf
Method 3: Cf – Design - SummarySummary:
1.) Ensure stability by placing:a) f(1/B zero) ≥ f(AOL = 0dBb) 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 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
C1 27p
+
VG1
T
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
200
-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
PM = 68°
Final Circuit
Method 4: Noise-Gain
V-
V+
+
-
+U1 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
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
T
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
200
-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*BPhase
AOL*B
ROC = 20dB/decade
1/B Pole1/B ZeroAOL Pole
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.
T
Time (s)
0.00 150.00u 300.00u
Vo
ltag
e (
V)
0.00
5.00m
10.00m
15.00m
20.00m
25.00m
0 150u 300uTime (seconds)
0
25m
10m
20m
15m
5m
Vo
ltag
e (
V)
V-
V+
+
-
+U1 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
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
2piRnCn
1/B Pole Equation:
f(1/B pole)=1
2pi(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
T
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
lta
ge
(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)
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
T
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
lta
ge
(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)
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
T
Frequency (Hz)
1.00 10.91 118.92 1.30k 14.14k 154.22k 1.68M 18.34M 200.00M
Vo
lta
ge
(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)
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 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
T
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
200
-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
PM = 56°
Method 4: Noise GainQuick reminder that inverting and non-inverting noise gain circuits are different!
T
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 300uTime (seconds)
0
25m
10m
20m
15m
5m
Volta
ge (V
)
0 150u 300uTime (seconds)
-24m
1m
-14m
-4m
-9m
-19m
Volta
ge (V
)T
Time (s)
0.00 150.00u 300.00u
Vo
lta
ge
(V
)
-24.00m
-19.00m
-14.00m
-9.00m
-4.00m
1.00m
V-
V+
+
-
+U1 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
+
VG1
Rn 75
V-
V+
+
-
+U1 OPA627E
CLoad 100n
Vo
Rf 100kRg 4.99k
Cn 820n
Rn 75
+
VG1
Circuits with High Feedback Resistance
Circuits with High Feedback Resistance
V-
V+
+
-
+U1 OPA627E
Vout
R1 499k
R2 100k
R6 499k
+
VinCstray 20p
T
Time (s)
0.00 150.00u 300.00u
VG2
0.00
20.00m
Vo
-13.01
13.01
Circuits with High Feedback ResistanceDetermine the Problem
Zero in 1/Beta
AOL unaffected
Phase Margin 0!!
T
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
V-
V+
+
-
+U1 OPA627E
Vo
R3 499k
R4 100k
R5 499k
+
VG2
L1 1T
C4
1T
Vin
Vfb
C5 25p
Circuits with High Feedback Resistance
V-
V+
+
-
+U1 OPA627E
Vo
R3 499k
R4 100k
R5 499k
+
VG2
L1 1T
C4
1TVin
Vfb
C5 25p
Ro 50
Rf 499k
Rg 499k Cin 27p
+
VG1 Beta
Loaded_AOL
R1 50
+
VG2
-
+
-
+
AOL 1MLoaded AOL
R3 499k
R4 499k C2 27p
Beta
C1
Circuits with High Feedback Resistance
Ro 50
Rf 499k
Rg 499k Cin 27p
+
VG1
Loaded_AOL
Beta
Beta Transfer function:
W(s)=Rg
Ro+Rf+Rg+(Ro+Rf)CinRg
s
Pole in Beta is Zero in 1/Beta
F(Pole) = 1/(2*pi*Cin*(Rf||Rg))
T
Beta
Loaded_AOL
Gai
n (d
B)
-78.55
-39.28
0.00
Frequency (Hz)
1.00 10.00k 100.00M
Pha
se [d
eg]
-89.99
-44.99
0.00
Beta
Loaded_AOL
Stabilize Circuits With High Feedback Resistance
Method 1: CfMethod 1 – 1/Beta Compensation, “Cf”
Theory: Cf feedback places a pole in 1/Beta to cancel the zero from the input capacitance.
When to use: Almost always a safe design practice. Limits gain at 1/(2*pi*Rf*Cf)
T
Time (s)
0.00 125.00u 250.00u
VG1
0.00
100.00u
Vload
-19.60m
0.00
V-
V+
+
-
+U1 OPA627E
Vo
R3 499k
R4 100k
R5 499k
+
VG2
C5 20p
C1 34p
Method 1: CfMethod 1 – 1/Beta Compensation, “Cf”
1/Beta Pole at 1/(2*pi*Rf*Cf)
V-
V+
+
-
+U1 OPA627E
Vo
R3 499k
R4 100k
R5 499k
+
VG2
C5 20p
C1 34p
T
Volta
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
Volta
ge (V
)
0.00
45.00
90.00
135.00
180.00
Questions/Comments?
Thank you!!Special Thanks to:Art Kay
Bruce Trump
Tim Green
PA Apps Team