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Solving Op Amp Stability IssuesPart 1
(For Voltage Feedback Op Amps)
Tim Green & Collin Wells
Precision Analog Linear Applications1
2
OverviewMain Presentation Focus:1) Op Amp Stability Basics2) Stability Analysis – Method 1 : Loaded Aol & 1/b Technique
A) Riso Compensation Technique for Output Capacitive Loads3) Stability Analysis – Method 2 : Aol & 1/b Technique
A) CF Compensation Technique for Input Capacitance 4) Stability Tricks and Rules of Thumb
Appendix:5) Additional Useful Tools for your Analog Stability Toolbox
A) Op Amp Output ImpedanceB) Pole and Zero: Magnitude and Phase on Bode PlotsC) Dual Feedback Paths and 1/bD) Non-Loop Stability Problems
2) Nine different ways to stabilize op amps with capacitive loadsA) Definition by example using TINA-TI simulations
The CulpritsOutput Capacitive Loads!
Input Capacitance and Large Value Resistors
Transimpedance Amplifiers!
Reference Buffers! Cable/Shield Drive! MOSFET Gate Drive!
Large Value Resistors 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
Transient Suppression!
V+
-
+
OPA
Rf 49kRg 4.99M
Cd 200p Vout
+Vin
D1
D2TVS
3
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
4
Vcc
Vcc
VOUT
+
-
+3
4
52
1
U1 OPA333
Vcc 5V
R2 49kOhm
R1 49kOhm
C1
VIN
CLoad 1uF
100nF
+2.5V
+2.5V
T
Time (s)
0 500u 1m 2m 2m
VOUT
1.5
2.0
2.5
3.0
But it worked fine
in the lab!Transient on:+Input or –InputVcc or VeeOutput
5
Check ALL Op Amp Circuits for Stability regardless of their closed loop signal frequency of operation!
But I’m only using it at DC!
Recognize Amplifier Stability Issues on the Bench
• Required Tools:– Oscilloscope– Signal Generator
• Other Useful Tools:– Gain / Phase Analyzer– Network / Spectrum Analyzer
6
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
7
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
8
Quick Op-Amp Theory Bode Plot ReviewBasic Stability Tools
9
Poles and Bode Plots
+90
-90
+45
+-45
10 100 1k 10k 100k 1M 10M
Frequency (Hz)
0
(d
egre
es)
-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 Function
Straight-Line Approximation
R
CVIN
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 = -90° (-84.3°)
Decade Below fP Phase = 0° (-5.7°)
RC2
1fp
10
VINR
VOUT
A = VOUT/VIN
Single Zero Circuit Equivalent
1Vpx
100k
L159H
100kRs
Zeros and Bode Plots
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 = +90° (+84.3°)
Decade Below fZ Phase = 0° (5.7°)
RL
*2
1fz
+90
-90
+45
+-45
10 100 1k 10k 100k 1M 10M
Frequency (Hz)0
(d
egre
es)
+90o
0o
+45o/Decade
+45o @ fZ
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (d
B)
fZ
+20dB/Decade+6dB/Octave
Straight-Line Approximation
G
1.414G = +3dB(1/0.707)G = +3dB Actual
Function
fp
11
Capacitor - Intuitive Model
frequencycontrolled
resistor
OPEN SHORT
DC XCHi-f XCDC < XC < Hi-f
XC = 1/(2fC)
12
Inductor - Intuitive Model
frequencycontrolled
resistor
SHORT OPEN
DC XLHi-f XLDC < XL < Hi-f
XL = 2fL
13
Capacitor and Inductor - Impedance vs FrequencyT
Capacitor Impedance
C = 159nF Inductor Impedance
L = 159mH
Frequency (Hz)100m 1 10 100 1k 10k 100k 1M 10M
Imp
ed
an
ce (
oh
ms)
100m
1
10
100
1k
10k
100k
1M
10M
Inductor Impedance
L = 159mH
Capacitor Impedance
C = 159nF
Capacitor and InductorImpedance vs Frequency
14
Low frequency=Low Impedance
High frequency=High Impedance
Low frequency=High Impedance
High frequency=Low Impedance
Op Amp - Intuitive Model
K(f)Ro
Rin
Vo
Vout
Vdiff+
-
IN+
IN-
x1
15
Op-Amp Loop Gain Model
VOUT/VIN = Acl = Aol/(1+Aolβ)
If Aol >> 1 then Acl ≈ 1/β
Aol: Open Loop Gain
β: Feedback Factor
Acl: Closed Loop Gain
VOUT
VFB
RF
RI
=VFB/VOUT
network
Aol+
-
VOUTVIN
+
-
RF
RI
VIN
+
-
network
VFB
VOUTAol
16
17
VOUT
VFB
RF
RI
=VFB/VOUT
network
+
-
RF
RI
VIN
+
-
network
VFB
VOUT
β is easy to calculate as feedback network around the Op Amp
1/β is reciprocal of β
Easy Rules-Of-Thumb and Tricks to Plot 1/β on Op Amp Aol Curve
Plotting Aol Curve and 1/β Curve shows Loop Gain
b and 1/b
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°
18
19
Aol+
-
VOUTVIN
Op Amp Loop Gain Model
Op Amp is “Closed Loop”
Loop Gain Test:
(An Open Loop Test)
Break the Closed Loop at b
Ground VIN
Inject AC Source, VTest, into b
Aolβ = VOUT
Aol+
-
VOUTVIN
+
-
VTest
Traditional Loop Gain Test
20
Op Amp Loop Gain Model
Op Amp is “Closed Loop”
VOUT/VIN = Aol / (1+Aolb)
SPICE Loop Gain Test:
Op Amp Loop Gain Test is an “Open Loop” Test
SPICE finds a DC Operating Point before it does an AC Analysis so loop must be closed for DC and open for AC.
Break the Closed Loop at VOUT
Ground VIN source impedance low for AC analysis
Inject: AC Source, VTest, into RF
(Inject: AC Source into High Impedance Node)
Read: Aolβ = Loop Gain = VOUT
(Read: Loop Gain from Low Impedance Node)
+
-
RF
RI
VIN
+
-
network
VFB
VOUT
+
-
VTest
1TF
1TH
Short for ACOpen for DC
Open for ACShort for DC
Aol+
-
RF
RI
VIN
+
-
network
VFB
VOUTAol
Traditional Loop Gain Test
-
++
4
3
5
1
2
U1 OPA2376V1 2.5V
V2 2.5V
VOUT
RI 1kOhm
RF 10kOhm
LT 1TH
CT 100nF
+
VG1
VFB
VF1 -279.24uV
-25.38uV
-279.24uV
-
++
4
3
5
1
2
U1 OPA2376V1 2.5V
V2 2.5V
VOUT
RI 1kOhm
RF 10kOhm
+
VG1
VFB CT Open
LT Short
-
++
4
3
5
1
2
U1 OPA2376V1 2.5V
V2 2.5V
VOUT
RI 1kOhm
RF 10kOhm
+
VG1
VFB CT Short
LT Open
21
SPICE Loop Gain Test
Loop Gain (Aol) = VOUT = VFB1/ = 1 / VFBAol = VOUT / VFB
DC Equivalent Circuit AC Equivalent Circuit
DC Analysis
DC Analysis DC Analysis
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
Aol (
dB)
fcl
Acl
Aol
Aol (Loop Gain)
Closed Loop Response
Open Loop Response
22
Plot (dB) 1/β on Op Amp Aol (dB)
Aolβ = Aol(dB) – 1/β(dB)
Aolβ = Aol / (1/β) = Aolβ
Note how Aolβ changes with frequency
Loop Gain (Aolb) from Aol and 1/b
23
“Rate-of-Closure” Stability Criteria using 1/β & Aol
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
Aol (
dB)
Aol
fcl1
fcl4
fcl3
fcl2
**
*
**
*
At fcl: Loop Gain (Aolb) = 1 (0dB)
Rate-of-Closure @ fcl =(Aol slope – 1/β slope)
*20dB/decade Rate-of-Closure @ fcl = STABLE
**40dB/decade Rate-of-Closure @ fcl = UNSTABLE
24
Loop Gain (Aolb) Example
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
Aol
fcl
fp1
fp2fz1
Aol
Rate-of-Closure @ fcl = 40dB/decade
UNSTABLE!
+
-
+
-
VIN
RI
RFCin
VOUT
10k
1k
0.15F
STABLE
Example 1: Note locations of poles and zeros in Aol & 1/b
Aol 1/ Loop Gainfp1 pole ----- polefp2 pole ----- polefz1 ----- zero pole
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (d
B)
fp1
fz1
fp2
fcl
25
To Plot Aolβ from Aol & 1/β Plot:Poles in Aol curve are Poles in Aolβ (Loop Gain)PlotZeros in Aol curve are Zeros in Aolβ (Loop Gain) Plot
Poles in 1/β curve are Zeros in Aolβ (Loop Gain) PlotZeros in 1/β curve are Poles in Aolβ ( Loop Gain) Plot[Remember: β is the reciprocal of 1/β]
Loop Gain (Aolβ) Plot from Aol & 1/β Plot
180
0
135
45
10 100 1k 10k 100k 1M 10M
Frequency(Hz)
90
(d
egre
es)
-45
fp1
fz1
fp2
fcl
Loop Gain (Aolb) Phase at fcl:
Phase Shift = -180
Phase Margin = 0
STABLE
STABLE
Example 1: Note locations of poles and zeros in Loop Gain
Aol 1/ Loop Gainfp1 pole ----- polefp2 pole ----- polefz1 ----- zero pole
26
1/β Always = Closed Loop Response
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
VOUT/VIN
Aol
fcl
SSBW(Small Signal BandWidth)
VOUT/VIN = Aol/(1+Aolβ)At fcl: Aolβ = 1 VOUT/VIN = Aol/(1+1) ~ Aol No Loop Gain left to correct for errors VOUT/VIN follows the Aol curve at f > fcl
Note:
1/β is the AC, Small Signal, Closed Loop, ”Noise Gain” for the Op Amp.
VOUT/VIN is often NOT the same as 1/β.
+
-
RI
RF
VOUT
10k
100k
1kRn
Cn16nF
+
-VIN
VNOISE
27
How to Modify 1/β for Stable Circuits
+
-
+
-
VIN
VOUT
RFRI
Rn Cn RpCp
ZIINPUT Network
ZFFEEDBACK Network
28
1/β “First Order Analysis” for ZF
+
-
+
-
VIN
VOUT
RFRI
RpCp
100k1k
10k1.59nF
1/β Low Frequency = RF/RI = 100 40dB
Cp = Open at Low Frequency 1/β High Frequency = (Rp//RF)/RI ≈ Rp/RI = 10 20dB
Cp = Short at High Frequency Pole in 1/β when Magnitude of XCp = RF
Magnitude XCp = 1/(2∙п∙f∙Cp)
fp = 1/(2∙п∙RF∙Cp) = 1kHz Zero in 1/β when Magnitude of XCp = Rp
fz = 1/(2∙п∙Rp∙Cp) = 10kHz)]RF//RI(Rp[Cp2
1fz
)RpRF(Cp21
fp
:equationsExact ZF
T
Aol
1/
fz
fp
Frequency (Hz)1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-40
-20
0
20
40
60
80
100
120
140
fp
fz
Aol
1/
ZF Network (fp and fz)Aol and 1/
29
TINA SPICE: 1/β for ZF
Lo fHi f
1st Order Actualfp 1kHz 917.020Hzfz 10kHz 9.038kHz
1st Order ActualLo f 40dB 40.086dBHi f 20dB 20.079dB
+
-
+
-
VIN
VOUT
RFRI
RpCp
100k1k
10k1.59nF
30
+
-
+
-
VIN
VOUT
RFRI
Rn Cn
100k
1k
10k
15.9nF
1/β Low Frequency = RF/RI = 10 20dB
Cn = Open at Low Frequency 1/β High Frequency = RF/(RI//Rn) ≈ RF/Rn =100 40dB
Cn = Short at High Frequency Zero in 1/β when Magnitude of XCn = RI
Magnitude XCn = 1/(2∙п∙f∙Cn)
fz = 1/(2∙п∙RI∙Cn) = 1kHz Pole in 1/β when Magnitude of XCn = Rn
fp = 1/(2∙п∙Rn∙Cn) = 10kHz
1/β “First Order Analysis” for ZI
)]RF//RI(Rn[Cn21
fz
RnCn21
fp
:equationsExact ZI
T
Aol
1/
fz
fp
Frequency (Hz)1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-40
-20
0
20
40
60
80
100
120
140
fp
fz
Aol
1/
ZI Network (fp and fz)Aol and 1/
31
TINA SPICE: 1/β for ZI
Lo f
Hi f
1st Order Actualfz 1kHz 999.496Hzfp 10kHz 9.935kHz
1st Order ActualLo f 20dB 20.828dBHi f 40dB 40.906dB
+
-
+
-
VIN
VOUT
RFRI
Rn Cn
100k
1k
10k
15.9nF
Stability Analysis - Method 1 (Loaded Aol & 1/b Technique)
(Riso Compensation)
V+
V-
+
-
+
U1 OPA627E
Vo
R2 100kR3 4.99k
+
Vin CLoad 1u
33
Capacitive Loading on Op Amp Outputs
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
Unity Gain Buffer Circuits Circuits with Gain
V+
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
Will this circuit behavior get you a raise in pay?
T
fp1
Aol Pole
Low Frequency
fp2
Loaded Aol
Additional Pole
-20dB/decade
-40dB/decade
Frequency (Hz)1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-80
-60
-40
-20
0
20
40
60
80
100
120
140
Rate-of-Closure
40dB/decade
fcl
1/
Loaded Aol due to CLoad
-40dB/decade
-20dB/decade
fp2
Loaded Aol
Additional Pole
fp1
Aol Pole
Low Frequency
34
Loaded Aol V+
V-
V+
V-V+ 15V
V- 15V+
-
+
U1 OPA627E
VOUT
CLoad 1uF
+
Vtest
LT 1THCT 1TF
VFB
Loaded Aol = VOUT / VFB
For AC Test VFB = Vtest
Loaded Aol = VOUT
353.900776nV
353.900776nV
STABLE
V+
V-
V+
V-V+ 15
V- 15+
-
+
U1 OPA627E
VOUT
CLoad 1u
+
Vtest
LT 1TCT 1T
VFB
Loaded Aol = VOUT / VFB
For AC Test VFB = Vtest
Loaded Aol = VOUT
35
Loaded Aol Model
Loaded AolRo 54
CLoad 1u
+
Vtest
-
+
-
+
Aol 1M
LT Open
CT Short
+
Aol
Ro 54
CLoad 1u
Loaded Aol
36
Loaded Aol Model
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
+
Aol
Ro 54
CLoad 1u
Loaded Aol
fp2
CLoadRo2
12fp
Equation Pole AolLoaded
37
Loaded Aol Model
+
=
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
fp1
fp1
fp2
fp2
Note: Addition on Bode Plots = Linear Multiplication
T
Ga
in (
dB
)
-80
-60
-40
-20
0
20
40
60
80
100
120
140
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-45
0
45
90
135
180
Gain :
VOUT A:(222.74k; -32.46f)
Phase :
VOUT A:(222.74k; 548.41m)
fcl
Loaded Aol
Loop Gain & Phase
a
38
Loaded Aol – Loop Gain & Phase
V+
V-
V+
V-V+ 15V
V- 15V+
-
+
U1 OPA627E
VOUT
CLoad 1uF
+
Vtest
LT 1THCT 1TF
VFB
Loop Gain (Aol) = VOUT
Phase Margin at fcl
STABLE
39
Riso Compensation
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 1uF+
VIN
Riso 6Ohm
VOA
Riso will add a zero in the Loaded Aol Curve
T
fp1
Aol Pole
Low Frequency
fp2
Loaded Aol
Additional Pole
fz1Loaded AolRiso CompensationAdditional Zero
-20dB/decade
-20dB/decade
-40dB/decade
Frequency (Hz)1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-80
-60
-40
-20
0
20
40
60
80
100
120
140Loaded Aol with Riso Compensation
1/Rate-of-Closure
20dB/decade
-40dB/decade
-20dB/decade
-20dB/decade
fz1Loaded AolRiso CompensationAdditional Zerofp2
Loaded Aol
Additional Pole
fp1
Aol Pole
Low Frequency
fcl
40
Riso Compensation Results
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 1uF
Riso 6Ohm
VOA
LT 1THCT 1TF
+
Vtest
Loaded Aol = VOA
STABLE
41
Riso Compensation Theory
VOUTRo 54
CLoad 1u
+
Vtest
-
+
-
+
Aol 1M
Riso 6
LT Open
CT Short
Loaded Aol
+
Aol
Ro 54
CLoad 1u
Loaded Aol
Riso 6
V+
V-
V+
V-V+ 15
V- 15+
-
+
U1 OPA627E
VOUT
CLoad 1u+
Vtest
LT 1T
CT 1T
Riso 6
VOA
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)
42
Riso Compensation Theory+
Aol
Ro 54
CLoad 1u
Loaded Aol
Riso 6
sCLoadRiso)(Ro1
sRisoCLoad1 (s)Loaded Aol
Function Transfer
CLoadRiso)(Ro2
1 2fp
:Pole
CLoadRiso2
1 1fz
:Zero
fp2fz1
43
Riso Compensation TheoryT
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
+
=
Aol
Aol Load
Loaded Aol
fp2 fz1
fp1
fp1
fp2 fz1
Note: Addition on Bode Plots = Linear Multiplication
Riso Compensation Design Steps
1) Determine fp2 in Loaded Aol due to CLoadA) Measure in SPICE with CLoad on Op Amp Output
2) Plot fp2 on original Aol to create new Loaded Aol
3) Add Desired fz2 on to Loaded Aol Plot for Riso CompensationA) Keep fz1 < 10*fp2 (Case A)B) Or keep the Loaded Aol Magnitude at fz1 > 0dB (Case B) (fz1>10dB will allow for Aol variation of ½ Decade in Unity Gain Bandwidth)
4) Compute value for Riso based on plotted fz1
5) SPICE simulation with Riso for Loop Gain (Aolb) Magnitude and Phase
6) Adjust Riso Compensation if greater Loop Gain (Aolb) phase margin desired
7) Check closed loop AC response for VOUT/VINA) Look for peaking which indicates marginal stabilityB) Check if closed AC response is acceptable for end application
8) Check Transient response for VOUT/VIN A) Overshoot and ringing in the time domain indicates marginal stability B) Determine if settling time is acceptable for end application
44
T
-40dB/decade
Case B: CLoad=2.9nF
-20dB/decade
Case A: CLoad=1uF
fp2
Case B
CLoad=2.9nF
fp2
Case A
CLoad=1uF
Vo
ltag
e (
V)
-80
-60
-40
-20
0
20
40
60
80
100
120
140
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Vo
ltag
e (
V)
-45
0
45
90
135
180
fp2
Case B
CLoad=2.9nF
fp2
Case A
CLoad=1uF
Case A: CLoad=1uF
Case B: CLoad=2.9nF
-40dB/decade
-20dB/decade
Loaded Aol
Case A: CLoad = 1uF
Case B: Cload = 2.9nF
VOA[1] 2.9n[F] A:(983.366787k; 21.799287)
VOA[1] 2.9n[F] A:(983.366787k; 45)
VOA[2] 1u[F] B:(2.980143k; 71.980276)
VOA[2] 1u[F] B:(2.980143k; 45)
ab
1),2) Loaded Aol and fp2
45
Case A, CLoad=1uF, fp2=2.98kHzCase B, CLoad=2.9nF, fp2=983.37kHz
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 2.9nF
Riso 0Ohm
VOA
LT 1THCT 1TF
+
Vtest
Loaded Aol = VOA
3) Add fz1 on Loaded Aol
46
T
fp2
Case B
CLoad=2.9nF
fz1
Case B
CLoad=2.9nF
fp2
Case A
CLoad=1uF
fz1
Case A
CLoad=1uF
Frequency (Hz)1 10 100 1k 10k 100k 1M 10M
Vo
ltag
e (
V)
-80
-60
-40
-20
0
20
40
60
80
100
120
140
Loaded Aol
Add Riso Compensation
4.07MHz
fz1
Case B
CLoad=2.9nF
fp2
Case B
CLoad=2.9nF
fz1
Case A
CLoad=1uF
fp2
Case A
CLoad=1uF983.37kHz
29.8kHz
2.98kHz
Case A, CLoad=1uF, fz1=29.8kHzCase B, CLoad=2.9nF, fz1=4.07MHz
4) Compute Value for Riso
47
Case A, CLoad=1uF, fz1=29.8kHzCase B, CLoad=2.9nF, fz1=4.07MHz
CLoad1fz2
1Riso
CLoadRiso2
1 1fz
:Zero
5.36Ω use
:29.8kHzfz1 F,1CLoad A,Case Zero,
34.5F1kHz8.292
1Riso
CLoadRiso21
1fz
13.7Ω use
:4.07MHzfz1 2.9nF,CLoad B, Case Zero,
48.13nF9.2MHz07.42
1Riso
CLoadRiso2
1 1fz
T
VOA
-20
0
20
40
60
80
100
120
140
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
VOA
0
45
90
135
180fcl
Loop Gain
Case A: CLoad=1uF
VOA:
VOA A:(1.519941M; 1.364794f)
VOA:
VOA A:(1.519941M; 87.522388)
a
5),6) Loop Gain, Case A
48
Phase Margin at fcl = 87.5 degrees
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 1uF
Riso 5.36Ohm
VOA
LT 1THCT 1TF
+
Vtest
Loop Gain (Aol) = VOA
5),6) Loop Gain, Case B
49
T
VOA
-20
0
20
40
60
80
100
120
140
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
VOA
0
45
90
135
180fcl
Loop Gain
Case B: CLoad=2.9nF
VOA:
VOA A:(4.48315M; -1.528291f)
VOA:
VOA A:(4.48315M; 54.167774)
a
Phase Margin at fcl = 54 degrees
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 2.9nF
Riso 13.7Ohm
VOA
LT 1THCT 1TF
+
Vtest
Loop Gain (Aol) = VOA
50
7) AC VOUT/VIN, Case A
T VOA
-3dB=1.58MHz
VOUT
-3dB=30.44kHz
Ga
in (
dB
)
-80
-60
-40
-20
0
20
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-180
-135
-90
-45
0
VOUT/VINRiso CompensationCase A, CLoad=1uF
VOA
-3dB=1.58MHz
VOUT
-3dB=30.44kHz
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 1uF
Riso 5.36Ohm
VOA
+
VIN
51
8) Transient Analysis, Case A
T
Time (s)
0 500u 1m 2m 2m
VIN
-10.00m
10.00m
VOA
-10.27m
10.27m
VOUT
-10.01m
10.01m
VOUT / VINTransient AnalysisCase A, CLoad=1uF
V+
V-
V+
V-
V+ 15V
V- 15V
+
-
+
U1 OPA627E VOUT
CLoad 1uF
Riso 5.36Ohm
VOA
+
VIN
V+
V-
V+
V-
V+ 15V
V2 15V
+
-
+
U1 OPA627E
VOUT
CLoad 1uF
Riso 6Ohm
VOA
VIN 5V RLoad 200Ohm
A+
ILoad 24.271845mA
5V
4.854369V
52
Riso Compensation: Key Design Consideration
V+
V-
V+
V-
V+ 15V
V2 15V
+
-
+
U1 OPA627E
VOUT
CLoad 1uF
Riso 6Ohm
VOA
VIN 5VRLoad 1kOhm
A+
ILoad 4.970179mA
5V
4.970179V
Accuracy of VOUT depends on Load Current
Light Load Current
Heavy Load Current
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