Download Non-Loop Stability

Solving Op Amp Stability Issues
Part 3
(For Voltage Feedback Op Amps)
Tim Green & Collin Wells
Precision Analog Linear Applications
1
Appendix Index
Appendix No.
Title
1
Op Amp Output Impedance
Pole and Zero:
2
Magnitude and Phase on Bode Plots
3
Dual Feedback Paths and 1/β
4
Non-Loop Stability Problems
Description/Stability Technique
Zo vs Zout difference and datasheet curves
Closed loop magnitude and phase shifts of a signal
frequency due to poles and zeroes on a Bode Plot
How to avoid problems when using dual feedback
paths for stability compensation
Oscillations and causes not seen in loop gain stability
simulations
5
Riso (Output Cload)
Stability: Isolation resistor with feedback at op amp
6
High Gain and CF (Output Cload)
Stability : High gain circuits and a feedback capacitor
7
CF Non-Inverting (Input Cload)
Stability : Non-inverting gain and feedback capacitor
Output Cload, closed loop gain >20dB
Input Cload, non-inverting gain, large value
input resistor
Stability: Inverting gain and feedback capacitor
Input Cload, non-inverting gain, large value
input resistor, photodiode type circuits
8
When to use the Stability Technique
Zo is a key parameter for stability analysis
Magnitude and phase shift at a frequency of
interest for closed loop poles and zeroes
Key tool in analyzing op amp circuits that use
dual feedback for stability
Check all designs to avoid oscillations that do
not show up in SPICE simulation
Output Cload, Note: accuracy of output is
dependent upon load current
9
CF Inverting (Input Cload)
Noise Gain Inverting and
Non-Inverting (Output Cload)
10
Noise Gain and CF (Output Cload)
Stability: Noise Gain added by input R-C network
Stability: Noise Gain (input R-C) and feedback
capacitor
11
13
Output Pin Compensation (Output Cload)
Riso w/Dual Feedback (Output Cload)
- Zo, 1/β, Aol Technique
Riso w/Dual Feedback (Output Cload)
- 1/β, Loaded Aol Technique
Stability: Series R-C on op amp output to ground
Stability: Isolation resistor with two feedback paths analysis by Zo, 1/β, and Aol technique
Stability: Isolation resistor with two feedback paths analysis by 1/β, and Loaded Aol technique
14
Riso w/Dual Feedback plus RFx (Output Cload) Stability: Isolation resistor with two feedback paths - 1/β, Loaded Aol Technique
analysis by 1/β, and Loaded Aol technique
Output Cload, closed loop gain <20dB
Output Cload, Loaded Aol has a second pole
located >20dB
Output Cload, no access to -input, monolithic,
integrated difference amplifiers, complex
feedback where not practical to use -input
Output Cload, some additional Vdrop across
isolation resistor is okay, accurate Vout at load
Output Cload, some additional Vdrop across
isolation resistor is okay, accurate Vout at load
Output Cload, some additional Vdrop across
isolation resistor is okay, accurate Vout at
load. RFx can provide wider BW control at
output load.
15
Discrete Difference Amplifier (Output Cload)
Output Cload, difference amp configuration,
2
any closed loop gain
12
Stability: Balanced use of noise gain (series R-C)
4) Non-Loop Stability Problems
Non-Loop Stability
• Loop Frequencies
• RB+
• PCB Traces
• Supply Bypass
• Ground Loops
• Output Stage Oscillations
Non-Loop Stability
Oscillations NOT predicted by Loop Gain (Aolb) Analysis
or
SPICE Simulations
4
Non-Loop Stability: Loop Frequency Definitions
fcl:
Where Loop Gain (Aolβ) = 1
Aol
100
fGBW:
Where Op Amp Aol Curve crosses 0dB
(Unity Gain Bandwidth)
A (dB)
80
fGBW
fcl
60
b
40
VOUT/VIN
20
SSBW
(Small Signal BandWidth)
0
1
10
100
1k
10k
100k
1M
10M
Frequency (Hz)
5
Non-Loop Stability: ? Diagnostic Questions ?
 Frequency of oscillation (fosc)?
 When does the oscillation occur?
 Oscillates Unloaded?
 Oscillates with VIN=0?
6
Non-Loop Stability:
RB+ Resistor
 fosc < fGBW
 oscillates unloaded? -- may or may not
 oscillates with VIN=0? -- may or may not
RF
100k
RI
100k
RB+ is Ib current match resistor to
reduce Vos errors due to Ib.
Ib
-
+
VIN
-
VOUT
Ib
+
RB+
49.9k
RB+ can create high impedance
node acting as antenna pickup for
unwanted positive feedback.
+
VNOISE
PROBLEM
RF
-
100k
RI
100k
RF
-
100k
SOLUTION
RI
100k
VOUT
+
VIN
-
+
RB+
49.9k
CB+
0.01F
or
0.1F
If you use RB+ bypass
it in parallel with 0.1μF
capacitor.
+
VIN
-
-
VOUT
+
RB+
SOLUTION
Many Op Amps have low Ib so error is
small. Evaluate DC errors w/o RB+.
7
Non-Loop Stability:
PCB Traces
 fosc < fGBW
 oscillates unloaded? -- may or may not
 oscillates with VIN=0? -- may or may not
RI
RF
+
+
Rs
VIN
-
VOUT
GND
DO NOT route high current, low impedance output traces near high
impedance input traces. Unwanted positive feedback path.
DO route high current output traces adjacent to each other (on top of each
other in a multi-layer PCB) to form a twisted pair for EMI cancellation.
8
Non-Loop Stability:
Supply Lines
 fosc < fGBW
 oscillates unloaded? -- no
 oscillates with VIN=0? -- may or may not
Ls
PROBLEM
Gain
Stage
PROBLEM
Power
Stage
+vs
RL
IL
-
Rs
+
CL
-vs
Load current, IL, flows through power
supply resistance, Rs, due to PCB trace
or wiring. Modulated supply voltages
appear at Op Amp Power pins.
Modulated signal couples into amplifier
which relies on supply pins as AC
Ground.
Power supply lead inductance, Ls,
interacts with a capacitive load,
CL, to form an oscillatory LC, high
Q, tank circuit.
9
Non-Loop Stability:
Proper Supply Line Decouple
CLF
SOLUTION
CLF: Low Frequency Bypass
< 4 in
<10 cm
RHF
10μF / Amp Out (peak)
Aluminum Electrolytic or Tantalum
CHF
+VS
< 4 in (10cm) from Op Amp
-
CHF: High Frequency Bypass
+
0.1μF Ceramic
-VS
< 4 in
<10 cm
Directly at Op Amp Power Supply Pins
CHF
RHF
RHF: Provisional Series CHF Resistance
1Ω < RHF < 10Ω
CLF
Highly Inductive Supply Lines
10
Non-Loop Stability:
Ground Loops
RI
 fosc < fGBW
 oscillates unloaded? -- no
 oscillates with VIN=0? -- yes
RI
RF
RF
+
-
-
+VS
VOUT
VIN
+
-VS
-
RGw
RL
IL
RGx
+
RGy
“Ground”
Ground loops are created from load current
flowing through parasitic resistances. If part
of VOUT is fed back to Op Amp +input,
positive feedback and oscillations can occur.
SOLUTION
VIN
PROBLEM
RGv
“Star”
Ground
Point
-
+VS
VOUT
+
-VS
RL
RG
Parasitic resistances can be made to look
like a common mode input by using a
“Single-Point” or “Star” ground connection.
11
Non-Loop Stability:
Output Stages
 fosc > fGBW
 oscillates unloaded? -- no
 oscillates with VIN=0? -- no
RF
100k
L
O
A
D
RI
100k
+
VIN
VOUT
+
RSN
10 to 100
-
CSN
F to 1F
-VS
PROBLEM
Some Op Amps use composite output
stages, usually on the negative output, that
contain local feedback paths. Under reactive
loads these output stages can oscillate.
SOLUTION
The Output R-C Snubber Network lowers
the high frequency gain of the output stage
preventing unwanted oscillations under
reactive loads.
12
5) Riso (Output Cload)
VFB 353.900776nV
Loaded Aol
CT 1TF
LT 1TH
+
V+
T
140
Vtest
V+ 15V
-
-20dB/decade
120
VOUT 353.900776nV
Loaded Aol = VOUT / VFB
For AC Test VFB = Vtest
Loaded Aol = VOUT
V- 15V
fp1
Aol Pole
Low Frequency
100
80
fp2
Loaded Aol
Additional Pole
40
1/
20
+
+
U1 OPA627E
CLoad 1uF
V+
V-
60
Gain (dB)
V-
Loaded Aol due to CLoad
-40dB/decade
Rate-of-Closure
40dB/decade
0
-20
STABLE
fcl
-40
-60
-80
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
14
Loaded Aol Model
CT 1T
V+
LT 1T
Vtest
V+ 15
VFB
+
+
Ro 54
V-
Loaded Aol
Aol
-
VOUT
+
V- 15
+
U1 OPA627E
CLoad 1u
CLoad 1u
V+
VLoaded Aol = VOUT / VFB
For AC Test VFB = Vtest
Loaded Aol = VOUT
LT Open
-
-
+
+
+
CT Short
Vtest
Ro 54
Loaded Aol
Aol 1M
CLoad 1u
15
Loaded Aol Model
T
fp2
0
0.00
Ro 54
Aol
Loaded Aol
GainGain(dB)
(dB)
+
-20
-20.00
-40
-40.00
CLoad 1u
Loaded AOL
Pole
-60
-60.00
-80
-80.00
0
0.00
Phase
(degrees)
Phase [deg]
Loaded Aol Pole Equation
1
fp 2 
2    Ro  CLoad
-45.00
-45
-90.00
-90
1.00
1
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
Frequency (Hz)
1.00M
1M
10.00M
10M
100.00M
100M
16
Loaded Aol Model
fp2
120
100
100.00
T 120.00
Aol
20
0
0.00
-20
-20.00
-40
-40.00
20.00
-60
-60.00
+
135.00
135
-80
-80.00
0
0.00
-45.00
-45
90
90.00
45
45.00
0 1.00
1
Aol Load
-40
-40.00
180.00
180
Phase
(degrees)
Phase [deg]
-20
-20.00
GainGain(dB)
(dB)
GainGain(dB)
(dB)
fp1
60.00
0
0.00
PhasePhase(degrees)
[deg]
80
60
40
40.00
80.00
T
0.00
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
1.00M
1M
Frequency (Hz)
120
120
100
100
10.00M
10M
100.00M
100M
-90.00
-90
1.00
1
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
Frequency (Hz)
1.00M
1M
10.00M
10M
fp1
80
80
60
60
40
40
Loaded Aol
fp2
20
20
00
-20
-20
-40
-40
180.00
180
PhaseVoltage
(degrees)
(V)
=
GainVoltage
(dB)
(V)
T
135.00
135
90
90.00
45
45.00
0
0.00
1.00
1
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
Frequency (Hz)
Note: Addition on Bode Plots = Linear Multiplication
1.00M
1M
10.00M
10M
100.00M
100M
17
100.00M
100M
VFB
LT 1TH
+
Loaded Aol –
Loop Gain & Phase
CT 1TF
V+
Vtest
V+ 15V
V-
VOUT
Loop Gain (Aol ) = VOUT
V- 15V
+
+
U1 OPA627E
CLoad 1uF
V+
V-
STABLE
Phase Margin at fcl
18
Riso Compensation
Riso will add a zero in the Loaded Aol Curve
V+
VV+ 15V
Riso 6Ohm
-
+
U1 OPA627E
VIN
V- 15V
VOUT
+
+
CLoad 1uF
V+
VOA
V-
19
Riso Compensation
Results
T
CT 1TF
+
V-
Vtest
V+ 15V
Riso 6Ohm
-
140
U1 OPA627E
Loaded Aol with Riso Compensation
Loaded Aol = VOA
fp1
Aol Pole
Low Frequency
80
V+
VOA
V-
-40dB/decade
60
fp2
Loaded Aol
Additional Pole
40
1/
20
+
CLoad 1uF
V- 15V
100
VOUT
+
-20dB/decade
120
Gain (dB)
LT 1TH
V+
fz1
Loaded Aol
Riso Compensation
Additional Zero
-20dB/decade
Rate-of-Closure
20dB/decade
0
-20
fcl
STABLE
-40
-60
-80
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
20
Riso Compensation Theory
V+
VOA
V-
V+ 15
LT 1T
-
Riso 6
VOUT
+
V- 15
+
U1 OPA627E
CLoad 1u
V+
Vtest
V-
Ro 54
+
+
CT 1T
Loaded Aol
Aol
Riso 6
CLoad 1u
LT Open
Loaded Aol
-
-
+
+
+
CT Short
Vtest
Ro 54
Riso 6
VOUT
Aol 1M
CLoad 1u
21
Riso Compensation Theory
T
0
0.00
fp2
Loaded Aol
Aol
Riso 6
fz1
GainGain(dB)
(dB)
+
Ro 54
-20.00
-20
-40
-40.00
CLoad 1u
Loaded Aol (s) 
1  CLoad  Riso  s
1  (Ro  Riso)  CLoad  s
-45.00
-45
-90.00
-90
1.00
1
Pole :
fp2 
Phase
(degrees)
Phase [deg]
Transfer Function
0
0.00
1
2(Ro  Riso)  CLoad
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
Frequency (Hz)
1.00M
1M
10.00M
10M
100.00M
100M
Zero :
fz1 
1
2  Riso  CLoad
22
Riso Compensation Theory
120
100
100.00
T 120.00
Aol
Aol Load
-40
-40.00
180.00
180
Phase
(degrees)
Phase [deg]
fz1
-20.00
-20
20
0
0.00
-20
-20.00
-40
-40.00
20.00
+
135.00
135
90
90.00
45
45.00
0 1.00
1
fp2
GainGain(dB)
(dB)
GainGain(dB)
(dB)
fp1
0
0.00
0
0.00
Phase
(degrees)
Phase [deg]
80
60
60.00
40
40.00
80.00
T
-90.00
-90
1.00
1
0.00
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency (Hz)
Frequency (Hz)
120
100.00
100
1.00M
1M
10.00M
10M
-45.00
-45
100.00M
100M
10.00
10
100.00
100
1.00k
1k
10.00k
100.00k
10k
100k
Frequency
(Hz)
Frequency (Hz)
1.00M
1M
10.00M
10M
T 120.00
fp1
80
60.00
60
40.00
40
Loaded Aol
GainGain(dB)
(dB)
80.00
20
0.00
0
-20.00
-20
-40.00
-40
20.00
180.00
180
PhasePhase(degrees)
[deg]
=
fz1
fp2
135.00
135
90.00
90
45.00
45
0.00
0
1.00
1
10.00
10
100.00
100
1.00k
1k
10.00k
10k
Frequency (Hz)
100.00k
100k
Frequency (Hz)
Note: Addition on Bode Plots = Linear Multiplication
1.00M
1M
10.00M
10M
100.00M
100M
23
100.00M
100M
Riso Compensation Design Steps
1) Determine fp2 in Loaded Aol due to CLoad
A) 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 Compensation
A) 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/VIN
A) Look for peaking which indicates marginal stability
B) 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
24
CT 1TF
1),2) Loaded Aol and fp2
LT 1TH
+
V+
V-
Vtest
V+ 15V
Riso 0Ohm
-
U1 OPA627E
VOUT
+
+
CLoad 2.9nF
V- 15V
Loaded Aol = VOA
V+
VOA
V-
25
Case A, CLoad=1uF, fp2=2.98kHz
Case B, CLoad=2.9nF, fp2=983.37kHz
3) Add fz1 on Loaded Aol
T
140
120
100
Loaded Aol
Add Riso Compensation
2.98kHz
80
Voltage (V)
60
fp2
Case B
983.37kHz
CLoad=2.9nF
fp2
Case A
CLoad=1uF
40
20
fz1
29.8kHz
Case A
CLoad=1uF
0
4.07MHz
fz1
Case B
CLoad=2.9nF
-20
-40
-60
-80
1
10
100
Case A, CLoad=1uF, fz1=29.8kHz
Case B, CLoad=2.9nF, fz1=4.07MHz
1k
10k
Frequency (Hz)
100k
1M
10M
26
4) Compute Value for Riso
Case A, CLoad=1uF, fz1=29.8kHz
Case B, CLoad=2.9nF, fz1=4.07MHz
Zero :
Zero, Case A, CLoad  1F, fz1  29.8kHz :
1
2  Riso  CLoad
1
Riso 
2  fz1 CLoad
1
2  Riso  CLoad
1
Riso 
 5.34  use 5.36Ω
2  29.8kHz  1F
fz1 
fz1 
Zero, Case B, CLoad  2.9nF, fz1  4.07MHz :
1
fz1 
2  Riso  CLoad
1
Riso 
 13.48  use 13.7Ω
2  4.07MHz  2.9nF
27
CT 1TF
5),6) Loop Gain, Case A
LT 1TH
+
V+
V-
Vtest
V+ 15V
Riso 5.36Ohm
-
U1 OPA627E
VOUT
+
+
CLoad 1uF
V- 15V
V+
VOA
Loop Gain (Aol ) = VOA
V-
Phase Margin at fcl = 87.5 degrees
28
CT 1TF
5),6) Loop Gain, Case B
LT 1TH
+
V+
V-
Vtest
V+ 15V
Riso 13.7Ohm
-
U1 OPA627E
VOUT
+
+
CLoad 2.9nF
V- 15V
V+
VOA
Loop Gain (Aol ) = VOA
V-
Phase Margin at fcl = 54 degrees
29
V+
7) AC VOUT/VIN, Case A
VV+ 15V
Riso 5.36Ohm
-
U1 OPA627E
VOUT
+
+
+
CLoad 1uF
V- 15V
VIN
V+
VOA
VT
20
VOA
-3dB=1.58MHz
Gain (dB)
0
VOUT/VIN
Riso Compensation
Case A, CLoad=1uF
-20
VOUT
-3dB=30.44kHz
-40
-60
-80
0
Phase [deg]
-45
-90
-135
-180
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
30
V+
8) Transient Analysis, Case A
VV+ 15V
Riso 5.36Ohm
-
U1 OPA627E
T
VOUT
+
+
10.00m
+
VIN
CLoad 1uF
V- 15V
VOUT / VIN
Transient Analysis
Case A, CLoad=1uF
VIN
V+
VOA
V-
-10.00m
10.27m
VOA
-10.27m
10.01m
VOUT
-10.01m
0
500u
1m
Time (s)
2m
2m
31
Riso Compensation: Key Design Consideration
Accuracy of VOUT depends on Load Current
Light Load Current
V+
VOA 5V
V-
ILoad 4.970179mA
V+ 15V
-
+
Riso 6Ohm
+
U1 OPA627E
VIN 5V
+
A
CLoad 1uF
V+
V2 15V
VOUT 4.970179V
RLoad 1kOhm
V-
V+
Heavy Load Current
VOA 5V
V-
ILoad 24.271845mA
-
V+ 15V
+
VIN 5V
Riso 6Ohm
+
U1 OPA627E
V+
+
A
CLoad 1uF
VOUT 4.854369V
RLoad 200Ohm
V2 15V
V32
6) High Gain and CF
(Output Cload)
33
Original Circuit: Transient Response
V+
RI 499
RF 49.9k
V-
C2 1u
V1 15
-
V2 15
+
C3 1u
Vo
+
+
U1 OPA627E
CLoad 1u
VG1
V+
V-
20.00m
Voltage (V)
T
Vin
Vo
0.00
0.00
100.00u
Time (s)
200.00u
34
High-Gain and CF Compensation Design Steps
1) Break the loop and plot Aol and 1/Beta
A. Determine fp2 in Loaded Aol due to Cload
B. Determine fcl of original Aol and 1/Beta
C. Determine f(Aol=0dB)
f(Aol=0dB): the frequency where the Loaded Aol Magnitude = 0dB
2) Add Desired fp3 to 1/Beta for CF compensation
(fz1 will occur when 1/Beta = 0dB)
A) Keep fp3 < *fcl and fz1 < f(Aol=0dB)
B) To prevent AolB phase dip, Keep fp3 < 10*fp2
3) Select value for CF based fp3, fcl, and f(Aol=0dB)
4) SPICE simulation with Riso for Loop Gain (Aolb) Magnitude and Phase
5) Adjust CF if greater Loop Gain (Aolb) phase margin desired
6) Check closed loop AC response for VOUT/VIN
A) Look for peaking which indicates marginal stability
B) Check if closed AC response is acceptable for end application
7) Check Transient response for VOUT/VIN
A) Overshoot and ringing in the time domain indicates marginal stability
35
1) Original Circuit: Break the Loop
Vfb
RI 499
RF 49k
C1 1T
+
V+
C2 1u
VV1 15
Vo
+
C3 1u
Vin
-
U1 OPA627E
V2 15
L1 1T
+
CLoad 1u
V+
V-
36
2) Compensate with 1/Beta Pole (CF)
37
3) 1/Beta Pole/Zero Equations
Vout
1/Beta Transfer Function:
Vout(s)
=
RI+CF RI RF s
+
Vfb(s)
RF+RI+(CI+CF) RI RF s
DC 1/Beta:
RF
CF
Vout
Vout(s)
RF
s=0,
= 1+
Vfb(s)
RI
Vfb
RI
1/Beta Pole Frequency:
fp3 =
1
2 pi RF CF
CI
=> Solve for CF
1
C F=
2 pi RF fp3
CI is the equivalent
input capacitance of
the op amp. (See
Appendix #7)
1/Beta Zero Frequency:
1
fz1=
2 pi (RI ll RF) (CF+CI)
=> Solve for CF
C F=
2
1
(RI ll RF) fz1
-CI
38
V1 15
From Step 1:
fp2 = 2.98 kHz
fcl = 22.67 kHz
f(Aol=0dB) = 222.7 kHz
V2 15
VCF 141p
For stability:
A) Keep fp3 < *fcl and fz1 < f(Aol=0dB)
RI 499
RF 49.9k
Calculate CF(min) from fp3 < *fcl :
V-
1
-
49.9k 22.67kHz
= 141pF
Vo
+
CFmin=
2
1
=
RF fp3 2
+
+
U1 OPA627E
VG1
V+
Calculate CF(max) from fz1 < f(Aol=0dB) :
CFmax=
2
C3 1u
3) Select CF to Compensate Circuit
C2 1u
V+
1
-C = =
(RI ll RF) fz1 I
2
1
(49.9k
ll 499 ) 222.7kHz
-10pF = 1.44nF
B) To prevent AolB phase dip, Keep fp3 < 10*fp2
CLoad 1u
4),5) Plot Aol and 1/Beta for Compensated Circuit
40
6) Plot Compensated Closed-Loop Gain
CF 1.44n
RI 499
RF 49.9k
V-
+
Vo
+
+
U1 OPA627E
CLoad 1u
VG1
V+
C2 1u
V+
C3 1u
V1 15
V2 15
V-
41
7) Plot Compensated Transient Response
CF 1.44n
C2 1u
V+
V1 15
RI 499
RF 49.9k
C3 1u
V-
Vo
+
V2 15
V-
+
+
U1 OPA627E
VG1
CLoad 1u
V+
42
High Gain and CF Summary
1) Select CF between CF(min) and CF(max) for stability
2) CF(min) and CF(max) produce similar phase-margins
3) CF(min) will have the largest closed-loop bandwidth and fastest transient
response
4) CF(max) will produce the smallest closed-loop BW and the slowest transient
response
5) Selecting a value between CF(min) and CF(max) will produce the most robust
design
43
7) CF Non-Inverting
(Input Cload)
44
Op Amp Input Capacitance
VEE 18V
INCcm- 7pF
Cdiff 10pF
IN+
+
U1 OPA140
VOUT
+
Ccm+ 7pF
OPA140 - Input Capacitance
VCC 18V
45
RI 90kOhm
RF 180kOhm
Op Amp Input Capacitance
VFB
VOUT
1 VOUT

b
VFB
b
V1 18V
Ccm- 7pF
Cdiff 10pF
+
VOUT
+
U2 OPA140
VOUT
RF 180kOhm
VFB
+
V2 18V
Ccm+ 7pF
Cin_eq 17pF
VIN
RI 90kOhm
VFB
RI 90kOhm
RF 180kOhm
Cin_eq 17pF
V3 18V
+
VOUT
+
U3 OPA140
V4 18V
46
Equivalent Input Capacitance and b
VOUT
(Set to 1V)
RF 180kOhm
1/β Computation :
1 RF (RI // X )

β
RI // X
Cin_eq
b
VFB
Cin_eq 17pF
RI 90kOhm
Cin_eq




1
s 
  Cin _ eq  RF  RI
RF

RI



Cin _ eq  


1
RF

RI

 

 (after simplification)
β
RI
1
RF  RI
RF
180k
DC 
 1
 1
 3  9.54dB
β
RI
RI
90k
1
1
1
zero: fz1 

 156kHz
β
2π  Cin_eq  (RF // RI) 2π  17pF  (180k // 90k)
47
CF Compensation Design Steps
1) Determine fz1 in 1/b due to Cin_eq
A) Measure in SPICE
OR
B) Compute by Datasheet CDIFF and CCM and Circuit RF and RI
2) Plot 1/b with fz1 on original Aol
3) Add Desired fp1 on 1/b for CF Compensation
A) Keep fp < 10*fz
B) Keep fp < 1/10 * fcl
4) Compute value for CF based on plotted fp
5) Check CF Compensation by 1/β plot on Aol
6) SPICE simulation with CF for Loop Gain (Aolb) Magnitude and Phase
7) Adjust CF Compensation if greater Loop Gain (Aolb) phase margin desired
8) Check closed loop AC response for VOUT/VIN
A) Look for peaking which indicates marginal stability
B) Check if closed AC response is acceptable for end application
9) Check Transient response for VOUT/VIN
A) Overshoot and ringing in the time domain indicates marginal stability
48
VFB
1),2),3) Plot Aol, 1/b,
Add fp in 1/b for Stability
T
Aol = Vout/VFB
1/ = 1/VFB
Loop Gain = Vout
140
CT 1TF
RF 180kOhm
+
LT 1TH
RI 90kOhm
V2 18V
Aol
120
+
Vout
+
100
V1 18V
80
Gain (dB)
U1 OPA140
OPA140
Aol and 1/ for High Value RF & RI
60
fz
156kHz
+3dB
40
1/
[A]
20
STABLE
fcl
[B]
0
-20
1/
Add fp
here?
A:(128.264983; 9.542429) B:(156k; 12.552628)
-40
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
49
VG1
4) Compute Value for CF based on location of fp
CF 8.5pF
1/β Computation :
1 (RF // X ) (RI // X

β
RI // X
VFB
CF
RI 90kOhm
RF 180kOhm
Cin_eq
V3 18V
Cin_eq 17pF
-
VOUT
+
+
+
U3 OPA140
V4 18V
VIN
CF 8.5pF
VFB
RI 90kOhm
RF 180kOhm
Cin_eq 17pF
VOUT
Cin_eq
)
Note: Location of fz
changes when CF is added




1


(Cin _ eq  CF) s 


 RI  RF 


Cin
_
eq

CF




1
RF  RI 


  after simplification

b
CF  s  1 
 RF  CF 
1
RF  RI
RF
180k
DC 
 1
 1
 3  9.54dB
β
RI
RI
90k
1
1
zero: fz 
β
2π  (Cin_eq // CF)(RF // RI)
1
1
zero:fz 
 104kHz
β
2π  (25.5pF)(180k // 90k)
1
1
pole: fp 
β
2π  CF  RF
1
1
pole: fp 
 104kHz
β
2π  8.5pF  180k
50
4) Compute Value for CF based on location of fp
Maximum Bandwidth CF Compensation for Cin
For maximum Closed Loop Bandwidth for VOUT / VIN:
1) CF needs to compensate input capacitance of Ccm- only since gain effects of Cdiff are nulled out
(Similar to Non-Inverting Noise Gain op amp configuration)
2) Stability and phase margin are still determined by Cin_eq (Cdiff // Ccm-)
Complete Circuit
Loop Gain Model
Closed Loop VOUT / VIN Model
CF 3.5pF
CF 3.5pF
VFB
RI 90kOhm
RF 180kOhm
VFB
RI 90kOhm
RI 90kOhm
RF 180kOhm
V1 18V
Ccm- 7pF
+
VOUT
+
V3 18V
Cin_eq 17pF
-
-
U2 OPA140
V2 18V
+
+
+
VG1
+
VOUT
+
VOUT
+
U3 OPA140
+
-
VIN
V3 18V
Ccm- 7pF
Cdiff 10pF
Ccm+ 7pF
RF 180kOhm
U3 OPA140
VIN
V4 18V
V4 18V
51
CF 8.5pF
VFB
5) Check CF Compensation
by 1/β on Aol
Aol = Vout/VFB
1/ = 1/VFB
Loop Gain = Vout
Aol
+
Voltage (V)
Vout
+
CF Compensation for Cin
1/ and Aol for OPA140
80
CF
(pF)
1.7
3.5
8.5
170
60
40
20
VG1
V2 18V
-
100
+
140
120
CT 1TF
RF 180kOhm
LT 1TH
T
RI 90kOhm
U1 OPA140
V1 18V
Maximum Closed Loop BW
Cin_eq (1/b) Cin (VOUT/VIN)
(pF)
(pF)
17
7
17
7
17
7
17
7
1/ @ CF=3.5pF
1/ @ CF=1.7pF
0
1/ @ CF=170pF
1/ @ CF=8.5pF
-20
-40
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
52
6),7) Loop Gain Check
CF
(pF)
1.7
3.5
8.5
170
T 140
120
100
Loop Gain
Phase Margin at fcl
Voltage (V)
80
60
40
Cin_eq (1/b) Cin (VOUT/VIN)
(pF)
(pF)
17
7
17
7
17
7
17
7
Vout[1] 1.7p[F] A:(994.855658k; -8.354428f)
Vout[1] 1.7p[F] A:(994.855658k; 59.254896)
20
Vout[2] 3.5p[F] A:(1.548148M; -9.769963f)
Vout[2] 3.5p[F] A:(1.548148M; 73.969004)
0
-20
Maximum Closed Loop BW
Vout[3] 8.5p[F] A:(2.730131M; -13.322676f)
Vout[3] 8.5p[F] A:(2.730131M; 80.688797)
-40
-60
Vout[4] 170p[F] A:(6.997683M; 6.092349f)
Vout[4] 170p[F] A:(6.997683M; 85.056643)
Voltage (V)
180
135
90
45
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
53
CF 8.5pF
RI 90kOhm
8) AC Closed Loop Vout/Vin
RF 180kOhm
V2 18V
-
T 20.00
U1 OPA140
Vout[1]: 1.7p[F]
+
+
Vout
+
Gain (dB)
Vin
V1 18V
Closed Loop Response
VOUT / VIN
Vout[4]: 170p[F]
0.00
CF
(pF)
1.7
3.5
8.5
170
-20.00
Cin_eq (1/b) Cin (VOUT/VIN)
(pF)
(pF)
17
7
17
7
17
7
17
7
Vout[3]: 8.5p[F]
Vout[2]: 3.5p[F]
Maximum Closed Loop BW
45
Vout[1]: 1.7p[F]
Vout[4]: 170p[F]
Phase [deg]
0
-45
Maximum Closed Loop BW
Vout[2]: 3.5p[F]
-90
Vout[3]: 8.5p[F]
-135
1
10
100
1k
10k
Frequency (Hz)
100k
1M
10M
54
CF 8.5pF
9) Transient Analysis
RI 90kOhm
RF 180kOhm
V2 18V
T
5.00m
-
Transient Analysis
VG1
+
+
U1 OPA140
+
-5.00m
32.60m
Vout
Vin
V1 18V
Vout[1]
Vout[1]: 1.7p[F]
-32.42m
18.26m
Vout[2]
Vout[2]: 3.5p[F]
-18.10m
15.09m
Vout[3]
Vout[3]: 8.5p[F]
-14.91m
15.09m
Vout[4]
Vout[4]: 170p[F]
-14.91m
0
550u
Time (s)
1m
55
9) Transient Analysis
T
5.00m
Transient Analysis: Zoom Falling Edge
VG1
-5.00m
15.09m
Vout[4]
Vout[4]: 170p[F]
-14.91m
15.09m
Vout[3]
Vout[3]: 8.5p[F]
-14.91m
18.26m
Vout[2]
Vout[2]: 3.5p[F]
-18.10m
32.60m
Vout[1]
Vout[1]: 1.7p[F]
-32.42m
487.62u
507.98u
Time (s)
528.33u
56
9) Transient Analysis
T
5.00m
VG1
Transient Analysis: Zoom Rising Edge
-5.00m
32.60m
Vout[1]
Vout[1]: 1.7p[F]
-32.42m
18.26m
Vout[2]
Vout[2]: 3.5p[F]
-18.10m
15.09m
Vout[3]
Vout[3]: 8.5p[F]
-14.91m
15.09m
Vout[4]
Vout[4]: 170p[F]
-14.91m
987.38u
1.01m
Time (s)
1.03m
57