Improved Howland Current Pump Stability

Report
Improved Howland Current Pump
Stability
Tim Green
Senior Analog Applications Engineers
Precision Analog Linear Applications
July 19, 2013
1
Improved Howland Current Pump
IL Accuracy Circuit
RT allows for trim to optimum ZOUT and improved DC Accuracy
RT 0
RF 5k
RI 1k
VM 100m
X1G
-
RS 5
-
VL
RZ 1k
VP 200m
+
VCV1
Ideal Op Amp
VO
+
A
RX 5k
RX  RF
RS 
RF  RX



VP 

 1 
 VM   


 RZ  RI
 RZ
 RI  RZ
IL 
 RS   1  RX    RS  RX   RF  RL
 
 


RL
RZ
RZ
RI
 
 


IL
RL 10
+
1 

2
Improved Howland Current Pump
V-I DC Accuracy Calculations
RT
2.858407
0
2.858407
2.858407
2.858407
2.858407
2.858407
2.858407
RF
RX
5000 5000
5000 5000
5050 5000
5000 5050
5000 5000
5000 5000
5000 5000
5000 5000
0
2.858407
5050
5050
4950
4950
RI
RZ
RS
RL
1000 1000
5
10
1000 1000
5
10
1000 1000
5
10
1000 1000
5
10
1010 1000
5
10
1000 1010
5
10
1000 1000 5.05
10
1000 1000
5 10.1
990
990
1010
1010
4.95
4.95
IL
0.100000052
0.099866893
0.102371216
0.098700599
0.097727653
0.101353602
0.099009365
0.099999329
10 0.108995522
10 0.109152449
VL
1.000000100
0.998668931
1.023712000
0.987005991
0.977276527
1.013536000
0.990094651
1.009993000
VO
1.500667000
1.498669000
1.536255000
1.481159000
1.466563000
1.520981000
1.490756000
1.510665000
1.089955000 1.630222000
1.091524000 1.632570000
AM1 Sensitivity
(%)
0.000000000
0.133158931
-2.371162767
1.299452324
2.272397818
-1.353549296
0.990686485
0.000723
Comments
Rt adjusted for Ideal IL
Rt=0, Nominal Values
1% Resistor Changes
1% Resistor Changes
1% Resistor Changes
1% Resistor Changes
1% Resistor Changes
1% Resistor Changes
-8.995465322 1% Worst Case w/RT=0)
-9.152392241 1% Worst Case w/RT=Nom)
1% Resistors (w/RT=0) could yield only 9% Accuracy at T=25°C
Still useful for V-I control in Motors/Valves  V-Torque Control
Outer position feedback adjusts V for final position
3
Improved Howland Current Pump
Simplified Equation
RF 5k
RI
RS
RI 1k
-
RI 1k
Imon
VO
Iflag
RS 5
U1 OPA569
VL
+ +
En
VP 200m
Tflag
R3 500k
VM 100m
Iset
R5 500k
IL 
RF
R4 500k
( VP  VM ) 
Rset 5.76k
Assume:
RF = RX
RI = RZ
RF>>RS
RF>>RL
LL 30m
RL 3
Vs+ 5
+
RF 5k
A
IL
4
Improved Howland AC Analysis
RI 1k
-
RZ1k
Imon
VO
Iflag
RS5
U1OPA569
VL
+ +
En
RI
VP 200m
Tflag
R3 500k
VM 100m
Iset
R5 500k
-
R4 500k
Rset 5.76k
RF5k
LL 30m
RL3
Vs+ 5
+
RF
RX5k
+
A
IL
Op Amp sees differential [(-IN) – (+IN)] feedback
 = - - + (Must be positive number else oscillation!)
5
Improved Howland AC Analysis

1/ =

Aol
1
(-) - (+)
VOUT
+
+
6
Improved Howland 1/ Plot - Full Load
120
OPA569 Aol
100
Gain (dB)
fp
31.83kHz
80
1/
RO=Full Load
60
STABLE
40
fz
44.08Hz
20
0
1
10
100
1K
10K
Frequency (Hz)
100K
1M
10M
7
Improved Howland 1/ Calculation
No Load & Full Load
IL
RO
No Load 0A 6.29W
fz
fp
DC 1/
Hi-f 1/
75.8Hz 31.83kHz 17.62dB 77.17dB
Full Load 1A 0.308W 44.08Hz 31.83kHz 19.45dB 77.15dB
Change in RO from No Load to Full Load
has no significant impact on the 1/ Plot
8
Improved Howland
Tina Transient Analysis Circuit
+/-10mV
100Hz
-
RI
Iset
Imon
R5 500k
VO
Iflag
RS 5
VL
U1 OPA569
RZ 1k
+ +
En
VP 500m
Tflag
R3 500k
VG2
+
RI 1k
R4 500k
Rset 5.76k
RF 5k
LL 30m
RL 3
Vs+ 5
+
RX 5k
A
IL
RF
9
Improved Howland
Tina Transient Analysis Results
T
514.33m
IL
476.55m
10.00m
VG2
-10.00m
2.57
STABLE
VL
-2.94
4.97
VO
-414.75m
0.00
5.00m
10.00m
Time (s)
15.00m
20.00m
10
Improved Howland
Modified 1/ for Stability
120
OPA569 Aol
100
Gain (dB)
fp
31.83kHz
80
+ FB#2 to
Modify 1/
1/
RO=Full Load
60
fz1
40
fz
44.08Hz
Modified 1/
20
0
1
10
100
1K
10K
Frequency (Hz)
100K
1M
10M
11
Improved Howland AC Analysis
Final Design for Stability
+
VP 200m
RZ 1k
Imon
LT 1G
Iflag
En
RS 5
VCV1
+
+
U1 OPA569
+ +
Cf 270n Rd 13k
VM 100m
Vbeta
Iset
VOA
VT
VO
VL
RO 309m
Tflag
-
CT 1G
-
LL 30m
+
RI
-
RO = 6.29 No Load
RO = 0.308 Full Load
R3 500k
V
R5 500k
Rset 5.76k
RI 1k
R4 500k
RF 5k
VM
Aol = VO/Vbeta
1/Beta = VT/Vbeta
Loop Gain = VO/VT
VG1
RL 3
Vs+ 5
+
A
IL
RX 5k
VP
RF
12
Improved Howland AC Analysis
1/ - Final Design for Stability
fcl
13
Improved Howland AC Analysis
Loop Gain - Final Design for Stability
fcl
14
Improved Howland AC Transfer Analysis
IL/VIN - Final Design for Stability
RI
En
Cd 270n
Rd 13k
+ +
VP 500m
Imon
Iflag
RS 5
VL
U1 OPA569
RZ 1k
VIN
Iset
VO
Tflag
R3 500k
+
-
R5 500k
RI 1k
R4 500k
Rset 5.76k
RF 5k
LL 30m
RL 3
Vs+ 5
+
RX 5k
A
IL
RF
15
Improved Howland AC Transfer Analysis
IL/VIN - Final Design for Stability
16
Improved Howland Transient Analysis
IL/VIN - Final Design for Stability
-
VP 500m
Imon
VO
Iflag
RS 5
VL
U1 OPA569
RZ 1k
+ +
En
Tflag
R3 500k
+/-10mV
100Hz
RI
Cf 270n Rd 13k
+
VIN
Iset
R5 500k
RI 1k
R4 500k
Rset 5.76k
RF 5k
LL 30m
RL 3
Vs+ 5
+
RX 5k
A
IL
RF
17
Improved Howland Transient Analysis
IL/VIN - Final Design for Stability
T
510.68m
IL
489.03m
10.00m
VIN
-10.00m
2.50
VL
12.44m
4.96
VO
2.55
0.00
5.00m
10.00m
Time (s)
15.00m
20.00m
18

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