1 Improved Howland Current Pump Stability Tim Green Senior Analog Applications Engineers Precision Analog Linear Applications July 19, 2013
Jan 01, 2016
1
Improved Howland Current Pump Stability
Tim GreenSenior Analog Applications EngineersPrecision Analog Linear Applications
July 19, 2013
2
Improved Howland Current PumpIL Accuracy Circuit
RS 5
RF 5kRI 1k
RZ 1k
RX 5k
RL
10
VO
VL
VM 100m
VP 200m
-
+
-
+VCV1
RT 0
A+
IL
X1G
RT allows for trim to optimum ZOUT and improved DC Accuracy
IL
VPRX
RZ
RF
RI1
RS
RZ
VMRF
RI
RX
RZ1
RS
RL1
RX
RZ
RS RXRZ
RF
RI
RL
Ideal Op Amp
3
Improved Howland Current PumpV-I DC Accuracy Calculations
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 ControlOuter position feedback adjusts V for final position
RT RF RX RI RZ RS RL IL VL VOAM1 Sensitivity
(%) Comments2.858407 5000 5000 1000 1000 5 10 0.100000052 1.000000100 1.500667000 0.000000000 Rt adjusted for Ideal IL
0 5000 5000 1000 1000 5 10 0.099866893 0.998668931 1.498669000 0.133158931 Rt=0, Nominal Values2.858407 5050 5000 1000 1000 5 10 0.102371216 1.023712000 1.536255000 -2.371162767 1% Resistor Changes2.858407 5000 5050 1000 1000 5 10 0.098700599 0.987005991 1.481159000 1.299452324 1% Resistor Changes2.858407 5000 5000 1010 1000 5 10 0.097727653 0.977276527 1.466563000 2.272397818 1% Resistor Changes2.858407 5000 5000 1000 1010 5 10 0.101353602 1.013536000 1.520981000 -1.353549296 1% Resistor Changes2.858407 5000 5000 1000 1000 5.05 10 0.099009365 0.990094651 1.490756000 0.990686485 1% Resistor Changes2.858407 5000 5000 1000 1000 5 10.1 0.099999329 1.009993000 1.510665000 0.000723 1% Resistor Changes
0 5050 4950 990 1010 4.95 10 0.108995522 1.089955000 1.630222000 -8.995465322 1% Worst Case w/RT=0)2.858407 5050 4950 990 1010 4.95 10 0.109152449 1.091524000 1.632570000 -9.152392241 1% Worst Case w/RT=Nom)
4
Improved Howland Current PumpSimplified Equation
RS 5
RF 5k
RI 1k
RI 1k
RF 5k
RL 3
VO
VLVM 100m
VP 200m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569
Rse
t 5
.76
k
R4
50
0k
R3
50
0k
R5
50
0k
LL 30m
A+
IL
Assume:RF = RXRI = RZRF>>RSRF>>RL
IL
VP VM( )RF
RI
RS
5
RS 5
RF 5k
RI 1k
RZ 1k
RX 5k
RL 3
VO
VLVM 100m
VP 200m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569
Rse
t 5.7
6k
R4
500
k
R3
500
k
R5
500
k
LL 30m
A+
IL
-
+
Improved Howland AC Analysis
Op Amp sees differential [(-IN) – (+IN)] feedback = - - + (Must be positive number else oscillation!)
RF
RI
6
Improved Howland AC Analysis
+
Aol VOUT
1/ = 1 (-) - (+)
+
-
7
Improved Howland 1/ Plot - Full Load
1 10 100 1K 10K 100K 1M 10M
Frequency (Hz)
Gai
n (d
B)
0
20
40
60
80
100
120
OPA569 Aol
fz44.08Hz
fp31.83kHz
1/RO=Full Load
STABLE
8
Improved Howland 1/ CalculationNo Load & Full Load
IL RO fz fp DC 1/ Hi-f 1/
No Load 0A 6.29 75.8Hz 31.83kHz 17.62dB 77.17dB
Full Load 1A 0.308 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
9
Improved Howland Tina Transient Analysis Circuit
RS 5
RF 5k
RI 1k
RZ 1k
RX 5k
RL 3
VO
VL
VP 500m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569
Rse
t 5
.76
k
R4
50
0k
R3
50
0k
R5
50
0k
LL 30m
A+
IL
+VG2
+/-10mV
100Hz
RF
RI
10
Improved Howland Tina Transient Analysis Results
T
Time (s)
0.00 5.00m 10.00m 15.00m 20.00m
IL
476.55m
514.33m
VG2
-10.00m
10.00m
VL
-2.94
2.57
VO
-414.75m
4.97
STABLE
11
Improved HowlandModified 1/ for Stability
1 10 100 1K 10K 100K 1M 10M
Frequency (Hz)
Gai
n (d
B)
0
20
40
60
80
100
120
OPA569 Aol
fz44.08Hz
fp31.83kHz
1/RO=Full Load
+ FB#2 toModify 1/
Modified 1/
fz1
12
Improved Howland AC AnalysisFinal Design for Stability
RS 5
RF 5k
RI 1k
RZ 1k
RX 5k
RL 3
VO
VLVM 100m
VP 200m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569R
set
5.7
6k
R4
50
0k
R3
50
0k
R5
50
0k
LL 30m
A+
IL
RO 309m
-
+
-
+VCV1LT 1G
CT 1G
VT
+
VG1
VOA
VM
VP
V+
Vbeta
Rd
13
kC
f 2
70
nAol = VO/Vbeta
1/Beta = VT/Vbeta
Loop Gain = VO/VT RO = 6.29 No Load
RO = 0.308 Full Load
RF
RI
13
Improved Howland AC Analysis1/ - Final Design for Stability
T
OPA569 Aol
1/Beta
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
OPA569 Aol
Aol A:(43.22; 89.66) B:(417.02; 69.97) Beta1 A:(43.22; 23.15) B:(417.02; 37.01)
1/Beta
a b
fcl
14
Improved Howland AC AnalysisLoop Gain - Final Design for Stability
T
Loop Gain
Loop Gain
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-80.00
-60.00
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-45.00
0.00
45.00
90.00
Gain : Loop A:(13.43k; -38.44m)
Phase : Loop A:(13.43k; 87.84)
Loop Gain
Loop Gain
a
fcl
15
RS 5
RF 5k
RI 1k
RZ 1k
RX 5k
RL 3
VO
VL
VP 500m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569
Rse
t 5
.76
k
R4
50
0k
R3
50
0k
R5
50
0k
LL 30m
A+
IL
+
VIN
Rd
13
kC
d 2
70
n
Improved Howland AC Transfer AnalysisIL/VIN - Final Design for Stability
RF
RI
16
Improved Howland AC Transfer AnalysisIL/VIN - Final Design for Stability
T
IL/VIN
IL/VIN
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-140.00
-120.00
-100.00
-80.00
-60.00
-40.00
-20.00
0.00
20.00
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-90.00
-45.00
0.00
45.00
90.00
135.00
180.00
Gain : IL A:(393.63; -2.18)
Phase : IL A:(393.63; 135.34)
IL/VIN
IL/VIN
a
17
Improved Howland Transient AnalysisIL/VIN - Final Design for Stability
RS 5
RF 5k
RI 1k
RZ 1k
RX 5k
RL 3
VO
VL
VP 500m
Vs+ 5
+
-
+
Iset
En
Imon IflagIflag
Tflag
U1 OPA569
Rse
t 5
.76
k
R4
50
0k
R3
50
0k
R5
50
0k
LL 30m
A+
IL
+VIN
Rd
13
kC
f 2
70
n
+/-10mV
100Hz
RF
RI
18
Improved Howland Transient AnalysisIL/VIN - Final Design for Stability
T
Time (s)
0.00 5.00m 10.00m 15.00m 20.00m
IL
489.03m
510.68m
VIN
-10.00m
10.00m
VL
12.44m
2.50
VO
2.55
4.96