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Transcript of 1 Tim Green High Current V-I Circuits. 2 Review - Essential Principles Poles, Zeros, Bode Plots Op...
1Tim Green
OUTIN+
-Volts Amps
+
-High Current V-I Circuits
2
Review - Essential Principles
Poles, Zeros, Bode Plots Op Amp Loop Gain Model Loop Gain Test β and 1/β Rate-of-Closure Stability Criteria Loop Gain Rules-of-Thumb for Stability RO and ROUT
3
R
CVIN
VOUT
A = VOUT/VIN
Single Pole Circuit Equivalent
X100,000
Poles and Bode Plots
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°
Decade Below fP Phase = 0°
A(dB) = 20Log10(VOUT/VIN)
+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
ActualFunction
Straight-Line Approximation
4
Zeros and Bode Plots
R
C
VOUT
A = VOUT/VIN
Single Zero Circuit Equivalent
X100,000
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°
Decade Below fZ Phase = 0°
A(dB) = 20Log10(VOUT/VIN)
+90
-90
+45
+-45
10 100 1k 10k 100k 1M 10M
Frequency(Hz)
0
(d
egr
ees)
+90o
0o
+45o/Decade
+45o @ fZ
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
fZ
+20dB/Decade+6dB/Octave
Straight-Line Approximation
G
1.414G = +3dB(1/0.707)G = +3dB Actual
Function
5
Op Amp: Intuitive Model
+
-
K(f)
VDIFF
IN+
IN-
RIN
RO
VO
VOUTx1
6
Op Amp Loop Gain Model
+
-
RF
RI
VIN
+
-
network
Aol+
-
VOUTVIN
VFBVOUT
VFB
RF
RI
=VFB/VOUT
VOUT
network
VOUT/VIN = Acl = Aol/(1+Aolβ)
If Aol >> 1 then Acl ≈ 1/β
Aol: Open Loop Gain
β: Feedback Factor
Acl: Closed Loop Gain
1/b
= S
mal
l Sig
nal A
C G
ain
b=
feed
back
att
enua
tion
7
Stability Criteria
VOUT/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 GainAolβ = -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°
8
Traditional Loop Gain Test
+
-
RF
RI
VIN
+
-
network
VFB
VOUT
Op Amp Loop Gain Model
Op Amp is “Closed Loop”
SPICE Loop Gain Test:
Break the Closed Loop at VOUT
Ground VIN
Inject AC Source, VX, into VOUT
Aolβ = VY/VX+
-
RF
RI
VIN
+
-
network
VFB
VOUT
+
-VX
VY
1GF
1GH
Short for ACOpen for DC
Open for ACShort for DC
9
β and 1/β
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
10
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
Aol
(dB
)
fcl Acl
Aol
Aol (Loop Gain)
Closed Loop Response
Open Loop Response
Plot (in dB) 1/β on Op Amp Aol (in dB)
Aolβ = Aol(dB) – 1/β(dB)
Note how Aolβ changes with frequency
Proof (using log functions):
20Log10[Aolβ] = 20Log10(Aol) - 20Log10(1/β)
= 20Log10[Aol/(1/β)]
= 20Log10[Aolβ]
Loop Gain Using Aol & 1/β
11
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
Rate-of-Closure @ fcl =(Aol slope – 1/β slope)
*20dB/decade Rate-of-Closure @ fcl = STABLE
**40dB/decade Rate-of-Closure@ fcl = UNSTABLE
12
180
0
135
45
10 100 1k 10k 100k 1M 10M
Frequency(Hz)
90
(d
egre
es)
-45
fp1
fp2 fz1
fcl
45o
“Phase Margin”
-135o
“Phase Shift”
Loop Gain Bandwidth Rule: 45 degrees for f < fcl
Aolβ (Loop Gain) Phase Plot
Loop Stability Criteria: <-180 degree phase shift at fclDesign for: <-135 degree phase shift at all frequencies <fclWhy?: Because Aol is not always “Typical”Power-up, Power-down, Power-transient Undefined “Typical” AolAllows for phase shift due to real world Layout & Component Parasitics
13
Poles & Zeros Transfer: (1/β, Aol) to Aolβ
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
Aol
fcl
fp1
fp2fz1
Aol
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
fp1
fz1
fp2
fcl
Aol & 1/β Plot Loop Gain Plot(Aolβ)
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]
14
Frequency Decade Rules for Loop Gain
+
-
+
-VIN
RI
RF
VOUT
CL
CnRn
0
20
40
60
80
100
10M1M100k10k1k100101
Frequency (Hz)
A (
dB)
fcl
fp1
fp2
fz1
fp3
Aol
1/Beta
VOUT/VIN
Loop Gain View: Poles: fp1, fp2, fz1; Zero: fp3
Rules of Thumb for Good Loop Stability:
Place fp3 within a decade of fz1 fp1 and fz1 = -135° phase shift at fz1 fp3 < decade will keep phase from dipping further
Place fp3 at least a decade below fcl Allows Aol curve to shift to the left by one decade
15
Op Amp Model for Derivation of ROUT
+
-
RDIFF
xAol
RO-IN
+IN
-
+
VE
Op Amp Model
1A
VOUT
VO
RF
RI
IOUTVFB
ROUT = VOUT/IOUTFrom: Frederiksen, Thomas M. Intuitive Operational Amplifiers. McGraw-Hill Book Company. New York. Revised Edition. 1988.
ROUT = RO / (1+Aolβ)
16
Op Amp Model for Loop Stability Analysis
RO is constant over the Op Amp’s bandwidth
RO is defined as the Op Amp’s Open Loop Output Resistance
RO is measured at IOUT = 0 Amps, f = 1MHz (use the unloaded RO for Loop Stability calculations since it will be the largest
value worst case for Loop Stability analysis)
RO is included when calculating b for Loop Stability analysis
17
RO & Op Amp Output Operation
Bipolar Power Op Amps CMOS Power Op Amps Light Load vs Heavy Load
18
RO Measure w/DC Operating Point: IOUT = 0mA
BipolarAll NPN Output
V+
V-
VOUT
19
RO Measure w/DC Operating Point: IOUT = 0mA
RO = VOA / AM1RO = 9.61mVrms / 698.17μArms RO = 13.765Ω
20
RO Measure w/DC Operating Point IOUT = 4.45mA Sink
21
RO Measure w/DC Operating Point IOUT = 4.45mA Sink
RO = VOA / AM1RO = 3.45Vrms / 706.25µArms RO = 4.885Ω
22
RO Measure w/DC Operating Point IOUT = 5.61mA Source
23
RO Measure w/DC Operating Point IOUT = 5.61mA Source
RO = VOA / AM1RO = 3.29mVrms / 700.98μArms RO = 4.693Ω
24
RO Measure w/DC Operating Point IOUT = 2.74A Source
25
RO Measure w/DC Operating Point IOUT = 2.74A Source
RO = VOA / AM1RO = 314.31uVrms / 550.1μArms RO = 0.571Ω
26
RO Measure w/DC Operating Point IOUT = 2.2A Sink
27
RO Measure w/DC Operating Point IOUT = 2.2A Sink
RO = VOA / AM1RO = 169.92uVrms / 635.16μArms RO = 0.267Ω
28
RO Measure w/DC Operating Point IOUT = 0A
V+
VOUT
MOSFETComplementary
Output
29
RO Measure w/DC Operating PointIOUT = 0A
RO = VOA / AM1RO = 4.42mVrms / 702.69μArms RO = 6.29Ω
30
RO Measure w/DC Operating PointIOUT = 1A Sink
31
RO Measure w/DC Operating PointIOUT = 1A Sink
RO = VOA / AM1RO = 166.76μVrms / 540.19μArms RO = 0.309Ω
32
RO Measure w/DC Operating PointIOUT = 1A Source
33
RO Measure w/DC Operating PointIOUT = 1A Source
RO = VOA / AM1RO = 166.61μVrms / 540.34μArms RO = 0.308Ω
34
Non-Inverting Floating Load V-I
Basic Topology Stability Analysis (w/effects of Ro)
1/b & Aol TestLoop Gain TestTransient Test
Small Signal BW for Current Control
35
Non-Inverting V-I Floating Load
V+ 15
V- 15
+
VINLL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VOA
VRS
VP
IOUT
IOUT = VP / RSIOUT = (R2*VIN) / (R1A + R1B + R2) / RS
+5V3.03A
-5V-3.03A
VP
VP
VP
Op Amp Point of Feedback is VRSOp Amp Loop Gain forces +IN (VP) = -IN = VRS
+1V -1V
36
Non-Inverting V-I Floating LoadRO Reflected Outside of Op Amp
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VRS
VP
VFB
VOA
+
VIN
V1 0
-
+
-
+VCV1 RO 13.77
VO
RO = 13.765 @ No Load
RO = 0.267 @ Full Load
x1
FB#1
37
Non-Inverting V-I Floating LoadFB#1 DC 1/b Derivation
LL 15m
RL 1.5
RS 330m
VRS
VOA
-
+
-
+VCV1 RO 13.77
VO
RF 1kVFB
+
-
+
Ilim
E/S
U2 OPA548
x1
DC Beta FB#1 = VFB/VO
VFB = VO*RS RO+RL+RS
Set VO = 1
VFB = RSVO (RO+RL+RS)
DC 1/Beta FB#1 = VO/VFB
VO = (RO+RL+RS)VFB RS
VO = (13.77+1.5+0.33)VFB 0.33
VO = 47.27 33.49dBVFB
20Log10 (47.27) = 33.49dB
FB#1 DC 1/BetaLL is a SHORT
38
Non-Inverting V-I Floating LoadFB#1 1/b Derivation
LL 15m
RL 1.5
RS 330m
VRS
VOA
-
+
-
+VCV1 RO 13.77
VO
RF 1kVFB
+
-
+
Ilim
E/S
U2 OPA548
x1
Beta FB#1 = VFB/VO
VFB = VO*RS RO+XLL+RL+RS
XLL = jLL
Set VO = 1
VFB = RSVO (RO+RL+RS) + jLL
VFB = RS / LLVO (RO+RL+RS) + j LL
Pole in Beta FB#1:fp = Ro+RL+RS 2LL
1/Beta FB#1 = VO/VFB
VO = (RO+RL+RS) + jLLVFB RS
VO = (RO+RL+RS) + jVFBLL RS / LL
Zero in 1/Beta FB#1:fz = Ro+RL+RS 2LL
fz = 13.77+1.5+0.33 215mH
fz = 165Hz
39
Non-Inverting V-I Floating LoadFB#1 1/ b Data for RO No Load & Full Load
IOUT RO fz DC 1/b
No Load 0A 13.765W 165Hz 33.49dB
Full Load 1A 0.267W 22.25Hz 16.06dB
40
OPA548 Data Sheet Aol
41
1 10 100 1K 10K 100K 1M 10M
Frequency (Hz)
Gai
n (d
B)
0
20
40
60
80
100
120
OPA548 Aol
1/ FB#1 w/RO=13.765
1/ FB#1 w/RO=0.267
fz
fz
Non-Inverting V-I Floating LoadFB#1 1/b Plot for RO No Load & Full Load
STABLE
42
Non-Inverting V-I Floating LoadFB#1 1/b Tina SPICE
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VRS
VP
VFB
VOA2
-
+
-
+VCV1 LT 1G
CT 1G
+
VG1
VTVOA
RO 13.77
RO = 13.765 @ No Load
RO = 0.267 @ Full Load
1/Beta FB#1 = VT/VFB
Aol = VOA/VFB
Loop Gain = VOA/VT
43
Non-Inverting V-I Floating LoadFB#1 1/b Tina SPICE Results
T
OPA548 Aol
1/Beta FB#1RO = 13.77 ohms
Frequency (Hz)
10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
OPA548 Aol
1/Beta FB#1RO = 13.77 ohms
STABLE
44
Non-Inverting V-I Floating LoadFB#1 1/b Tina SPICE Results
T
OPA548 Aol
1/Beta FB#1
RO = 0.267 ohms
Frequency (Hz)
10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
1/Beta FB#1
RO = 0.267 ohms
OPA548 Aol
STABLE
45
Non-Inverting V-I Floating LoadFB#1 Loop Gain Tina SPICE Results
TLoop Gain Magnitude
RO = 0.267 ohms
Loop Gain Phase
RO = 0.267 ohms
Frequency (Hz)
10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
Frequency (Hz)
10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-45.00
0.00
45.00
90.00
135.00
180.00
fcl
Loop Gain Phase
RO = 0.267 ohms
Loop Gain Magnitude
RO = 0.267 ohms
a
STABLE
46
Non-Inverting V-I Floating LoadFB#1 Transient Analysis Tina SPICE Circuit
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VRS
VP
VOA2
-
+
-
+VCV1
VOA
RO 267m
V1 0
+
VG1
A+
AM1
RO = 13.765 @ No Load
RO = 0.267 @ Full Load
100Hz
330mVpk
tr=tf =10ns
47
Non-Inverting V-I Floating LoadFB#1 Transient Analysis Tina SPICE Results
T
Time (s)
0.00 5.00m 10.00m 15.00m 20.00m
AM1
-252.74m
282.89m
VG1
-330.00m
330.00m
VOA
-14.74
13.25
VOA2
-14.79
13.30
VP
-66.20m
68.12m
VRS
-83.40m
93.35m
STABLE
48
Non-Inverting V-I Floating LoadAdd FB#2 and Predict 1/b
1 10 100 1K 10K 100K 1M 10M
Frequency (Hz)
Ga
in (
dB)
0
20
40
60
80
100
120
OPA548 Aol
1/ FB#1 w/RO=13.765
1/ FB#1 w/RO=0.267
fz
fz
fz140Hz
36dB
FB#1
FB#2
1/
Note: Load Current Control begins to roll-off in frequency where FB#2 dominates
49
-
Large β
Small β
Answer:
The largest β (smallest 1/β) will dominate!
How will the two feedbacks combine?
50
Non-Inverting V-I Floating LoadFB#2 Circuit
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VRS
VP
VFB
VOA2
-
+
-
+VCV1 LT 1G
+
VT
VTVOA
RO 267m
Rd 61.9k CF 68n
CT 1G
RO = 13.765 @ No Load
RO = 0.267 @ Full Load1/Beta = VT/VFB
Aol = VOA/VFB
Loop Gain = VOA/VT
Ope
n FB
#1
Analy
ze F
B#2
Separ
ate
FB#2
FB#1
51
Non-Inverting V-I Floating LoadFB#2 High Frequency 1/b
RO 13.77
Rd 61.9k
RF 1k
CF 68n
RS 330m
VOA
VFB
Hi-F Beta FB#2 = VFB/VO
Hi-F Beta FB#2 = 1/63 = 0.15848931
Set VO = 1Beta=VFB
IFB = VFB/(RF+RS)IFB = 0.15848931/(1k+0.33)=15.85uA
VOA-VFB = Rd IFB
1 - 0.15848931 = 62.09k use 61.9k 15.85uA
Hi-f 1/Beta FB#2 = VOA/VFB
Hi-f 1/Beta FB#2 = 36dB
36dB 10(36/20) = 63
FB#2 High Frequency 1/BetaCF is a SHORT
IFB
52
Non-Inverting V-I Floating LoadFB#2 fz1
RO 13.77
Rd 61.9k
RF 1k
CF 68n
RS 330m
VOA
VFB
FB#2 1/Beta - fz1
fz1 = 1 2CF*(RO+Rd+RF+RS)
But if: Rd > 10*RF Rd > 10*RS Rd > 10*RoThen:fz1 1 2CF*Rd
CF 1 2fz1*Rd
CF = 1 = 64.2nF 240Hz*61.9k
Use: CF = 68nF
53
Non-Inverting V-I Floating LoadTina SPICE Loop Test
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Ilim
E/S
U2 OPA548
VRS
VP
VFB
VOA2
-
+
-
+VCV1 LT 1G
+
VT
VTVOA
RO 267m
Rd 61.9k CF 68n
CT 1G
RO = 13.765 @ No Load
RO = 0.267 @ Full Load1/Beta = VT/VFB
Aol = VOA/VFB
Loop Gain = VOA/VT
54
Non-Inverting V-I Floating LoadAol and 1/b Tina SPICE Results
T
Aol
1/Beta
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
aol A:(21.54; 87.71) B:(197.05; 75.74) beta1 A:(21.54; 19.14) B:(197.05; 33.04)
1/Beta
Aol
a b
55
Non-Inverting V-I Floating LoadLoop Gain Tina SPICE Results
T
Loop Gain Magnitude
Loop Gain Phase
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-60.00
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
45.00
90.00
135.00
180.00
fcl
Gain : loop A:(20.02k; -135.8m)
Phase : loop A:(20.02k; 89.43)
Loop Gain Phase
Loop Gain Magnitude
a
56
Non-Inverting V-I Floating LoadIOUT/VIN AC Response Circuit
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Il im
E/S
U2 OPA548
VRS
VP
VFB
VOA2
-
+
-
+VCV1
VOA
RO 267m
Rd 61.9k CF 68n+
VIN A+
IOUT
RO = 13.765 @ No Load
RO = 0.267 @ Full Load1/Beta = VT/VFB
Aol = VOA/VFB
Loop Gain = VOA/VT
57
Non-Inverting V-I Floating LoadIOUT/VIN AC Tina SPICE Results
T
IOUT / VIN Magnitude
IOUT / VIN Phase
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-160.00
-140.00
-120.00
-100.00
-80.00
-60.00
-40.00
-20.00
0.00
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ph
ase
[de
g]
-270.00
-225.00
-180.00
-135.00
-90.00
-45.00
0.00
Gain : IOUT A:(202.21; -6.45)
Phase : IOUT A:(202.21; -45.23)
IOUT / VIN Phase
IOUT / VIN Magnitude
a
58
Non-Inverting V-I Floating LoadIOUT/VIN Transient Circuit
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
RF 1k
R1B 20k
R2 10k
R1A 20k+
-
+
Il im
E/S
U2 OPA548
VRS
VP
VFB
VOA2
-
+
-
+VCV1
VOA
RO 267m
Rd 61.9k CF 68n
A+
IOUT
+
VIN
RO = 13.765 @ No Load
RO = 0.267 @ Full Load
330mVp
100Hz
tr=tf =10ns
59
Non-Inverting V-I Floating LoadIOUT/VIN Transient Tina SPICE Results
T
Time (s)
0.00 2.50m 5.00m 7.50m 10.00m
IOUT
-197.99m
231.12m
VIN
-330.00m
330.00m
VOA
-7.59
4.06
VRS
-65.33m
76.27m
60
V+ 15
V- 15
+VIN
LL 15m
RL 1.5
RS 330m
RF 2k
+
-
+
Ilim
E/S
U2 OPA548
VOA
VRS
RI 10k
IOUT
Inverting V-I Floating Load
IOUT = -VIN*(RF/RI) / RSIOUT = -VIN*RF/ (RI*RS)
+5V
-3.03A-5V
+3.03A
Op Amp Point of Feedback is VRSOp Amp Loop Gain forces VRS = -VIN (RF/RI)
-1V +1V
Stability Analysis & Compensation Techniques similar to Non-Inverting V-I Floating Load
61
Grounded Load V-IImproved Howland Current
Pump
Basic Topology Stability Analysis (w/effects of Ro)
1/b & Aol TestLoop Gain TestTransient Test
Small Signal BW for Current Control
62
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
63
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)
64
Improved Howland Current PumpGeneral Equation
IL
VP 1RF
RI
RS
RF
RF
RI1
VM
RS 1RI
RF
RL
RF
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
Set RX=RF and RZ=RI
65
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
66
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)] feedbackb = b- - b+ (Must be positive number else oscillation!)
RF
RI
67
Improved Howland AC Analysis
+
Aol VOUT
1/ = 1 (-) - (+)
68
Improved Howland AC AnalysisInclude Effects of RO
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
Aol = VO/Vbeta
1/Beta = VT/Vbeta
Loop Gain = VO/VT RO = 6.29 No Load
RO = 0.308 Full Load
RF
RI
69
Improved Howland b- Calculation
RO 6.29
RF 5k
RI 1k
VO
VM
- = VM/VOSet VO = 1 - = VM
VM = VO * RI RO + RF + RI
VM = 1 * 1k = 0.166492127 6.29 + 5k + 1k
- = 0.166492127
- is constant over frequency since justresistors are in feedback path.
- Calculation
70
Improved Howland b+ Calculation
+ AC Calculation
+ = VP/VOSet VO = 1 + = VP
1/+ Poles and Zeros:Since RF & RI >> RS & RL then:
fz = RO + RS +RL 2*LL
fz = 6.29 + 5 +3 = 75.8Hz 2*30m
fp = RF + RI 2*LL
fp = 5k + 1k = 31.83kHz 2*30m
+ Hi-f:
VP = RI RF + RI + RO + RS
VP = 1k = 0.166353644 5k + 1k + 6.29 + 5
+ Hi-f = 0.166353644
+ DC Calculation
+ = VP/VOSet VO = 1 + = VP
Since RF & RI >> RS & RL:VL = VO * RL RO + RS + RL
VL = 1 * 3 = 0.2099937018 6.29 + 5 + 3
VP = VL * RI RF+ RI
VP = 0.2099937018 * 1k = 0.03499895 5k +1k
+ DC = 0.03499895
+ Calculation
RO 6.29
RF 5k
RI 1k
VO
VP
RS 5
RL 3
LL 30m
VL
LL Inductor:Short for + DCOpen for + Hi-f
71
Improved Howland 1/b Calculation
Calculation
DC = -) - + DC) DC = 0.166492127 - 0.03499895 = 0.1314937771/ DC = 7.6 17.62dB
Hi-f = (-) - (+ Hi-f)Hi-f = 0.166492127 - 0.166353644 = 0.0001384831/ Hi-f = 7221.1 77.17dB
1/Poles and Zeros directly from 1/+fz = 75.8Hzfp = 31.83kHz
72
Improved Howland b- CalculationRO = Full Load
- = VM/VOSet VO = 1 - = VM
VM = VO * RI RO + RF + RI
VM = 1 * 1k = 0.166658111 308m + 5k + 1k
- = 0.166658111
- is constant over frequency since justresistors are in feedback path.
- CalculationRO = Full Load
RO 308m
RF 5k
RI 1k
VO
VM
73
Improved Howland b+ CalculationRO = Full Load
+ AC Calculation
+ = VP/VOSet VO = 1 + = VP
1/+ Poles and Zeros:Since RF & RI >> RS & RL then:
fz = RO + RS +RL 2*LL
fz = 308m + 5 +3 = 44.08Hz 2*30m
fp = RF + RI 2*LL
fp = 5k + 1k = 31.83kHz 2*30m
+ Hi-f:
VP = RI RF + RI + RO + RS
VP = 1k = 0.166519352 5k + 1k + 308m + 5
+ Hi-f = 0.166519352
+ DC Calculation
+ = VP/VOSet VO = 1 + = VP
Since RF & RI >> RS & RL:VL = VO * RL RO + RS + RL
VL = 1 * 3 = 0.361054278 309m + 5 + 3
VP = VL * RI RF+ RI
VP = 0.361054278 * 1k = 0.060175713 5k +1k
+ DC = 0.060175713
+ CalculationRO = Full Load
LL Inductor:Short for + DCOpen for + Hi-f
RO 308m
RF 5k
RI 1k
VO
VP
RS 5
RL 3
LL 30m
VL
74
Improved Howland 1/b CalculationRO = Full Load
CalculationRO = Full Load
DC = -) - + DC) DC = 0.166658111 - 0.060175713 = 0.1064823981/ DC = 9.39 19.45dB
Hi-f = (-) - (+ Hi-f)Hi-f = 0.166658111 - 0.166519352 = 0.0001387591/ Hi-f = 7206.7 77.15dB
1/Poles and Zeros directly from 1/+fz = 44.08Hzfp = 31.83kHz
75
Improved Howland 1/b CalculationNo Load & Full Load
IL RO fz fp DC 1/b Hi-f 1/b
No Load 0A 6.29W 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 nosignificant impact on the 1/b Plot
76
OPA569 Data Sheet Aol
77
Improved Howland 1/b 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
78
Improved Howland 1/b Tina SPICE Plot - Full Load
T
OPA569 Aol
1/BetaRO=Full Load
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
140.00
Aol A:(44; 89.51) B:(31.34k; 32.47) beta1 A:(44; 22.98) B:(31.34k; 74.07)
1/BetaRO=Full Load
OPA569 Aol
a b
STABLE
79
Improved Howland Loop Gain Tina SPICE Plot - Full Load
T
Loop Gain
Loop Gain
Frequency (Hz)
1 10 100 1k 10k 100k 1M 10M
Ga
in (
dB
)
-100.00
-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]
0.00
45.00
90.00
Loop Gain
Loop Gain
Gain : LoopGain A:(2.4k; 110.92m)
Phase : LoopGain A:(2.4k; 5.29)
a
STABLE
80
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
81
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
82
Improved HowlandModified 1/b 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
83
b+ FB#2 Calculation to Modify 1/b for Stability
RO 308m
RF 5k
RI 1k
VO
VP
RS 5
RL 3
VL
Rd 13k
Cf 270n
LL 30m Inductor is open
for Hi-f Analysis
+ FB#2 Calculation
Capacitor is short for Hi-f Analysis
+ FB#2
If
Ii
Id
(0.15658111)
(1)+ FB#2 Calculation: Hi-f Analysis
Desired 1/ = 40dB x100Desired = 0.01- = 0.166658111
+ = (-) - + = 0.166658111 - 0.01+ = 0.15658111 = VP
If = VO - VP [set VO = 1, RF >> RO, RS] RFIf = 1 - 0.15658111 = 168.68377A 5k
Ii = VP RI
Ii = 0.15658111 = 156.58111A 1k
Id = If - IiId = 168.68377A - 156.58111A Id = 12.10266A
Rd = VP IdRd = 0.15658111 = 12.937743k 12.10266A
Rd = 13k (standard value)
+ FB#2 fz1 Calculation
fz1 = 1 2RdCf
Cf = 1 fz1*2*Rd
Cf = 1 = 0.2782429F 44Hz*2*13k
Cf = 0.27F (standard value)
84
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
85
Improved Howland AC Analysis1/b - 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
86
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
87
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
88
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
89
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
90
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
91
High Current V-I General Checklist
Large Signal & Transient SOA Considerations (V=L*di/dt)
Bipolar Output Stages & Oscillations
High Current Grounding
High Current PCB Traces
High Current Supply Issues
Power Supply Bypass (Low f & High f)
Transient Protection (Supply, VIN, VOUT)
Power Dissipation Considerations (see “V-I Circuits Using External Transistors” section)
Consider:
Short Circuit to Ground Power Dissipation
Heatsink Selection
Current Sense Resistor (RS) Power Dissipation
92
V-I Large Signal Limits: V=Ldi/dt
Laws of Physics dictate:V=Ldi/dtdt = Ldi/V
Rule of Thumb:VLL = VOA - VRL - VRSVLL = VOA - IL*RL - IL*RS
VLL = 12 - 1*1.5 - 1*0.330 = 10.17V
IL dt = LL*dIL/VLLIL dt = 15m*1/10.17 = 1.47msFastest IL/VIN Slew Rate = 1A/1.47msLimit VIN Slew Rate x V-I Gain to match IL/VIN Slew Rate
OPA548 Slew Rate = 10V/usVOA dt = VOA/(Slew Rate)VOA dt = 12V/(10V/us) = 1.2us
Rule of Thumb:VOA dt < (IL dt)/101.2us < 1470us/101.2us < 147usOp Amp Slew Rate < (IL/VIN Slew Rate)/10
V+ 15
V- 15
LL 15m
RL 1.5
RS 330m
+
-
+
Il im
E/S
U2 OPA548 VOA
A+
IL
(12V)
(1A)
93
+15V
-15V
RL
LL
RS
1.5
0.33
30mH
IL
3A
13.17V
+
-
4.5V
+
-0.99V
Instant Current ChangeSteady State Current Flow
+15V
-15V
RL
LL
RS
1.5
0.33
30mH
IL3A
+
-
15V
-15V
+15V
30V
Violate the Laws of Physics and Pay the Price!
94
Instant V-I Reversal SOA Violations
95
Output Stages
-VS
LOAD
fosc > UGBW oscillates unloaded? -- no oscillates with VIN=0? -- no
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.
The Output R-C Snubber Network lowers the high frequency gain of the output stage preventing unwanted oscillations under reactive loads.
+
-
+
-
VIN
RF
RI100k
100k
VOUT
RSN
CSN
10 to 100
F to 1F
PROBLEM SOLUTION
96
Ground Loops
+
-+
- -VS
+VS
RL
RGyRGx
RGv
RGw
RFRI
“Ground”
IL
VIN
VOUT
fosc < UGBW oscillates unloaded? -- no oscillates with VIN=0? -- yes
+
-+
- -VS
+VS
RL
RFRI
RG“Star”
GroundPoint
VIN
VOUT
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.
Parasitic resistances can be made to look like a common mode input by using a “Single-Point” or “Star” ground connection.
SO
LU
TIO
N
PR
OB
LE
M
97
PCB Traces fosc < UGBW oscillates unloaded? -- may or may not oscillates with VIN=0? -- may or may not
DO NOT route high current, low impedance output traces near high impedance input traces.
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.
+
-
+
-
VIN VOUT
RI RF
Rs
GND
98
Supply Lines
GainStage
PowerStage
RLIL
-vs
Rs
+
-
+vs
Ls
CL
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.
fosc < UGBW oscillates unloaded? -- no oscillates with VIN=0? -- may or may not
PROBLEM PROBLEM
99
Proper Supply Line Decouple
+
-
RHF
RHF
CHF
CHF
CLF
CLF
+VS
-VS
< 4 in<10 cm
< 4 in<10 cm
CLF: Low Frequency Bypass
10μF / Amp Out (peak)
Aluminum Electrolytic or Tantalum
< 4 in (10cm) from Op Amp
CHF: High Frequency Bypass
0.1μF Ceramic
Directly at Op Amp Power Supply Pins
RHF: Provisional Series CHF Resistance
1Ω < RHF < 10Ω
Highly Inductive Supply Lines
SOLUTION
100
Transient Protection
V+ 15
V- 15
+
-
+
Ilim
E/S
U2 OPA548
Z1 1N5246
Z2 1N5246
D1 MUR140
D2 MUR140LL 30m
RL 3
C1
10
0n
C3
10
0n
C4
22
uC
2 2
2u
D3 1N4148
D4 1N4148
D5 1N4148
D6 1N4148
D7 1N4148D8 1N4148
T1 2N3369
Anode
Cathode
VIN+
VIN-
CF 100n
+
+
For lower leakage & lowercapacitance use diodeconnected JFET
OUTPUTProtectionINPUT
Protection
POWER SUPPLYProtection
Fast reverse-recovery flybackdiodes rate at least 2x Vsupply
Stack diodes to allow fordifferential overdrive toachieve fastest slew rate
Zeners or Semiconductor Transient Suppressorsprevent Power Supply overvoltage, reverse polarityprotection, low impedance for transient energy fromouptut flyback diodes.
Semiconductor Transient Suppressors have largerjunction areas than zeners and can diddpate largeramounts of power for short periods of time.
High frequency bypass, ceramic (0.1F)Low frequency bypass, Tantalum or Aluminum Electrolytic, (10F per peak amp of output current)
POWER SUPPLYBypass
