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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