1 Tim Green 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  R O and R OUT

3 Poles and Bode Plots  Pole Location = f P  Magnitude = -20dB/Decade Slope  Slope begins at f P and continues down as frequency increases  Actual Function = -3dB f P  Phase = -45°/Decade Slope through f P  Decade Above f P Phase = -90°  Decade Below f P Phase = 0°  A(dB) = 20Log 10 (V OUT /V IN )

4 Zeros and Bode Plots  Zero Location = f Z  Magnitude = +20dB/Decade Slope  Slope begins at f Z and continues up as frequency increases  Actual Function = +3dB f Z  Phase = +45°/Decade Slope through f Z  Decade Above f Z Phase = +90°  Decade Below f Z Phase = 0°  A(dB) = 20Log10(VOUT/VIN)

5 Op Amp: Intuitive Model

6 Op Amp Loop Gain Model V OUT /V IN = Acl = Aol/(1+Aolβ) If Aol >> 1 then Acl ≈ 1/β Aol: Open Loop Gain β: Feedback Factor Acl: Closed Loop Gain 1/  = Small Signal AC Gain  = feedback attenuation

7 Stability Criteria

8 Traditional Loop Gain Test Op Amp Loop Gain Model Op Amp is “Closed Loop” SPICE Loop Gain Test: Break the Closed Loop at V OUT Ground V IN Inject AC Source, V X, into V OUT Aolβ = V Y /V X

9 β and 1/β 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 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): 20Log 10 [Aolβ] = 20Log 10 (Aol) - 20Log 10 (1/β) = 20Log 10 [Aol/(1/β)] = 20Log 10 [Aolβ] Loop Gain Using Aol & 1/β

11 Stability Criteria using 1/β & Aol At fcl: Loop Gain (Aol  ) = 1 fcl = (Aol slope – 1/β slope) *20dB/decade fcl = STABLE **40dB/decade fcl = UNSTABLE

12 Loop Gain Bandwidth Rule: 45 degrees for f < fcl Aolβ (Loop Gain) Phase Plot Loop Stability Criteria: <-180 degree phase shift at fcl Design for: <-135 degree phase shift at all frequencies <fcl Why?: Because Aol is not always “Typical” Power-up, Power-down, Power-transient  Undefined “Typical” Aol Allows for phase shift due to real world Layout & Component Parasitics

13 Poles & Zeros Transfer: (1/β, Aol) to Aolβ Aol & 1/β PlotLoop Gain Plot (Aolβ) To Plot Aolβ from Aol & 1/β Plot: Poles in Aol curve are poles in Aolβ (Loop Gain)Plot Zeros in Aol curve are zeros in Aolβ (Loop Gain) Plot Poles in 1/β curve are zeros in Aolβ (Loop Gain) Plot Zeros 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 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 R OUT From: Frederiksen, Thomas M. Intuitive Operational Amplifiers. McGraw-Hill Book Company. New York. Revised Edition R OUT = R O / (1+Aolβ)

16 Op Amp Model for Loop Stability Analysis  R O is constant over the Op Amp’s bandwidth  R O is defined as the Op Amp’s Open Loop Output Resistance  R O is measured at I OUT = 0 Amps, f = 1MHz (use the unloaded R O for Loop Stability calculations since it will be the largest value  worst case for Loop Stability analysis)  R O is included when calculating  for Loop Stability analysis

17 R O & Op Amp Output Operation  Bipolar Power Op Amps  CMOS Power Op Amps  Light Load vs Heavy Load

18 R O Measure w/DC Operating Point: I OUT = 0mA

19 R O Measure w/DC Operating Point: I OUT = 0mA R O = VOA / AM1 R O = 9.61mVrms / μArms R O = Ω

20 R O Measure w/DC Operating Point I OUT = 4.45mA Sink

21 R O Measure w/DC Operating Point I OUT = 4.45mA Sink R O = VOA / AM1 R O = 3.45Vrms / µArms R O = 4.885Ω

22 R O Measure w/DC Operating Point I OUT = 5.61mA Source

23 R O Measure w/DC Operating Point I OUT = 5.61mA Source R O = VOA / AM1 R O = 3.29mVrms / μArms R O = 4.693Ω

24 R O Measure w/DC Operating Point I OUT = 2.74A Source

25 R O Measure w/DC Operating Point I OUT = 2.74A Source R O = VOA / AM1 R O = uVrms / 550.1μArms R O = 0.571Ω

26 R O Measure w/DC Operating Point I OUT = 2.2A Sink

27 R O Measure w/DC Operating Point I OUT = 2.2A Sink R O = VOA / AM1 R O = uVrms / μArms R O = 0.267Ω

28 R O Measure w/DC Operating Point I OUT = 0A

29 R O Measure w/DC Operating Point I OUT = 0A R O = VOA / AM1 R O = 4.42mVrms / μArms R O = 6.29Ω

30 R O Measure w/DC Operating Point I OUT = 1A Sink

31 R O Measure w/DC Operating Point I OUT = 1A Sink R O = VOA / AM1 R O = μVrms / μArms R O = 0.309Ω

32 R O Measure w/DC Operating Point I OUT = 1A Source

33 R O Measure w/DC Operating Point I OUT = 1A Source R O = VOA / AM1 R O = μVrms / μArms R O = 0.308Ω

34 Non-Inverting Floating Load V-I  Basic Topology  Stability Analysis (w/effects of Ro) 1/  & Aol Test Loop Gain Test Transient Test  Small Signal BW for Current Control

35 Non-Inverting V-I Floating Load IOUT = VP / RS IOUT = {(R2*VIN) / (R1A + R1B + R2)} / RS +5V 3.03A -5V -3.03A VP Op Amp Point of Feedback is VRS Op Amp Loop Gain forces +IN (VP) = -IN = VRS +1V -1V

36 Non-Inverting V-I Floating Load R O Reflected Outside of Op Amp

37 Non-Inverting V-I Floating Load FB#1 DC 1/  Derivation

38 Non-Inverting V-I Floating Load FB#1 1/  Derivation

39 Non-Inverting V-I Floating Load FB#1 1/  Data for R O No Load & Full Load I OUT RORO fz DC 1/  No Load0A  165Hz33.49dB Full Load1A  22.25Hz16.06dB

40 OPA548 Data Sheet Aol

41 Non-Inverting V-I Floating Load FB#1 1/  Plot for R O No Load & Full Load

42 Non-Inverting V-I Floating Load FB#1 1/  Tina SPICE

43 Non-Inverting V-I Floating Load FB#1 1/  Tina SPICE Results

44 Non-Inverting V-I Floating Load FB#1 1/  Tina SPICE Results

45 Non-Inverting V-I Floating Load FB#1 Loop Gain Tina SPICE Results

46 Non-Inverting V-I Floating Load FB#1 Transient Analysis Tina SPICE Circuit

47 Non-Inverting V-I Floating Load FB#1 Transient Analysis Tina SPICE Results

48 Non-Inverting V-I Floating Load Add FB#2 and Predict 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 Load FB#2 Circuit

51 Non-Inverting V-I Floating Load FB#2 High Frequency 1/ 

52 Non-Inverting V-I Floating Load FB#2 fz1

53 Non-Inverting V-I Floating Load Tina SPICE Loop Test

54 Non-Inverting V-I Floating Load Aol and 1/  Tina SPICE Results

55 Non-Inverting V-I Floating Load Loop Gain Tina SPICE Results

56 Non-Inverting V-I Floating Load I OUT /V IN AC Response Circuit

57 Non-Inverting V-I Floating Load I OUT /V IN AC Tina SPICE Results

58 Non-Inverting V-I Floating Load I OUT /V IN Transient Circuit

59 Non-Inverting V-I Floating Load I OUT /V IN Transient Tina SPICE Results

60 Inverting V-I Floating Load IOUT = {-VIN*(RF/RI)} / RS IOUT = -VIN*{RF/ (RI*RS)} +5V -3.03A -5V +3.03A Op Amp Point of Feedback is VRS Op 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-I Improved Howland Current Pump  Basic Topology  Stability Analysis (w/effects of Ro) 1/  & Aol Test Loop Gain Test Transient Test  Small Signal BW for Current Control

62 Improved Howland Current Pump IL Accuracy Circuit RT allows for trim to optimum Z OUT and improved DC Accuracy

63 Improved Howland Current Pump V-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 Control Outer position feedback adjusts V for final position

64 Improved Howland Current Pump General Equation Set RX=RF and RZ=RI

65 Improved Howland Current Pump Simplified Equation

66 Improved Howland AC Analysis Op Amp sees differential [(-IN) – (+IN)] feedback  =  - -  + (Must be positive number else oscillation!) RF RI

67 Improved Howland AC Analysis

68 Improved Howland AC Analysis Include Effects of RO RF RI

69 Improved Howland  - Calculation

70 Improved Howland  + Calculation

71 Improved Howland 1/  Calculation

72 Improved Howland  - Calculation RO = Full Load

73 Improved Howland  + Calculation RO = Full Load

74 Improved Howland 1/  Calculation RO = Full Load

75 Improved Howland 1/  Calculation No Load & Full Load ILROfzfp DC 1/  Hi-f 1/  No Load0A 6.29  75.8Hz31.83kHz17.62dB77.17dB Full Load1A  44.08Hz31.83kHz19.45dB77.15dB Change in RO from No Load to Full Load has no significant impact on the 1/  Plot

76 OPA569 Data Sheet Aol

77 Improved Howland 1/  Plot - Full Load

78 Improved Howland 1/  Tina SPICE Plot - Full Load

79 Improved Howland Loop Gain Tina SPICE Plot - Full Load

80 Improved Howland Tina Transient Analysis Circuit RF RI

81 Improved Howland Tina Transient Analysis Results

82 Improved Howland Modified 1/  for Stability

83  + FB#2 Calculation to Modify 1/  for Stability

84 Improved Howland AC Analysis Final Design for Stability RF RI

85 Improved Howland AC Analysis 1/  - Final Design for Stability fcl

86 Improved Howland AC Analysis Loop Gain - Final Design for Stability fcl

87 Improved Howland AC Transfer Analysis IL/VIN - Final Design for Stability RF RI

88 Improved Howland AC Transfer Analysis IL/VIN - Final Design for Stability

89 Improved Howland Transient Analysis IL/VIN - Final Design for Stability RF RI

90 Improved Howland Transient Analysis IL/VIN - Final Design for Stability

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

93 Violate the Laws of Physics and Pay the Price!

94 Instant V-I Reversal  SOA Violations

95 Output Stages fosc > UGBW oscillates unloaded? -- no oscillates with V IN =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. PROBLEM SOLUTION

96 Ground Loops fosc < UGBW oscillates unloaded? -- no oscillates with V IN =0? -- yes Ground loops are created from load current flowing through parasitic resistances. If part of V OUT 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. SOLUTION PROBLEM

97 PCB Traces fosc < UGBW oscillates unloaded? -- may or may not oscillates with V IN =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.

98 Supply Lines 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 V IN =0? -- may or may not PROBLEM

99 Proper Supply Line Decouple C LF : Low Frequency Bypass 10μF / Amp Out (peak) Aluminum Electrolytic or Tantalum < 4 in (10cm) from Op Amp C HF : High Frequency Bypass 0.1μF Ceramic Directly at Op Amp Power Supply Pins R HF : Provisional Series C HF Resistance 1Ω < R HF < 10Ω Highly Inductive Supply Lines SOLUTION

100 Transient Protection