1. 1 of 75 Capacitive Loads on Gamma Buffer Outputs Analysis Techniques and Solutions Tim Green, Linear Apps Manager Texas Instruments Inc, Tucson, Arizona 520-750-2193 green_tim@ti.com

2. 2 of 75 BUF18830 SPICE Model for AC Analysis and Small Signal Transient Analysis

3. 3 of 75 Appendix: Loop Stability Basics

4. 4 of 75 BUF18830 Zo

5. 5 of 75 BUF18830 Aol

6. 6 of 75 BUF18830 Aol

7. 7 of 75 Transient Cap Load Test Circuit

8. 8 of 75 1uF Load Transient

9. 9 of 75 Loop Gain Test Circuit

10. 10 of 75 Modified Aol, 1/Beta Results

11. 11 of 75 Loop Gain Results

12. 12 of 75 Loop Gain Test Circuit

13. 13 of 75 Modified Aol, 1/Beta Results

14. 14 of 75 Loop Gain Results

15. 15 of 75 Transient Test Circuit

16. 16 of 75 Transient Results

17. 17 of 75 Modified Aol, 1/Beta Results

18. 18 of 75 Loop Gain Results

19. 19 of 75 Transient Results

20. 20 of 75 TINA SPICE SIMULATION Free Tina-TI Spice Tool: http://focus.ti.com/docs/toolsw/folders/print/tina-ti.htmlhttp://focus.ti.com/docs/toolsw/folders/print/tina-ti.html If you do not already have it, you may download a free version of Tina-TI Spice: The previous simulations were performed in TINA-SPICE. Click on the following embedded link/links to perform simulations:

21. 21 of 75 Appendix: Loop Stability Basics

22. 22 of 75 Op Amp: Intuitive Model

23. 23 of 75 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

24. 24 of 75 Stability Criteria V OUT /V IN = Aol / (1+ Aolβ) If: Aolβ = -1 Then: V OUT /V IN = Aol / 0  ∞ If V OUT /V IN = ∞  Unbounded Gain Any small changes in V IN will result in large changes in V OUT which will feed back to V IN and result in even larger changes in V OUT  OSCILLATIONS  INSTABILITY !! Aolβ: Loop Gain Aolβ = -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°

25. 25 of 75 Traditional Loop Gain Test Op Amp Loop Gain Model Op Amp is “Closed Loop” 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

26. 26 of 75 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

27. 27 of 75 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

28. 28 of 75 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

29. 29 of 75 Stability Criteria using 1/β & Aol At fcl: Loop Gain (Aol  ) = 1 Rate-of-Closure @ fcl = (Aol slope – 1/β slope) *20dB/decade Rate-of-Closure @ fcl = STABLE **40dB/decade Rate-of-Closure@ fcl = UNSTABLE

30. 30 of 75 Loop Gain Example Rate-of-Closure @ fcl = 40dB/decade  UNSTABLE!

31. 31 of 75 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] Loop Gain (Aolβ) Plot from Aol & 1/β Plot At fcl: Phase Shift = -180 Phase Margin = 0

32. 32 of 75 1/β & Closed Loop Response V OUT /V IN = Aol/(1+Aolβ) At fcl Aolβ = 1  V OUT/ V IN = Aol/(1+1) ~ Aol No Loop Gain left to correct for errors. V OUT /V IN follows the Aol curve. Note: 1/β is the AC Small Signal Closed Loop Gain for the Op Amp. V OUT /V IN is often NOT the same as 1/β.

33. 33 of 75 Definition of Terms: R O = Op Amp Open Loop Output Resistance R OUT = Op Amp Closed Loop Output Resistance Op Amps and “Output Resistance”

34. 34 of 75 Op Amp Model for Derivation of R OUT From: Frederiksen, Thomas M. Intuitive Operational Amplifiers. McGraw-Hill Book Company. New York. Revised Edition. 1988.

35. 35 of 75 1)  = V FB / V OUT = [V OUT (R I / {R F + R I })]/V OUT = R I / (R F + R I ) 2) R OUT = V OUT / I OUT 3) V O = -V E Aol 4) V E = V OUT [R I / (R F + R I )] 5) V OUT = V O + I OUT R O 6) V OUT = -V E Aol + I OUT R O Substitute 3) into 5) for V O 7) V OUT = -V OUT [R I /(R F + R I )] Aol+ I OUT R O Substitute 4) into 6) for V E 8) V OUT + V OUT [R I /(R F + R I )] Aol = I OUT R O Rearrange 7) to get V OUT terms on left 9) V OUT = I OUT R O / {1+[R I Aol/(R F +R I )]} Divide in 8) to get V OUT on left 10) R OUT = V OUT /I OUT =[ I OUT R O / {1+[R I Aol / (R F +R I )]} ] / I OUT Divide both sides of 9) by I OUT to get R OUT [from 2)] on left 11) R OUT = R O / (1+Aolβ) Substitute 1) into 10) Derivation of R OUT (Closed Loop Output Resistance) R OUT = R O / (1+Aolβ)

36. 36 of 75 R OUT vs R O  R O does NOT change when Closed Loop feedback is used  R OUT is the effect of R O, Aol, and β controlling V O Closed Loop feedback (β) forces V O to increase or decrease as needed to accommodate V O loading Closed Loop (β) increase or decrease in V O appears at V OUT as a reduction in R O R OUT increases as Loop Gain (Aolβ) decreases Note: Some op amps have Z O characteristics other than pure resistance – consult data sheet / manufacturer.

37. 37 of 75 R ISO & CL: Modified Aol Model Extra Pole in Aol Plot due to R O & CL: fpo1 = 1/(2∙П∙R O ∙CL) fpo1 = 1/(2∙П∙28.7Ω∙1μF) fpo1 = 5.545kHz Create a new “Modified Aol” Plot

38. 38 of 75 R ISO & CL: OPA542 Modified Aol First Order

39. 39 of 75 R ISO & CL: Compensation Extra Pole in Aol Plot due to (RO + RISO) & CL: fpo1 = 1/[2∙П∙(R O + R ISO )∙CL] Extra Zero in Aol Plot due to R ISO & CL: fzo1 = 1/[2∙П∙R ISO ∙CL] R ISO “Isolates” CL from Op Amp Output Check: V OUT error vs. V OA (point of feedback) depending on I OUT

40. 40 of 75 R ISO & CL: Modified Aol fpo1 = 1/[2∙П∙(R O + R ISO )∙CL] fpo1 = 1/[2∙П∙(28.7Ω+ 4.99Ω)∙1μF] fpo1 = 4.724kHz fzo1 = 1/[2∙П∙R ISO ∙CL] fzo1 = 1/[2∙П∙4.99Ω∙1μF] fzo1 = 31.89kHz

41. 41 of 75 R ISO & CL: V OUT /V IN – AC First Order

42. 42 of 75 Transient Real World Stability Test Test Tips:  Choose test frequency << fcl  Adjust V IN amplitude to yield “Small Signal” AC Output Square Wave  Worst case is usually when V Offset = 0  Largest Op Amp R O (I OUT = 0)  Use V Offset as desired to check all output operating points for stability  Set scope = AC Couple & expand vertical scope scale to look for amount of overshoot, undershoot, ringing on V OUT small signal square wave

43. 43 of 75 2nd Order Transient Curves From: Dorf, Richard C. Modern Control Systems. Addison-Wesley Publishing Company. Reading, Massachusetts. Third Edition, 1981.

44. 44 of 75 2nd Order Damping Ratio vs Phase Margin From: Dorf, Richard C. Modern Control Systems. Addison-Wesley Publishing Company. Reading, Massachusetts. Third Edition, 1981.

45. 45 of 75 Commercial Break (Shameless Author Self-Promotion) For Further Reading & Details: “Operational Op Amp Stability – Part ? Of 15” http://www.en-genius.net/site/zones/acquisitionZONE/technical_notes/acqt_092407 Tim Green, Linear Apps Manager Texas Instruments Inc, Tucson, Arizona 520-750-2193 green_tim@ti.com