1. FE8113 ”High Speed Data Converters”

2. Part 2: Digital background calibration

4. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”, IEEE Transactions on Circuits and Systems-I: Regular Papers, Vol. 52,No. 1, January 2005, pp 32-43Background Interstage Gain Calibration Technique for Pipelined ADCs” J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”, IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 50, No. 9, September 2003, pp 531- 538Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Papers 5 and 6

5. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Outline: A background self-calibration technique is proposed that can correct both linear and nonlinear errors in the inter-stage amplifiers of pipeline and algorithmic ADCs. Simulations show that the proposed algorithm yields a 72dB SNDR and a 112dB SFDR for a 12-bit pipeline. The calibration tracking time constant is approximately 8*10 5 samples

6. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Ideal N-bit ADC with input range (-V ref, V ref ) Assuming an ideal stage DASC, and an interstage gain of G 1, the ADC output is calculated by: The interstage gain G 1 and the M ADSC levels must satisfy the condition M≥G 1 to prevent the backend from overloading. Typically, M>G 1, introducing redundancy with digital correction. The primary remaining error sources are errors in the interstage amplifier and nonmlinearity in the DASC. In a switch-cap stage, DASC nonlinearity results primarily from capacitor mismatch and can be measured and corrected for separately, as presented by Galton. The remaining error source is the interstage amplifier, and the paper describes how gain error and nonlinearity in these can be measured an corrected for.

7. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Correction of gain errors, two approaches: I: II:

8. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” With DASC output V DASC =K1D1Vref, where K1 1 is the DASC gain, the Input of a pipeline stage is a) b) c)

9. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Equivalent model of pipeline stage Output word: where

10. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Interstage gain estimation Allow at least two D 1 levels for a given input The output is then

11. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Define: Then: Multiply z by R: If R is a pseudorandom sequence with zero mean, then RI(y 0 ) will have zero mean. Then E[Rz]=e, which is proportional to Rz can be considered a noisy estimate of the error coefficient and used to adjust this:

12. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Equivalent model of pipeline stage including amplifier nonlinearity (Weakly nonlinear) Modified correction algorithm Assuming ideal backend Rewriting and simplifying Assume Adding test sequence where

13. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Z written in general form where Multiplying by R Comparing samples whereIs small to those where is large gives an estimate of b 1 independent of m 1 However, this is depentent on backend behaviour. This means that tracking speed is signal dependent

14. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Another technique that does nor rely on specific backend codes is presented. By calculating covariance betrween Rz and where

15. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Update equation Integrating over a large number of samples

16. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

17. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Correction of backend errors

18. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs” Example implementation

19. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

20. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

21. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

22. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

23. J.Keane et.al: “Background Interstage Gain Calibration Technique for Pipelined ADCs”Background Interstage Gain Calibration Technique for Pipelined ADCs”

24. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Outline: The proposed digital background calibration scheme, applicable to multistage ADCs, corrects the linearity errors resulting from capacitor mismatches and finite opamp gain. The calibration is achieved by recalculating the digital output based on each stage’s equivalent radix. The equivalent radices are extracted in the background by using a digital correlation method. The calibration technique takes advantage of the digital redundancy architecture inherent to most pipelined ADCs. The SNR is not degraded from the pseudorandom noise sequence injected into the system

25. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Introduction - Correlation-based background digital calibration scheme in the context of a 1.5b-per-stage pipelined or cyclic ADC - The input signal need not be reduced to allow the injection of pseudorandom calibration signal - Minimal addition of analog hardware for calibration

26. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Capacitor flip-over MDAC

27. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy For cyclic: Error sources

28. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy ”Non-capacitor-flip-over” MDAC

29. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Rearranging error terms for capacitor flip-over MDAC

30. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Test signal injection

31. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Suggested implementaion of test signal injection

32. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Interference Cancelling

33. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Interference Cancelling

34. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Interference Cancelling

35. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Interference Cancelling

36. J.Li, U-K.Moon: “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy Simulation results