1. DNC, GEC & Non-linear Interpolation carsten@wulff.no DNC, GEC & Non-linear interpolation A Review of ”A Digitally Enhanced 1.8V 15-bit 40-MSample/s CMOS Pipelined ADC”[1] & ”Background Digital Calibration Techniques for Pipelined ADC’s”[2]

2. DNC, GEC & Non-linear Interpolation carsten@wulff.no Pipelined ADC review Non-linearities in DAC levels cause harmonic distortion –Common solution: Try to randomly distribute non- linearities in DAC so energy is spread out in the frequency spectrum Interstage gain errors reduce SNDR/SNR –Solution: Apply correction gain digitally

3. DNC, GEC & Non-linear Interpolation carsten@wulff.no Detecting a known signal component in the output of an unknown system Mean of t d = 0 Td with a mean of zero: –Periodic signal Pro: Can have a small N since power of t d is evenly distributed in time Con: Delta function in the frequency domain –White noise signal Pro: Flat power density spectrum Con: Need large N, ideally N=∞

4. DNC, GEC & Non-linear Interpolation carsten@wulff.no A Digitally Enhanced 1.8V 15-bit 40- MSample/s CMOS Pipelined ADC

5. DNC, GEC & Non-linear Interpolation carsten@wulff.no Dynamic Element Matching (DEM) DAC Noise Cancellation (DNC) Gain Error Correction (GEC) Bootstrapped Switches Timing Outline

6. DNC, GEC & Non-linear Interpolation carsten@wulff.no Pipeline ADC from [1]

7. DNC, GEC & Non-linear Interpolation carsten@wulff.no Dynamic Element Matching (1) Errors in DAC paths cause signal dependent error Signal dependent error => Distortion

8. DNC, GEC & Non-linear Interpolation carsten@wulff.no Dynamic Element Matching (2) Scrambler randomly selects a sequence of S n such that V out equals (1) The error, e, is uncorrelated with the input signal if it is done correctly This will effectively spread DAC noise power in the frequency spectrum (1)

9. DNC, GEC & Non-linear Interpolation carsten@wulff.no With DEM encoder from [1] it can be shown that DAC noise inherits statistical properties of the pseudorandom sequence used in DEM This can be used to estimate the mismatch in the DAC paths Each path error is related to a specific pseduorandom sequence DEM encoder from [1] DAC path errors Known sequences

10. DNC, GEC & Non-linear Interpolation carsten@wulff.no DAC Noise Cancellation Detect presence of known pseduorandom signal, s[n], in output, u[n] + εs[n], by calculating the covariance Estimate DAC path error, ε, from covariance Multiply psedurandom sequence by path error estimate and subtract from output Repeat for all DAC paths

11. DNC, GEC & Non-linear Interpolation carsten@wulff.no Gain Error Calibration (GEC) from [1] Estimate gain error from covariance of digitized residue and pseudorandom signal Assuming small ε =>(1 + ε ) ≈ 1, multiply digitized residue by gain estimate and subtract from output

12. DNC, GEC & Non-linear Interpolation carsten@wulff.no Bootstrapped switches Used on continous-time input sampling switches –Increased linearity Used on switches connected to mid-supply or time- constant matching constrains –Reduced resistance

13. DNC, GEC & Non-linear Interpolation carsten@wulff.no Timing First stage amplification is most important Steal time for first stage Flash from second stage

14. DNC, GEC & Non-linear Interpolation carsten@wulff.no Results from [1] SFDR is improved by 12dB with DNC and GEC enabled SNDR is improved by 20dB with DNC and GEC enabled Signal Without calibrationWith calibration

15. DNC, GEC & Non-linear Interpolation carsten@wulff.no Background Digital Calibration Techniques for Pipelined ADC’s

16. DNC, GEC & Non-linear Interpolation carsten@wulff.no Outline Error Model Calibration Method Non-linear Interpolation Quantization Effects on Interpolation

17. DNC, GEC & Non-linear Interpolation carsten@wulff.no Error Model

18. DNC, GEC & Non-linear Interpolation carsten@wulff.no Error measurement Measure gain error in each stage by applying known calibration voltage, V cal-i Positive calibration voltageNegative calibration voltage

19. DNC, GEC & Non-linear Interpolation carsten@wulff.no Simulation results Simulated performance (DNL & INL) with and without gain calibration

20. DNC, GEC & Non-linear Interpolation carsten@wulff.no Non-linear Interpolation Uses fitting of high order polynomials to estimate missing sample. Uses causal and noncausal taps Normalized coefficients

21. DNC, GEC & Non-linear Interpolation carsten@wulff.no Limits input bandwidth of converter below Nyquist Non-linear Interpolation Fin < ½ NyquistFin < Nyquist

22. DNC, GEC & Non-linear Interpolation carsten@wulff.no Non-linear Interpolation Interpolation error depends on the number of taps Achieve higher bandwith with a certain error by using more taps

23. DNC, GEC & Non-linear Interpolation carsten@wulff.no Quantization Effects on Interpolation Quantization noise limits performance of interpolation Each tap adds quantization noise to total noise power Limits the number of taps Variance vs number of taps

24. DNC, GEC & Non-linear Interpolation carsten@wulff.no References 1.Eric Siragusa & Ian Galton; ”A Digitally Enhanced 1.8V 15-bit 40-MSample/s CMOS Pipelined ADC”; IEEE Journal of Solid State, Vol. 39, NO. 12, December 2004 2.Un-Ku Moon & Bang-Sup Song;” Background Digital Calibration Techniques for Pipelined ADC’s”; IEEE Transatctions on Circuits and Systems-II, Vol. 44, NO. 2, Febuary 1997