1. FE8113 ”High Speed Data Converters”

2. Part 2: Digital background calibration

3. Stewart Clark, ”Broken english spoken perfectly”

4. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”, Proceedings of the 2004 International Symposium on Circuits and Systems, 2004. ISCAS '04, Vol. 1, 23-26 May 2004, pp I-5 - I-8A New Digital Background Calibration Technique for Pipelined ADC B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”, IEEE Journal of Solid-State Circuits, Vol. 38, No. 12, December 2003, pp2040-2050A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Papers 7 and 8

5. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC Outline:  Compensation of finite opamp dc gain ”By transforming the ADC to parallell ADCs and measuring the gain ratios between different configurations...”

6. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC Radix 2 and Radix <2 MDACs

7. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC If ratios G 1,radix2 /G 2.radix2 and G 1,radix<2 /G 2,radix<2 are known, x and A can be computed Calculation of finite dc gain & parasitics

8. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC Calibration system, swaps between two gain configurations M = 2 Can be drawn as a time interleaved ADC It should be noted that config 1 and config 2 refers to different n on previous slide, not different radix Calibration method

9. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC TIADC Theory: Gain mismatch between two paths leads to inband image at kf s /2 +- f in The spectrum of digitized output V gd of V g is given by Time-Interleaved Theory

10. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC Choppes digitized output, multiplies with a small constant and integrate to get an estimate of g 1 /g 2. This ratio is used to modify g 2 so the image frequency dissapears. When the system has converged g 1 /g 2 = G 1,radix2 /G 2,radix2 Repeated with different configuration to get G 1,radix<2 /G 2,radix<2 Calibration System

11. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC MADC Implementation

12. K.El-Sanakry, M.Sawan: “A New Digital Background Calibration Technique for Pipelined ADC”A New Digital Background Calibration Technique for Pipelined ADC Without CalibWith CalibUnit SNR4260.8dB ENOB6.99.8bits SFDR4676dB Simulation results

13. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Outline: A digital background calibration technique as an enabling element to replace precision amplifiers by simple powerefficient open-loop stages. At Nyquist input frequencies, the measured signal-to- noise ratio is 67 dB and the total harmonic distortion is 74 dB. The IC consumes 290 mW at 3 V and occupies 7.9 mm 2.

14. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Based on: W. Yang, D. Kelly, I. Mehr,M. T. Sayuk, and L. Singer, “A 3-V 340- mW 14-b 75-Msample/s CMOS ADC with 85-dB SFDR at Nyquist input,” IEEE J. Solid-State Circuits, vol. 36, pp. 1931–1936, Dec. 2001. Architecture

15. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Conventional closed loop architecture is replaced with an open loop transconductance driving a resistance Conventional vs Open Loop

16. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Assuming square law transistors and memoryless nonlinearities V OV is gate overdrive, Δβ/β is current mismatch between transistors Non-linearity model

17. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification With V x-pp = 250mV, choose V OV > 250mV to get low second and fifth order distortion. 3rd order distortion is unavoidable and is compensated for digitally. Shown below is the equivalent model Gain error in amplifier Cubic distortion Offset in amplifier Offset in SADC Error model

18. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Offset in SADC and DAC: extra redundancy in second stage Gain error corrected using previously described techniques; A. Karanicolas et al., “A 15-b 1-MSample/s digitally self-calibrated pipeline ADC,” IEEE J. Solid-State Circuits, vol. 28, pp. 1207–1215, Dec. 1993. The new technique is the approach to cubic distortion correction Through inversion of the of the overall cubic polynomial with gain compression (a 3 < 0 ) Nonlinearity correction

19. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Since the backend ADC quantize V res1 the nonlinearity can be corrected by operating on the backend code. This assumes that the backend error, ε b, is small. Components of ε b : Linear and nonlinear or code dependent errors: must be kept small by design Static input-referred offset: comparator redundancy and digital correction arithmetic Quantization noise: two redundant bits Backend ADC requirements

20. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Switches between distinct overlapping residue functions. Digital linearity correction operates on both residues (p 2 ). Measure h 1 and h 2, if h 1 = h 2 then we have perfect adjustment of residues into straight lines. If h 1 > h 2 we have incomplete nonlinearity error cancellation. Nonlinearity detection

21. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Uses signal statistics to determine h 1 and h 2. Requires well behaved probability density function. Generates cumulative histograms for digital backend conversion results Nonlinearity estimation

22. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Correction architecture

23. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Sub-DAC must be linear, nonlinearity only present in gain stage Needs a busy signal around which the distance estimates (h 1 and h 2 ) is measured. Inactivity can be detected, thus miscalibration can be avoided. Activity spanning 1/16th of the fullscale range is sufficient for calibration Tradoff between accuracy and tracking speed of LMS method Calibration Limitations

24. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Cascode devices used to improve PSRR Pi-load used to decouple choice of common mode output level from differential gain requirements Replica tail biasing used to improve CMRR G m R replica bias reduce sensitivity to ambient temperature changes 1 Stage implementation

25. B.Murmann, B.E.Boser: ”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification Murmann03 Yang01 Measured performence