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Digital background calibration algorithm and its FPGA implementation for timing mismatch correction of time-interleaved ADC

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Abstract

Sample time error can degrade the performance of time-interleaved analog to digital converters (TIADCs). A fully digital background algorithm is presented in this paper to estimate and correct the timing mismatch errors between four interleaved channels, together with its hardware implementation. The proposed algorithm provides low computation burden and high performance. It is based on the simplified representation of the coefficients of the Lagrange interpolator. Simulation results show that it can suppress error tones in all of the Nyquist band. Results show that, for a four-channel TIADC with 10-bit resolution, the proposed algorithm improves the signal to noise and distortion ratio (SNDR) and spurious-free dynamic range (SFDR) by 19.27 dB and 35.2 dB, respectively. This analysis was done for an input signal frequency of \(0.09f_s\). In the case of an input signal frequency of \(0.45f_s\), an improvement by 33.06 dB and 43.14 dB is respectively achieved in SNDR and SFDR. In addition to the simulation, the algorithm was implemented in hardware for real-time evaluation. The low computational burden of the algorithm allowed an FPGA implementation with a low logic resource usage and a high system clock speed (926.95 MHz for four channel algorithm implementation). Thus, the proposed architecture can be used as a post-processing algorithm in host processors for data acquisition systems to improve the performance of TIADC.

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References

  1. Wepman, J. A., & Hoffman, J. R. (1996). RF and IF digitization in radio receivers: Theory, concepts, and examples. US Department of Commerce, National Telecommunications and Information Administration.

  2. Vernhes, J.-A., Chabert, M., Lacaze, B., Lesthievent, G., Baudin, R., & Boucheret, M.-L. (2016). Blind estimation of unknown time delay in periodic non-uniform sampling: Application to desynchronized time interleaved-ADCs. In IEEE international conference on acoustics, speech and signal processing (ICASSP), 2016 (pp. 4478–4482). IEEE.

  3. El-Chammas, M., & Murmann, B. (2011). A 12-GS/s 81-mW 5-bit time-interleaved flash ADC with background timing skew calibration. IEEE Journal of Solid-State Circuits, 46(4), 838–847.

    Article  Google Scholar 

  4. Chen, H., Pan, Y., Yin, Y., & Lin, F. (2017). All-digital background calibration technique for timing mismatch of time-interleaved ADCs. Integration, the VLSI Journal, 57, 45–51.

    Article  Google Scholar 

  5. Jamal, S. M., Fu, D., Singh, M. P., Hurst, P. J., & Lewis, S. H. (2004). Calibration of sample-time error in a two-channel time-interleaved analog-to-digital converter. IEEE Transactions on Circuits and Systems-I-Regular Papers, 51(1), 130–139.

    Article  MATH  Google Scholar 

  6. Razavi, B. (2013). Design considerations for interleaved ADCs. IEEE Journal of Solid-State Circuits, 48(8), 1806–1817.

    Article  Google Scholar 

  7. Abbaszadeh, A., & Dabbagh-Sadeghipour, K. (2009). A new FPGA-based postprocessor architecture for channel mismatch correction of time interleaved ADCS. In IEEE workshop on signal processing systems, 2009. SiPS 2009 (pp. 202–207). IEEE.

  8. Abbaszadeh, A., & Dabbagh-Sadeghipour, K. (2010). An efficient postprocessor architecture for channel mismatch correction of time interleaved ADCs. In 18th Iranian conference on electrical engineering (ICEE), 2010 ( pp. 382–385). IEEE.

  9. Qin, G.-J., Liu, G.-M., Gao, M.-G., Fu, X.-J., & Xu, P. (2014). Correction of sample-time error for time-interleaved sampling system using cubic spline interpolation. Metrology and Measurement Systems, 21(3), 485–496.

    Article  Google Scholar 

  10. Reyes, B. T., Sanchez, R. M., Pola, A. L., & Hueda, M. R. (2017). Design and experimental evaluation of a time-interleaved ADC calibration algorithm for application in high-speed communication systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 64(5), 1019–1030.

    Article  Google Scholar 

  11. Jamal, S. M., Fu, D., Chang, N. C.-J., Hurst, P. J., & Lewis, S. H. (2002). A 10-b 120-Msample/s time-interleaved analog-to-digital converter with digital background calibration. IEEE Journal of Solid-State Circuits, 37(12), 1618–1627.

    Article  Google Scholar 

  12. Law, C. H., Hurst, P. J., & Lewis, S. H. (2010). A four-channel time-interleaved ADC with digital calibration of interchannel timing and memory errors. IEEE Journal of Solid-State Circuits, 45(10), 2091–2103.

    Article  Google Scholar 

  13. Razavi, B. (2012). Problem of timing mismatch in interleaved ADCs. In CICC (pp. 1–8).

  14. Li, D., Zhu, Z., Zhang, L., & Yang, Y. (2016). A background fast convergence algorithm for timing skew in time-interleaved ADCs. Microelectronics Journal, 47, 45–52.

    Article  Google Scholar 

  15. Yu, B., Chen, C., Ye, F., & Ren, J. (2013). A mixed sample-time error calibration technique in time-interleaved ADCs. IEICE Electronics Express, 10(24), 20130882.

    Article  Google Scholar 

  16. Yi, R., Wu, M., Asami, K., Kobayashi, H., Khatami, R., Katayama, A., Shimizu, I., & Katoh, K. (2013). Digital compensation for timing mismatches in interleaved ADCs. In 2013 22nd Asian test symposium (pp. 134–139). IEEE.

  17. Wang, Z., Guo, L., Tian, S., & Liu, T. (2014). Estiamtion and correction of mismatch errors in time-interleaved ADCs. Journal of Electronic Testing, 30(5), 629–635.

    Article  Google Scholar 

  18. Shahmansoori, A. (2015). Adaptive blind calibration of timing offsets in a two-channel time-interleaved analog-to-digital converter through lagrange interpolation. Signal, Image and Video Processing, 9(5), 1047–1054.

    Article  Google Scholar 

  19. Schmidt, C. A., Cousseau, J. E., Figueroa, J. L., Reyes, B. T., & Hueda, M. R. (2016). Efficient estimation and correction of mismatch errors in time-interleaved ADCs. IEEE Transactions on Instrumentation and Measurement, 65(2), 243–254.

    Article  Google Scholar 

  20. Pillai, A. K. M., & Johansson, H. (2013). Efficient signal reconstruction scheme for m-channel time-interleaved ADCs. Analog Integrated Circuits and Signal Processing, 77(2), 113–122.

    Article  Google Scholar 

  21. Vogel, C., Pammer, V., & Kubin, G. (2005). A novel channel randomization method for time-interleaved adcs. In 2005 IEEE instrumentation and measurement technology conference proceedings (Vol. 1, pp. 150–155). IEEE.

  22. McNeill, J., Coln, M. C., & Larivee, B. J. (2005). “Split ADC” architecture for deterministic digital background calibration of a 16-bit 1-MS/s ADC. IEEE Journal of Solid-State Circuits, 40(12), 2437–2445.

    Article  Google Scholar 

  23. McNeill, J. A., David, C., Coln, M., & Croughwell, R. (2009). “Split ADC” calibration for all-digital correction of time-interleaved ADC errors. IEEE Transactions on Circuits and Systems II: Express Briefs, 56(5), 344–348.

    Article  Google Scholar 

  24. Kumar, R., & Gupta, R. (2014). Design and considerations of ADC0808 as interleaved ADCs, arXiv preprint. arXiv:1404.6040.

  25. Chen, V. H.-C., & Pileggi, L. (2014). A 69.5 Mw 20 GS/s 6b time-interleaved ADC with embedded time-to-digital calibration in 32 nm CMOS SOI. IEEE Journal of Solid-State Circuits, 49(12), 2891–2901.

    Article  Google Scholar 

  26. Nakamura, Y., & Oshima, T. (2014). A 1-GS/s 11.5-ENOB time-interleaved ADC with fully digital background calibration. In IEEE international symposium on circuits and systems (ISCAS), 2014 (pp. 1332–1335). IEEE.

  27. Bazrafshan, A., Taherzadeh-Sani, M., & Nabki, F. (2013). A low-complexity digital background calibration of sample-time error in time-interleaved A/D converters. Analog Integrated Circuits and Signal Processing, 76(2), 245–249.

    Article  Google Scholar 

  28. Liu, S. J., Qi, P. P., Wang, J. S., Zhang, M. H., & Jiang, W. S. (2014). Adaptive calibration of channel mismatches in time-interleaved ADCs based on equivalent signal recombination. IEEE Transactions on Instrumentation and Measurement, 63(2), 277–286.

    Article  Google Scholar 

  29. Liu, S., Lv, N., Ma, H., & Zhu, A. (2017). Adaptive semiblind background calibration of timing mismatches in a two-channel time-interleaved analog-to-digital converter. Analog Integrated Circuits and Signal Processing, 90(1), 1–7.

    Article  Google Scholar 

  30. Lei, Q., Zheng, Y., Zhu, D., & Siek, L. (2014). A statistic based time skew calibration method for time-interleaved ADCs. In IEEE international symposium on circuits and systems (ISCAS), 2014 (pp. 2373–2376). IEEE.

  31. Elbornsson, J., Gustafsson, F., & Eklund, J.-E. (2005). Blind equalization of time errors in a time-interleaved ADC system. IEEE Transactions on Signal Processing, 53(4), 1413–1424.

    Article  MathSciNet  MATH  Google Scholar 

  32. Johansson, H., & Löwenborg, P. (2002). Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters. IEEE Transactions on Signal Processing, 50(11), 2757–2767.

    Article  Google Scholar 

  33. Namgoong, W. (2002). Finite-length synthesis filters for non-uniformly time-interleaved analog-to-digital converter. In IEEE international symposium on circuits and systems, 2002. ISCAS 2002 (Vol. 4, pp. IV–815). IEEE.

  34. Jin, H., & Lee, E. K. (2000). A digital-background calibration technique for minimizing timing-error effects in time-interleaved ADCs. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 47(7), 603–613.

    Article  Google Scholar 

  35. Tsui, K. M., & Chan, S. (2014). A novel iterative structure for online calibration of M-channel time-interleaved ADCs. IEEE Transactions on Instrumentation and Measurement, 63(2), 312–325.

    Article  Google Scholar 

  36. Wei, H., Zhang, P., Sahoo, B. D., & Razavi, B. (2014). An 8 bit 4 GS/s 120 Mw CMOS ADC. Journal of Solid-State Circuits, 49(8), 1751–1761.

    Article  Google Scholar 

  37. Diaz-Carmona, J., & Dolecek, G. J. (2011). Fractional delay digital filters. INTECH Open Access Publisher.

  38. Majdinasab, E., & Farshidi, E. (2014). A new approach for digital calibration of timing-mismatch in four-channels time-interleaved analog-to-digital converters. Journal of Instrumentation, 9(09), T09001.

    Article  Google Scholar 

  39. 7 series dsp48e1 slice user guide (v1.8), Xilinx, Inc, technical report UG479, November 2014. (Online). http://www.xilinx.com/ support/documentation/usern guides/ug479n 7Series DSP48E1.pdf.

  40. Xu, S., Lim, Y. C., & Lee, J. W. (2016). Recursive filters for time-interleaved ADC mismatch compensation. IEEE Transactions on Circuits and Systems I: Regular Papers, 63(6), 848–858.

    Article  MathSciNet  Google Scholar 

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Correspondence to Esmaeil N. Aghdam.

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Abbaszadeh, A., Aghdam, E.N. & Rosado-Muñoz, A. Digital background calibration algorithm and its FPGA implementation for timing mismatch correction of time-interleaved ADC. Analog Integr Circ Sig Process 99, 299–310 (2019). https://doi.org/10.1007/s10470-019-01443-9

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  • DOI: https://doi.org/10.1007/s10470-019-01443-9

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