Data driven modeling for linearization of particle accelerator RF power source

Rajesh T. Keshwani; Siddhartha Mukhopadhyay; Ravindra D. Gudi; Gopal Joshi

doi:10.1515/freq-2024-0156

Article

Data driven modeling for linearization of particle accelerator RF power source

Rajesh T. Keshwani , Siddhartha Mukhopadhyay , Ravindra D. Gudi and Gopal Joshi

Published/Copyright: March 17, 2025

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From the journal Frequenz Volume 79 Issue 5-6

Abstract

Radiofrequency (RF) power source during high power operation of a particle accelerator often exhibit saturation nonlinearity in amplitude and phase for sinusoidal input signal. This leads to an undesirable distorted RF signal as input to the RF cavity, which is the basic building block of an accelerator. Linearization of RF power source is an important necessity for an operational accelerator to improve and simplify RF cavity control performance, in addition to improving efficiency. The RF power source being a final control element of the RF cavity electric field control loop, its linear operation over a wider RF input amplitude range is often sought. Digital predistortion has been one of the preferred approaches for linearizing RF power source. This approach needs the determination of the input-output characteristics of the predistorter from those of an RF power source. Among many approaches, least squares estimation techniques are suitable for the design of digital predistorter. Among them, a recursive least squares estimation is most suitable and is elaborated in this paper. Amplifier nonlinearity and its handling using adaptive least squares estimation is explained, followed by modeling and simulation results. Input-output data acquired from an experimental 200 W, 30 MHz RF amplifier is used as input for simulations to demonstrate linearization capability by predistortion. After building up the basics, a technique for amplitude and phase linearization for data generated from the Saleh model of an RF power amplifier is presented. For an assessment of linearization capability, one needs to measure it. The effect of nonlinearity extent on linearity as a function of the number of model coefficients is analyzed. Experimental data is used to analyze the effect of nonlinearity extent and measurement noise. This paper is a comprehensive coverage of the design and analysis of a linearization scheme and is applicable for any general engineering application. A digital predistortion algorithm needs to be implemented in a control system for the RF cavity. This problem forms an important inverse problem of general nature under the purview of the modern control system community.

Keywords: linearization; digital predistortion; nonlinearity; amplitude error; phase error; recursive least squares; estimation

Corresponding author: Rajesh T. Keshwani, Homi Bhabha National Institute (HBNI) and Bhabha Atomic Research Centre (BARC), Mumbai, India, E-mail: rtk@barc.gov.in

Funding source: Work is supported by Bhabha Atomic Research Centre (BARC), Mumbai, India

Acknowledgments

The authors are thankful to colleagues of Accelerator Control Division, Bhabha Atomic Research Canter, Mumbai-400085, India for infrastructure and equipment’s supporting the research work.

Informed consent: Not applicable.
Research ethics: Not applicable.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission. Individual contributions: Rajesh T. Keshwani: Drafting manuscript, experiment design and data analysis. S. Mukhopadhyay, R. D. Gudi and Gopal Joshi: Supervision, guidance and technical advisors.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors state no conflict of interest.
Research funding: Work is supported by Bhabha Atomic Research Centre (BARC), Mumbai, India.
Data availability: The raw data can be provided by corresponding author on request.

References

[1] Johanssan, A. J. and Zeng, R., “Challenges for the low level RF design for ESS,” in Proceedings of the 2011 International Particle Accelerator Conference, San Sebastián, Spain, Geneva, Switzerland, JACoW, 2011, pp. 460–462.Search in Google Scholar

[2] Ceylan, N., Linearization of Power Amplifiers by means of Digital Predistortion, Berlin, Germany, Springer, 2006.Search in Google Scholar

[3] Tripathi, G. C. and Rawat, M., “Predistortion linearizer design for Ku Band RF power amplifier,” in Proceedings of the National Conference on Communications (NCC), Bangalore, India, IEEE, 2019, pp. 1–6.10.1109/NCC.2019.8732215Search in Google Scholar

[4] Omet, M., Michizono, S., and Matsumoto, T., “FPGA-based klystron linearization implementations in scope of ILC,” Nucl. Instrum. Methods Phys. Res., Sect. A, vol. 768, no. 1, pp. 69–76, 2014. https://doi.org/10.1016/j.nima.2014.09.007.Search in Google Scholar

[5] A. Bellandi, V. Ayvazyan, L. Butkowski, “Results on FPGA-based high-power tube amplifier linearization at DESY,” IEEE Trans. Nucl. Sci., vol. 67, no. 5, pp. 762–767, 2020, https://doi.org/10.1109/TNS.2020.2980929.Search in Google Scholar

[6] He, Y., Jin, K., and Jiang, G., “Research on the newest GaN-Based solid-state power amplifier for CiADS project,” Nucl. Instrum. Methods Phys. Res., Sect. A, vol. 1055, no. 1, p. 168403, 2023. https://doi.org/10.1016/j.nima.2023.168403.Search in Google Scholar

[7] Lebedev, Valeri, The PIP-II Reference Design Report, Batavia, IL, Fermi National Accelerator Laboratory, 2015.10.2172/1365571Search in Google Scholar

[8] Kapoor, S. S., “Accelerator-driven sub-critical reactor system (ADS) for nuclear energy generation,” Pramana, vol. 59, no. 6, pp. 941–950, 2002. https://doi.org/10.1007/s12043-002-0143-z.Search in Google Scholar

[9] Liepe, M., “Latest results and test plans from the 100 mA cornell ERL injector SCRF cryomodule,” in Proceedings of the 1st International Particle Accelerator Conference (IPAC 2010), Kyoto, Japan, Geneva, Switzerland, JACoW, 2010, pp. 3043–3045.Search in Google Scholar

[10] Simrock, S., “Digital low-level RF controls for future superconducting linear colliders (DESY),” in Conference Proceedings C 0505161, Hamburg, Germany, DESY, 2005, p. 515.10.1109/PAC.2005.1590484Search in Google Scholar

[11] S. Wibowo, T. Matsumoto, S. Michizono, T. Miura, F. Qiu, and N. Liu, “Digital low level RF control system for the International linear collider,” Phys. Rev. Acc. Beams, vol. 21, p. 08, 2018, https://doi.org/10.1103/physrevaccelbeams.21.082004.Search in Google Scholar

[12] Ayvazyan, V., “Digital RF control system for the pulsed superconducting linear accelerator,” in Proceedings of the 2012 International Particle Accelerator Conference (IPAC 2012), New Orleans, LA, USA, vol. 03, Geneva, Switzerland, JACoW, 2012.10.5772/36912Search in Google Scholar

[13] Lynch, M., Kwon, S., Regan, A., and Wang, Y. M., “Excess RF power required for RF control of the spallation neutron source(SNS) linac, a pulsed high-intensity superconducting proton accelerator,” in Proceedings of the 2001 Particle Accelerator Conference, Chicago, IL, USA, vol. 1, IEEE, 2001, pp. 503–505.10.1109/PAC.2001.987553Search in Google Scholar

[14] H. Jiang and P. A. Wilford, “Digital predistortion for power amplifiers using separable functions,” IEEE Trans. Signal Process., vol. 58, no. 8, pp. 4121–4130, 2010, https://doi.org/10.1109/TSP.2010.2049742.Search in Google Scholar

[15] Y. Li, X. Wang, and A. Zhu, “Reducing power consumption of digital predistortion for RF power amplifiers using real-time model switching,” IEEE Trans. Microw. Theor. Tech., vol. 70, p. 1500, 2022, https://doi.org/10.1109/TMTT.2021.3132347.Search in Google Scholar

[16] Hussein, M. A., Venard, O., Feuvrie, B., and Wang, Y., “Digital predistortion for RF power amplifiers: state of the art and advanced approaches,” in IEEE 11th International New Circuits and Systems Conference (NEWCAS), Paris, France, IEEE, 2013.10.1109/NEWCAS.2013.6573671Search in Google Scholar

[17] Wood, J., “Digital pre-distortion of RF power amplifiers,” in Proceedings of the 2017 IEEE Topical Conference on RF/Microwave Power Amplifiers for Radio and Wireless Applications (PAWR)), Phoenix, AZ, USA, IEEE, 2017.10.1109/PAWR.2017.7875557Search in Google Scholar

[18] H. Qian, S. Yao, H. Huang, and W. Feng, “A low-complexity digital predistortion algorithm for power amplifier linearization,” IEEE Trans. Broadcast., vol. 60, no. 4, pp. 670–678, 2014, https://doi.org/10.1109/TBC.2014.2352911.Search in Google Scholar

[19] S. D. Muruganathan and A. B. Sesay, “A QRD-RLS-based predistortion scheme for high-power amplifier linearization,” IEEE Trans. Circuits Syst. Express Briefs, vol. 53, no. 10, pp. 1108–1112, 2006, https://doi.org/10.1109/TCSII.2006.882182.Search in Google Scholar

[20] Zhu, A., Pedro, J. C., and Brazil, T. J., “Dynamic deviation reduction-based Volterra behavioral modelling of RF power amplifiers,” IEEE Trans. Microw. Theor. Tech., vol. 54, no. 9, p. 4323, 2006. https://doi.org/10.1109/tmtt.2006.883243.Search in Google Scholar

[21] Mohamed, H., Boumaiza, S., Ghazel, A., and Ghannouchi, F., “Power and efficiency enhancement of 3G multicarrier amplifiers using digital signal processing with experimental validation,” IEEE Trans. Microw. Theor. Tech., vol. 54, no. 4, p. 1396, 2006. https://doi.org/10.1109/tmtt.2006.871238.Search in Google Scholar

[22] Ding, L., Zhou, G., and Morgan, D., “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun., vol. 52, no. 1, p. 159, 2004. https://doi.org/10.1109/TCOMM.2003.822188.Search in Google Scholar

[23] Ding, L., Digital Predistortion of Power Amplifiers for Wireless Applications, Hoboken, NJ, USA, Wiley, 2004.Search in Google Scholar

[24] Zhu, A., Draxler, P. J., Yan, J. J., Brazil, T. J., Kimball, D. F., and Asbeck, P. M., “Open-LoopDigital predistorter for RF power amplifiers using dynamic deviation reduction-BasedVolterra series,” IEEE Trans. Microw. Theor. Tech., vol. 56, no. 7, p. 1524, 2008. https://doi.org/10.1109/TMTT.2008.925211.64.Search in Google Scholar

[25] H. Simon, Adaptive filter Theory, 4th ed., Upper Saddle River, NJ, Prentice Hall, 2002.Search in Google Scholar

[26] Choi, S., Jeong, E., and Lee, Y. H., “A direct learning structure for adaptive polynomial-based predistortion for power amplifier linearization,” in IEEE 65th Vehicular Technology Conference VTC2007 Spring, Dublin, Ireland, New Jersey, IEEE, 2007.10.1109/VETECS.2007.372Search in Google Scholar

[27] Saleh, A., “Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers,” IEEE Trans. Commun., vol. 29, no. 11, p. 1715, 1981. https://doi.org/10.1109/tcom.1981.1094911.Search in Google Scholar

[28] Ghorbani, A. and Sheikhan, M., “The effect of solid state power amplifiers (SSPAs) nonlinearities on MPSK and M-QAM signal transmission,” in Proceedings of the 1991 Sixth International Conference on Digital Processing of Signals in Communications, Cairo, Egypt, IEEE, 1991, p. 193.Search in Google Scholar

[29] R. T. Keshwani, S. Mukhopadhyay, R. D. Gudi, and G. Joshi, “Statistical Methods for assessment of RF amplifier linearization,” in 11th Indian Particle Accelerator Conference, 2023, Mumbai, India, Bhabha Atomic Research Centre, 2023.Search in Google Scholar

Received: 2024-05-12

Accepted: 2025-02-19

Published Online: 2025-03-17

Published in Print: 2025-06-26

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Articles in the same Issue

https://doi.org/10.1515/freq-2024-0156

Keywords for this article

linearization; digital predistortion; nonlinearity; amplitude error; phase error; recursive least squares; estimation