Skip to main content

Injection-Locking of Oscillators: An Overview

  • Chapter
  • First Online:

Abstract

This chapter provides an overview of injection-locking and its applications in mixed-mode signal processing. The classification of oscillators is provided. It browses through the development of the injection-locking of oscillators with an emphasis on the characterization of injection-locked oscillators. First-harmonic methods for analyzing harmonic oscillators in weak injection are presented. It is followed with the presentation of first-harmonic methods for the analysis of harmonic oscillators in both weak and strong injection. Frequency regenerative injection specifically tailored for frequency multiplication and frequency division is explored. First-harmonic balance method capable of analyzing harmonic oscillators in first-harmonic, superharmonic, and subharmonic injections is studied. The progressive multiphase injection of ring oscillators with multiple injections is examined. The effective injection signaling arising from the nonlinearity of oscillators under injection and obtained by analyzing the Volterra circuits of the oscillators under injection is described. The chapter also briefly browses through the key applications of the injection-locking of oscillators.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The parallel RLC network in Fig. 1.2 is derived from the network consisting of a series RL network depicting the spiral inductor and a parallel capacitor. The quality factor is dictated by the RL network.

  2. 2.

    Such an assumption is clearly not always correct since during the locking process, the period of the oscillator differs from that of the injection signal.

References

  1. R. Adler, A study of locking phenomena in oscillators. Proc. Inst. Radio Eng. 34(6), 351–357 (1946)

    Google Scholar 

  2. E. Appleton, The automatic synchronization of triode oscillators. Proc. Camb. Philos. Soc. 21, 231–248 (1922–1923)

    Google Scholar 

  3. J. Bae, L. Yan, H. Yoo, A low energy injection-locked FSK transceiver with frequency-to-amplitude conversion for body sensor applications. IEEE J. Solid State Circuits 46(4), 928–937 (2011)

    Google Scholar 

  4. J. Bae, H. Yoo, A 45 μW injection-locked FSK wake-up receiver with frequency-to-envelope conversion for crystal-less wireless body area network. IEEE J. Solid State Circuits 50(6), 1351–1360 (2015)

    Google Scholar 

  5. G. Balamurugan, N. Shanbhag, Modeling and mitigation of jitter in multi Gbps source-synchronous I/O links, in Proceedings of the International Conference on Computer Design (IEEE, Piscataway, 2003), pp. 254–260

    Google Scholar 

  6. G. Beers, A frequency-dividing locked-in oscillator frequency-modulation receiver. Proc. Inst. Radio Eng. 32(12), 730–737 (1944)

    Google Scholar 

  7. A. Buonomo, A. Lo Schiavo, M. Awan, M. Asghar, M. Kennedy, A CMOS injection-locked frequency divider optimized for divide-by-two and divide-by-three operation. IEEE Trans. Circuits Syst. I 60(12), 3126–3135 (2013)

    Article  Google Scholar 

  8. B. Casper, F. O’Mahony, Clocking analysis, implementation and measurement techniques for high-speed data links—a tutorial. IEEE Trans. Circuits Syst. I 56(1), 17–39 (2009)

    Article  MathSciNet  Google Scholar 

  9. H. Chen, D. Chang, Y. Juang, S. Lu, A 30-GHz wideband low-power CMOS injection-locked frequency divider for 60-GHz wireless-LAN. IEEE Microwave Wireless Lett 18(2), 145–147 (2008)

    Article  Google Scholar 

  10. J. Chien, L. Lu, Analysis and design of wideband injection-locked ring oscillators with multiple-input injection. IEEE J. Solid State Circuits 42(9), 1906–1915 (2007)

    Article  Google Scholar 

  11. S. Cho, S. Kim, M. Choo, J. Lee, H. Ko, S. Jang, S. Chu, W. Bae, Y. Kim, D. Jeong, A 5-GHz subharmonically injection-locked all-digital PLL with complementary switched injection, in Proceedings of the European Solid-State Circuits Conference (IEEE, Piscataway, 2015), pp. 384–387

    Google Scholar 

  12. M. Choo, H. Ko, S. Cho, K. Lee, D. Jeong, An optimum injection-timing tracking loop for 5-GHz, 1.13-mW/GHz RO-based injection-locked PLL with 152-fs integrated jitter. IEEE Trans. Circuits Syst. II 65(12), 1819–1823 (2018)

    Article  Google Scholar 

  13. Y. Chuang, S. Lee, S. Jang, J. Chao, M. Juang, A ring-oscillator-based wide locking range frequency divider. IEEE Microwave Wireless Compon. Lett. 16(8), 470–472 (2006)

    Article  Google Scholar 

  14. F. Ellinger, L. Rodoni, G. Sialm, C. Kromer, G. von Buren, M. Schmatz, C. Menolfi, T. Toifl, T. Morf, M. Kossel, H. Jackel. 30–40-GHz drain-pumped passive-mixer MMIC fabricated on VLSI SOI CMOS technology. IEEE Trans. Microwave Theory Tech. 52(5), 1382–1391 (2004)

    Article  Google Scholar 

  15. D. Fraser, Synchrobization of oscillators by periodically interrupted waves. Proc. Inst. Radio Eng. 45(9), 1256–1268 (1957)

    Google Scholar 

  16. W. Grollitsch, R. Nonis, A fractional-N, all-digital injection-locked PLL with wide tuning range digitally controlled ring oscillator and bang-bang phase detection for temperature tracking in 40 nm CMOS, in Proceedings of the European Solid-State Circuits Conference (IEEE, Piscataway, 2016), pp. 201–204

    Google Scholar 

  17. M. Hossain, A. Carusone, 7.4 Gb/s 6.8 mW source synchronous receiver in 65 nm CMOS. IEEE J. Solid State Circuits 46(6), 1337–1348 (2011)

    Article  Google Scholar 

  18. K. Hu, T. Jiang, J. Wang, F. O’Mahony, P. Chiang, A 0.6 m W/Gb/s, 6.4–7.2 Gb/s serial link receiver using local injection-locked ring oscillators in 90 nm CMOS. IEEE J. Solid State Circuits 45(4), 899–908 (2010)

    Article  Google Scholar 

  19. J. Hu, B. Otis, A 3 μW, 400 MHz divide-by-5 injection-locked frequency divider with 56% lock range in 90 nm CMOS, in 2008 IEEE Radio Frequency Integrated Circuits Symposium (IEEE, Piscataway, 2008), pp. 665–668

    Google Scholar 

  20. R. Huntoon, A. Weiss, Synchronization of oscillators. Proc. Inst. Radio Eng. 34(12), 1415–1423 (1947)

    Google Scholar 

  21. S. Jang, C. Chang, W. Cheng, C. Lee, M. Juang, Low-power divide-by-3 injection-locked frequency dividers implemented with injection transformers. IET Electron. Lett. 45(5), 240–241 (2009)

    Article  Google Scholar 

  22. S. Jang, P. Lu, M. Juang, Divide-by-3 LC injection locked frequency divider with a transformer as an injector’s load. Microw. Opt. Technol. Lett. 50(10), 2722–2725 (2008)

    Article  Google Scholar 

  23. U. Karthaus, M. Fischer, Fully integrated passive UHF RFID transponder IC with 16.7 μW minimum RF input power. IEEE J. Solid State Circuits 38(10), 1602–1608 (2003)

    Article  Google Scholar 

  24. F. Kocer, M. Flynn, A new transponder architecture with on-chip ADC for long-range telemetry applications. IEEE J. Solid State Circuits 41(5), 1142–1148 (2006)

    Article  Google Scholar 

  25. S. Lee, S. Amakawa, N. Ishihara, K. Masu, Low-phase-noise wide-frequency-range ring-VCO-based scalable PLL with subharmonic injection locking in 0.18 μm CMOS, in Proceedings of the IEEE MTT-S International Microwave Symposium (IEEE, Piscataway, 2010), pp. 1178–1181

    Google Scholar 

  26. M. Lee, W. Dally, T. Greer, H. Ng, R. Farjad-Rad, J. Poulton, R. Senthinathan, Jitter transfer characteristics of delay-locked loops—theories and design techniques. IEEE J. Solid State Circuits 38(4), 614–621 (2003)

    Article  Google Scholar 

  27. K. Lee, S. Kim, Y. Shin, D. Jeong, G. Lim, B. Kim, V. Da Costa, D. Lee, A jitter-tolerant 4.5 Gb/s CMOS interconnect for digital display, in 1998 IEEE International Solid-State Circuits Conference. Digest of Technical Papers, ISSCC (IEEE, Piscataway, 1998), pp. 310–311

    Google Scholar 

  28. D. Lee, T. Lee, Y. Kim, Y. Kim, L. Kim, An injection locked PLL for power supply variation robustness using negative phase shift phenomenon of injection locked frequency divider, in Proceedings of the IEEE Custom Integrated Circuits Conference (IEEE, Piscataway, 2015), pp.1–4

    Google Scholar 

  29. J. Lee, H. Wang, Study of subharmonically injection-locked PLLs. IEEE J. Solid State Circuits 44(5), 1539–1553 (2009)

    Article  Google Scholar 

  30. L. Lin, L. Tee, P. Gray, A 1.4 GHz differential low-noise CMOS frequency synthesizer using a wideband PLL architecture, in 2000 IEEE International Solid-State Circuits Conference. Digest of Technical Papers (IEEE, Piscataway, 2000), pp. 204–205

    Google Scholar 

  31. S. Liu, Y. Zheng, W. M. Lim, W. Yang, Ring oscillator based injection locked frequency divider using dual injection paths. IEEE Microwave Wireless Compon. Lett. 25(5), 322–324 (2015)

    Article  Google Scholar 

  32. L. Lu, J. Chien, A wide-band CMOS injection-locked ring oscillator. IEEE Microwave Wireless Compon. Lett. 15(10):676–678 (2005)

    Article  Google Scholar 

  33. R. Mackey, Injection locking of klystron oscillators. IRE Trans. Microwave Theory Tech. 10(4), 228–235 (1962)

    Article  Google Scholar 

  34. R. Miller, Fractional-frequency generators utilizing regenerative modulation. Proc. Inst. Radio Eng. 27(7), 446–457 (1939)

    Google Scholar 

  35. A. Mirzaei, M. Heidari, A. Abidi, Analysis of oscillators locked by large injection signals: generalized Adler’s equation and geometrical interpretation, in IEEE Custom Integrated Circuits Conference 2006 (IEEE, Piscataway, 2006), pp. 737–740

    Google Scholar 

  36. A. Mirzaei, M. Heidari, R. Bagheri, A. Abidi, Multi-phase injection widens lock range of ring-oscillator-based frequency dividers. IEEE J. Solid State Circuits 43(3), 656–671 (2008)

    Article  Google Scholar 

  37. A. Mirzaei, M. Heidari, R. Bagheri, S. Chehrazi, A. Abidi, The quadrature LC oscillator: a complete portrait based on injection locking. IEEE J. Solid State Circuits 42(9), 1916–1932 (2007)

    Article  Google Scholar 

  38. H. Moyer, A. Daryoush, A unified analytical model and experimental validations of injection-locked processes. IEEE Trans. Microwave Theory Tech. 48(4), 493–499 (2000)

    Article  Google Scholar 

  39. A. Musa, K. Okada, A. Matsuzawa, Progressive mixing technique to widen the locking range of high division-ratio injection-locked frequency dividers. IEEE Trans. Microwave Theory Tech. 61(3), 1161–1173 (2013)

    Article  Google Scholar 

  40. H. Ng, R. Farjad-Rad, M. Lee, W. Dally, T. Greer, J. Poulton, J. Edmondson, R. Rathi, R. Senthinathan, A second-order semidigital clock recovery circuit based on injection locking. IEEE J. Solid State Circuits 38(12), 2101–2110 (2003)

    Article  Google Scholar 

  41. F. O’Mahony, S. Shekhar, M. Mansuri, G. Balamurugan, J. Jaussi, J. Kennedy, B. Casper, D. J. Allstot, R. Mooney, A 27 Gb/s forwarded-clock I/O receiver using an injection-locked LC-DCO in 45 nm CMOS, in 2008 IEEE International Solid-State Circuits Conference. Digest of Technical Papers (IEEE, Piscataway, 2008), pp. 452–627

    Google Scholar 

  42. L. Paciorek, Injection locking of oscillators. Proc. IEEE 53(11), 1723–1727 (1965)

    Article  Google Scholar 

  43. F. Plessas, F. Gioulekas, G. Kalivas, Phase noise performance of fully differential sub-harmonic injection-locked PLL. Electron. Lett. 46(19), 1319–1321 (2010)

    Article  Google Scholar 

  44. H. Rategh, T. Lee, Superharmonic injection-locked frequency dividers. IEEE J. Solid State Circuits 34(6), 813–821 (1999)

    Article  Google Scholar 

  45. I. Schmideg, Harmonic synchronization of nonlinear oscillators. Proc. IEEE 59(8), 1250–1251 (1971)

    Article  Google Scholar 

  46. S. Shekhar, M. Mansuri, F. O’Mahony, G. Balamurugan, J. E. Jaussi, J. Kennedy, D. Allstot, R. Mooney, B. Casper, Strong injection locking in low-Q LC oscillators: modeling and application in a forwarded-clock I/O receiver. IEEE Trans. Circuits Syst. I 56(8), 1818–1829 (2009)

    Article  MathSciNet  Google Scholar 

  47. D. Shin, S. Park, S. Raman, K. Koh, A subharmonically injection-locked PLL with 130 fs RMS jitter at 24 GHz using synchronous reference pulse injection from nonlinear VCO envelope feedback, in Proceedings of the IEEE Radio Frequency Integrated Circuits Symposium (IEEE, Piscataway, 2017), pp . 100–103

    Google Scholar 

  48. N. Soltani, F. Yuan, Non-harmonic injection-locked phase-locked loops with applications in remote frequency calibration of passive wireless transponders. IEEE Trans. Circuits Syst. I 57(12), 2381–2393 (2010)

    Article  MathSciNet  Google Scholar 

  49. M. Tiebout, A CMOS direct injection-locked oscillator topology as high-frequency low-power frequency divider. IEEE J. Solid State Circuits 39(7), 1170–1174 (2004)

    Article  Google Scholar 

  50. A. Tofangdarzade, A. Jalali, An efficient method to analyze lock range in ring oscillators with multiple injections. IEEE Trans. Circuits Syst. II 62(11), 1013–1017 (2015)

    Article  Google Scholar 

  51. A. Tofangdarzade, A. Tofangdarzade, N. Saniei, Strong injection locking and pulling in LC multiphase oscillators with multiple injection signals. IEEE Trans. Circuits Syst. II (2018, accepted)

    Google Scholar 

  52. D. Tucker, Forced oscillations in oscillator circuits, and the synchronization of oscillators. J. Inst. Radio Eng. Part III: Radio Commun. Eng. 92(19), 226–234 (1945)

    Google Scholar 

  53. D. Tucker, Forced oscillations in oscillator circuits, and the synchronization of oscillators. J. Inst. Radio Eng. Part I: Gen. 93(61), 57–58 (1946)

    Google Scholar 

  54. B. van der Pol, The nonlinear theory of electric oscillations. Proc. Inst. Radio Eng. 22(9), 1051–1086 (1934)

    MATH  Google Scholar 

  55. S. Verma, H. Rategh, T. Lee, A unified model for injection-locked frequency divider. IEEE J. Solid State Circuits 38(6), 1015–1027 (2003)

    Article  Google Scholar 

  56. J. Vincent, On some experiments in which two neighbouring maintained oscillatory circuits affect a resonating circuit. Proc. Phys. Soc. Lond. 32, 84–91 (1919)

    Article  Google Scholar 

  57. C. Wei, T. Kuan, S. Liu, A subharmonically injection-locked PLL with calibrated injection pulsewidth. IEEE Trans. Circuits Syst. II 62(6), 548–552 (2015)

    Article  Google Scholar 

  58. K. Yamamoto, M. Fujishima, 55 GHz CMOS frequency divider with 3.2 GHz locking range, in Proceedings of the 30th European Solid-State Circuits Conference (IEEE, Piscataway, 2004), pp. 135–138

    Google Scholar 

  59. X. Yi, C. Boon, M. Do, K. Yeo, W. Lim, Design of ring-oscillator-based injection-locked frequency dividers with single-phase inputs. IEEE Microwave Wireless Compon. Lett. 21(10), 559–561 (2011)

    Article  Google Scholar 

  60. X. Yu, H. Cheema, R. Mahmoudi, A. van Roermund, X. Yan, A 3 mW 54.6 GHz divide-by-3 injection locked frequency divider with resistive harmonic enhancement. IEEE Microwave Wireless Compon. Lett. 19(9), 575–577 (2009)

    Google Scholar 

  61. F. Yuan, Y. Zhou, A phasor-domain study of lock range of harmonic oscillators with multiple injections. IEEE Trans. Circuits Syst. II 59(8), 466–470 (2012)

    Article  Google Scholar 

  62. F. Yuan, Y. Zhou, Frequency-domain study of lock range of non-harmonic oscillators with multiple multi-tone injections. IEEE Trans. Circuits Syst. I 60(6), 1395–1406 (2013)

    Article  MathSciNet  Google Scholar 

  63. F. Yuan, Y. Zhou, Injection signaling in relaxation oscillators. Analog Integr. Circ. Sig. Process 2019, 1–6 (2019)

    Google Scholar 

  64. L. Zhang, B. Ciftcioglu, M. Huang, H. Wu, Injection-locked clocking: a new GHz clock distribution scheme, in Proceedings of the IEEE Custom Integrated Circuits Conference (IEEE, Piscataway, 2006), pp. 785–788

    Google Scholar 

  65. Z. Zhang, L. Liu, N. Wu, A novel 2.4-to-3.6 GHz wideband subharmonically injection-locked PLL with adaptively-aligned injection timing, in Proceedings of the IEEE Asian Solid-State Circuits Conference (IEEE, Piscataway, 2014), pp. 369–372

    Google Scholar 

  66. X. Zhang, X. Zhou, A. Daryoush, A theoretical and experimental study of the noise behavior of subharmonically injection locked local oscillators. IEEE Trans. Microwave Theory Tech. 40(5), 895–902 (1992)

    Article  Google Scholar 

  67. Y. Zhou, F. Yuan. A study of lock range of injection-locked CMOS active-inductor oscillators using a linear control system approach. IEEE Trans. Circuits Syst. II 58(10), 627–631 (2011)

    Article  Google Scholar 

  68. Y. Zhou, F. Yuan, Study of injection-locked non-harmonic oscillators using volterra series. IET Circuits Devices and Syst. 9(2), 119–130 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Yuan, F. (2020). Injection-Locking of Oscillators: An Overview. In: Injection-Locking in Mixed-Mode Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-030-17364-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-17364-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17362-3

  • Online ISBN: 978-3-030-17364-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics