Scalable wideband equivalent circuit model for silicon-based on-chip transmission lines

Abstract: A scalable wideband equivalent circuit model of silicon-based on-chip transmission lines is presented in this paper along with an efficient analytical parameter extraction method based on improved characteristic function approach, including a relevant equation to reduce the deviation caused by approximation. The model consists of both series and shunt lumped elements and accounts for high-order parasitic effects. The equivalent circuit model is derived and verified to recover the frequency-dependent parameters at a range from direct current to 50 GHz accurately. The scalability of the model is proved by comparing simulated and measured scattering parameters with the method of cascade, attaining excellent results based on samples made from CMOS 0.13 and 0.18μm process.

Key words: on-chip transmission line, equivalent circuit model, wideband, characteristic function, scalability

References:

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[15]	Chen H H, Zhang H W, Chung S J. Accurate systematic model-parameter extraction for on-chip spiral inductors[J]. IEEE Trans Electron Devices, 2008, 55(11): 3267. doi: 10.1109/TED.2008.2005131
[16]	Dhaene T, De Zutter D. Selection of lumped element models for coupled lossy transmission lines[J]. IEEE Trans Comput Aided Design Integr Circuits Syst, 1992, 11(7): 805. doi: 10.1109/43.144845

[1]	Singh U, Garg A, Raghavan B. A 780 mW 4×28 Gb/s transceiver for 100 GbE gearbox PHY in 40 nm CMOS[J]. IEEE J Solid-State Circuits, 2014, 49(12): 3116. doi: 10.1109/JSSC.2014.2352299
[2]	Hu S, Kousai S, Wang H. A broadband mixed-signal CMOS power amplifier with a hybrid class-G doherty efficiency enhancement technique[J]. IEEE J Solid-State Circuits, 2016, 51(3): 598. doi: 10.1109/JSSC.2015.2508023
[3]	Yu T, Wang H Z, Zhou B. Multi-agent correlated equilibrium Q.(λ)learning for coordinated smart generation control of interconnected power grids[J]. IEEE Trans Power Syst, 2015, 30(4): 1669. doi: 10.1109/TPWRS.2014.2357079
[4]	Kan R, Tanaka T, Sugizaki G. A 10th generation 16-core SPARC64.processor for mission-critical UNIX server[J]. IEEE J Solid-State Circuits, 2014, 49(1): 32. doi: 10.1109/JSSC.2013.2284650
[5]	Therdsteerasukdi K, Byun G S, Ir J. Utilizing radiofrequency interconnect for a many-DIMM DRAM system[J]. IEEE J Emerg Sel Topic Circuits Syst, 2012, 2(2): 210. doi: 10.1109/JETCAS.2012.2193843
[6]	Antonsen T M, Vlasov A N, Chernin D P. Transmission line model for folded waveguide circuits[J]. IEEE Trans Electron Devices, 2013, 60(9): 2906. doi: 10.1109/TED.2013.2272659
[7]	Syms R R A, Sydoruk O, Solymar L. Transmission-line model of noisy electromagnetic media[J]. IEEE Trans Microw Theory Tech, 2013, 61(1): 14. doi: 10.1109/TMTT.2012.2226742
[8]	Yang C, Yu H, Shang Y. Characterization of CMOS metamaterial transmission line by compact fractional-order equivalent circuit model[J]. IEEE Trans Electron Devices, 2015, 62(9): 3012. doi: 10.1109/TED.2015.2458931
[9]	Zhu Y, Kang K, Wu Y. An equivalent circuit model with current return path effects for on-chip interconnect up to 80 GHz[J]. IEEE Trans Compon Packag Technol, 2015, 5(9): 1320. doi: 10.1109/TCPMT.2015.2448572
[10]	Zheng Z, Ren K, Sun L. A comparative study of three transmission line models for on-chip interconnects[J]. IEEE Int Conf Commun Pro Sol, 2014: 332.
[11]	Sun S, Kumar R, Rustagi S C. Wideband lumped element model for on-chip interconnects on lossy silicon substrate[J]. IEEE Radio Freq Integr Circuits Symp, 2006: 4.
[12]	Kang K, Nan L, Rustagi S C. A wideband scalable and SPICE-compatible model for on-chip interconnects up to 110 GHz[J]. IEEE Trans Microw Theory Tech, 2008, 56(4): 942. doi: 10.1109/TMTT.2008.919374
[13]	Gupta K C, Garg R, Chadha R. Computer aided design of microwave circuits[J]. Dedham, MA:Artech House, 1981.
[14]	Eisenstadt W R, Eo Y. S-parameter-based IC interconnect transmission line characterization[J]. IEEE Trans Compon, Hybrids, Manuf Technol, 1992, 15(4): 483. doi: 10.1109/33.159877
[15]	Chen H H, Zhang H W, Chung S J. Accurate systematic model-parameter extraction for on-chip spiral inductors[J]. IEEE Trans Electron Devices, 2008, 55(11): 3267. doi: 10.1109/TED.2008.2005131
[16]	Dhaene T, De Zutter D. Selection of lumped element models for coupled lossy transmission lines[J]. IEEE Trans Comput Aided Design Integr Circuits Syst, 1992, 11(7): 805. doi: 10.1109/43.144845

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H S Wang, W L He, M H Zhang, L Tang. Scalable wideband equivalent circuit model for silicon-based on-chip transmission lines[J]. J. Semicond., 2017, 38(6): 065004. doi: 10.1088/1674-4926/38/6/065004.

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