隨著射頻(radio frequency, RF)電路與通訊IC的設計越來越多，對於晶片上螺旋型電感(on-chip spiral inductors)以及晶片上變壓器(on-chip transformers)探討也越來越多。傳統上，使用晶片上螺旋型電感以及晶片上變壓器的設計者，都是經由量測或模擬軟體來抽取S-parameters，再將S-parameters轉換成RLGCK模型分析。所以我們認為提供設計者一個方便合成與分析的系統是非常重要的，本論文提供一個的GUI介面AutoHenry，讓設計者使用我們的方法更容易以及方便，這是一套可以自動化合成傳輸線、晶片上螺旋型電感以及晶片上變壓器的工具，並且可以大量的模擬，AutoHenry可以自動產生包含所有RLGCK與S-parameters輸出檔。AutoHenry可以建立傳輸線、晶片上螺旋型電感以及晶片上變壓器的模型。當然，AutoHenry是可以選擇不同的製程，只要在AutoHenry界面上輸入規格，即可以幫助設計者合成出他們想要的片上螺旋型電感以及晶片上變壓器。AutoHenry在模擬時間上也比其他電磁模擬軟體來的快，大概有快2倍以上。在設計時間上，因為可以自動化的模擬以及大量化的掃瞄而讓使用者可以免去重複設計的困擾，所以節省了設計者大量的時間。

本論文提出時域與頻域方法來分析晶片上的被動元件參數，如晶片上螺旋型電感以及晶片上變壓器。在頻域方法提供了S2-function與S4-function，S2-function可以將晶片上螺旋型電感的S-parameters轉換成被動元件的RLGCK參數而S4-function使用在晶片上變壓器。這些RLGCK參數可以讓設計者更容易了解元件的物理特性與模型化。在時域方法上，先直接抽取元件的RLGCK參數，接者將抽取好的RLGCK參數輸入到HSPICE產生S-parameters，此方法提供設計者一種不同的方法得到S-parameters。經由我們所作的大量測試結構，這種方法的精確是可以被接受的。而我們也發現，將晶片上螺旋型電感以及晶片上變壓器被使用的集總模型(lumped model)直接用在HSPICE輸入檔裡會有很大的誤差，尤其是在高頻上誤差更是很大。所以我們提出了使用分散式模型(distributed model)來模擬，顯示在內文圖3-6與3-7。而圖3-8至3-11顯示必須要切成100段才能模擬準確，否則會有15%到17倍的誤差。

而在晶片上變壓器我們提供2-port與4-port的模擬結果，來證明我們的方法也可以使用在四埠的被動元件。在測試結構模擬中，我們使用HFSS(3D)、ADS(2.5D)與IE3D(2.5D)等商業電磁模擬軟體來與我們的方法比較與驗證。模擬過程中，我們也發現，這些模擬軟體在抽出S-parameters後，要將S-parameters轉換為元件的模型參數過程並不是那麼容易，有些參數甚至給的不精確，而且在小尺寸的被動元件，這些模擬軟體模擬出來的參數也有不精確的現象，所以本論文提供的方法與AutoHenry可以提供設計者使用解決此問題。

With the rapid growing design of RF circuit and communication integrated circuit, researches in interconnects, on-chip spiral inductors, and transformers become more and more important. Traditionally, designers of on-chip spiral inductors and transformers almost extract S-parameter by measurement or electromagnetic simulation software tools. They then use S-parameters to analyze or convert S-parameters to RLGCK model. So we think it is important to provide a designer a convenient system of synthesis and analysis. This thesis also provides a GUI called AutoHenry to let users use the method easily and quickly. This is a tool which can synthesize interconnects, on-chip spiral inductors and on-chip transformers. AutoHenry also has a large number of simulations. AutoHenry can automatically produce output files which provide all RLGCK parameters. AutoHenry can construct interconnects, on-chip spiral inductors and on-chip transformers model, and it can also construct these devices for any process. AutoHenry can help designers to synthesize desirable on-chip spiral inductors and on-chip transformers. AutoHenry is more than two times faster than electromagnetic simulation software. Because AutoHenry can automatic simulation and a large number of sweeping, user can reduce the repeat design and save a lot of time.

This thesis proposes frequency-domain and time-domain methods to analyze the on-chip passive device parameters as on-chip spiral inductors and transformers. The frequency-domain methods are S2-function and S4-function. S2-function can convert on-chip spiral inductors’s S-parameters to the RLGCK parameters of modeled circuitry, and S4-function uses on on-chip transformers. The RLGCK parameters can provide designers insight of the physical characteristic of devices and modeling. The time-domain methods provide designers a different way to get S-parameters by directly extracting time domain RLGCK parameters of the device, and then use HSPICE to output S-parameters. The accuracy of our methods can be accepted by a lot of experiments. We also find the lumped model of on-chip spiral inductors and transformers, which input HSPICE have enormous errors. The errors are larger at high frequency especially. So we propose using distributed model to simulate which are shown in Fig. 3-6 and Fig. 3-7. The Fig. 3-8 to Fig. 3-11 are shown that we must cut device model into one hundred segments and the results would be accurate, otherwise the error have between 15% and seventeen times.

This thesis provides 2-port and 4-port results to prove our methods which can apply to 4-port passive devices. We use commercial electromagnetic simulation software as HFSS(3D), ADS(2.5D) and IE3D(2.5D) to compare and verify our methods. We find that converting S-parameters to device’s modeling parameters are not easy after extracting S-parameters by these simulation software tools. Moreover, these simulation software tools are not accurate for passive devices of small dimensions. Hence our methods and AutoHenry can provide designs to solve it.

[1] S. S. Mohan, M. del Mar Hershenson, S. P. Boyd, and T. H. Lee, "Simple accurate expressions for planar spiral inductances," IEEE Journal of Solid-State Circuits, vol. 34, no. 10, pp. 1419-1424, Oct. 1999.
[2] H. M. Hsu, J. Z. Chang, and H. C. Chien, "Coupling effect of on-chip inductor with variable metal width," IEEE Microwave and Wireless Components Letters, vol. 17, no. 7, pp. 498-500, July 2007.
[3] C. P. Yue and S. S. Wong, "On-chip spiral inductors with patterned ground shields for Si-based RF ICs," IEEE Journal of Solid-State Circuits, vol. 33, no. 5, pp. 743-752, May 1998.
[4] H. M. Hsu, C. W. Tseng, and K. Y. Chan, "Characterization of on-chip transformer using microwave technique," IEEE Trans. Electron Devices, vol. 55, no. 3, pp. 833-837, March 2008.
[5] Q. El-Gharniti, E. Kerherve, and J.-B. Begueret, "Design and modeling of on-chip monolithic transformers with patterned ground shield," in Proc. IEEE International Symposium on Circuits and Systems, ISCAS 2006, pp. 4, 2006.
[6] H. M. Hsu, S. H. Lai, and C. J. Hsu, "Compact layout of on-chip transformer," IEEE Trans. Electron Devices, vol. 57, no. 5, pp. 1076-1083, May 2010.
[7] J. N. Burghartz, D. C. Edelstein, M. Soyuer, H. A. Ainspan, and K. A. Jenkins, "RF circuit design aspects of spiral inductors on silicon," IEEE Journal of Solid-State Circuits, vol. 33, no. 12, pp. 2028-2034, Dec. 1998.
[8] M. Kamon, M. J. Tsuk, and J. K. White, "FASTHENRY: A multipole-accelerated 3-D inductance extraction program," IEEE Trans Microwave Theory and Techniques, vol. 42, no. 9, pp. 1750-1758, Sept. 1994.
[9] W. R. Eisenstadt, and Y. Eo, "S-parameter-based IC interconnect transmission line characterization," IEEE Trans. Components, Hybrids, and Manufacturing Technology, vol. 15, no. 4, pp. 483-490, Aug. 1992.
[10] H. Murphy, K. G. McCarthy, C. J. P. Delabie, A. C. Murphy, and P. J. Murphy, "Design of multiple-metal stacked inductors incorporating an extended physical model," IEEE Trans. Microwave Theory and Techniques, vol. 53, no. 6, pp. 2063- 2072, June 2005.
[11] K. M. Ho, K. Vaz, and M. Caggiano, "Scattering parameter characterization of differential four-port networks using a two-port vector network analyzer," in Proc. Electronic Components and Technology Conf. ECTC’06, Vol. 2, Piscataway, NJ, USA, 31 May-3 June, pp. 1846- 1853, 2005.
[12] K. Kang, J. Brinkhoff, J. Shi, and F. Lin, "On-chip coupled transmission line modeling for millimeter-wave applications using four-port measurements," IEEE Trans. Advanced Packaging, vol. 33, no. 1, pp. 153-159, Feb. 2010.
[13] P. Arcioni, R. Castello, L. Perregrini, E. Sacchi, and F. Svelto, "An innovative modelization of loss mechanism in silicon integrated inductors," IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, no. 12, pp. 1453-1460, Dec. 1999.
[14] [Online]. Abailable: http://www.ifixit.com/Teardown/Nexus-One-Teardown/1654
/2
[15] T. H. Wang and K. J. Chang, “AutoHenry: a method to extract on-chip device parameters and s-parameters,” in Proc. VLSI Design/ CAD Symposium , Yunlin, Taiwan, Aug. 2-5, 2011, pp. 636-639.