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2023 | OriginalPaper | Buchkapitel

2. Fundamental Physics of Planar Inductors, Embedded Planar Transformers, and Planar (Patch) Antennas

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Abstract

This chapter provides a comprehensive review of the existing information|knowledge of planar spiral inductors, embedded planar transformers, and planar (patch) antennas. The review starts with examining Maxwell’s laws of electrodynamics that govern propagation of electromagnetic waves through conductors and dielectrics (insulators)—here the focus is on electromagnetic wave propagation through conductors. This key knowledge is then applied to analyze and understand the properties and performance metrics of planar spiral inductors, embedded planar transformers, and planar (patch) antennas.

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Literatur
1.
Zurück zum Zitat Long, J. R., & Cop. (1997). In addition, a periodic structure of transverse slots is used to suppress excitation of the fundamental even mode. Figure 9 shows the cross section of the antenna’s electric field profile with and without the mode suppressor. In the top figure, a substantial amount of asymmetry in the vertical field can be observed, indicating that both the fundamental (even) and the leakyeland, M. A. The Modeling, Characterization and Design of Monolithic Inductors for Silicon RF ICs. IEEE Journal of Solid-State Circuits, 32, 357–369. Long, J. R., & Cop. (1997). In addition, a periodic structure of transverse slots is used to suppress excitation of the fundamental even mode. Figure 9 shows the cross section of the antenna’s electric field profile with and without the mode suppressor. In the top figure, a substantial amount of asymmetry in the vertical field can be observed, indicating that both the fundamental (even) and the leakyeland, M. A. The Modeling, Characterization and Design of Monolithic Inductors for Silicon RF ICs. IEEE Journal of Solid-State Circuits, 32, 357–369.
2.
Zurück zum Zitat Niknejad, A. M., & Meyer, R. G. (1998). Analysis, design, and optimization of spiral inductors and transformers for Si RF ICs. IEEE Journal of Solid-State Circuits, 33, 1470–1481.CrossRef Niknejad, A. M., & Meyer, R. G. (1998). Analysis, design, and optimization of spiral inductors and transformers for Si RF ICs. IEEE Journal of Solid-State Circuits, 33, 1470–1481.CrossRef
3.
Zurück zum Zitat Reyes, A. C., El-Ghazaly, S. M., Dorn, S. J., Dydyk, M., Schrider, D. K., & Patterson, H. (1995). Coplanar waveguides and microwave inductors on silicon substrates. IEEE Transactions on Microwave Theory and Technology, 43, 2016–2022.CrossRef Reyes, A. C., El-Ghazaly, S. M., Dorn, S. J., Dydyk, M., Schrider, D. K., & Patterson, H. (1995). Coplanar waveguides and microwave inductors on silicon substrates. IEEE Transactions on Microwave Theory and Technology, 43, 2016–2022.CrossRef
4.
Zurück zum Zitat Ashby, K. B., Koullias, I. C., Finley, W. C., Bastek, J. J., & Moinian, S. (1996). High Q inductors for wireless applications in a complementary silicon bipolar process. IEEE Journal of Solid-State Circuits, 31, 4–9.CrossRef Ashby, K. B., Koullias, I. C., Finley, W. C., Bastek, J. J., & Moinian, S. (1996). High Q inductors for wireless applications in a complementary silicon bipolar process. IEEE Journal of Solid-State Circuits, 31, 4–9.CrossRef
5.
Zurück zum Zitat Lu, L. H., Ponchak, G. E., Bhattacharya, P., & Katehi, L. (2000). High-Q X-band and K‘-band micromachined spiral inductors for use in Si-based integrated circuits. Proceedings of Silicon Monolithic Integrated Circuits RF Systems, 108–112. Lu, L. H., Ponchak, G. E., Bhattacharya, P., & Katehi, L. (2000). High-Q X-band and K‘-band micromachined spiral inductors for use in Si-based integrated circuits. Proceedings of Silicon Monolithic Integrated Circuits RF Systems, 108–112.
6.
Zurück zum Zitat Bahl, I. J. (1999). Improved quality factor spiral inductor on GaAs substrates. IEEE Microwave Guided Wave Letters, 9, 398–400.CrossRef Bahl, I. J. (1999). Improved quality factor spiral inductor on GaAs substrates. IEEE Microwave Guided Wave Letters, 9, 398–400.CrossRef
7.
Zurück zum Zitat Ribas, R. P., Lescot, J., Leclercq, J. L., Bernnouri, N., Karam, J. M., & Courtois, B. (1998). Micromachined planar spiral inductor in standard GaAs HEMT MMIC technology. IEEE Electron Device Letters, 19, 285–287.CrossRef Ribas, R. P., Lescot, J., Leclercq, J. L., Bernnouri, N., Karam, J. M., & Courtois, B. (1998). Micromachined planar spiral inductor in standard GaAs HEMT MMIC technology. IEEE Electron Device Letters, 19, 285–287.CrossRef
8.
Zurück zum Zitat Takenaka, H., & Ueda, D. (1996). 0.15μm T-shaped gate fabrication for GaAs MODFET using phase shift lithography. IEEE Transactions on Electron Devices, 43, 238–244.CrossRef Takenaka, H., & Ueda, D. (1996). 0.15μm T-shaped gate fabrication for GaAs MODFET using phase shift lithography. IEEE Transactions on Electron Devices, 43, 238–244.CrossRef
9.
Zurück zum Zitat Chiou, M. H., & Hsu, K. Y. J. (2006). A new wideband modeling technique for spiral inductors. IET Microwave, Antennas, and Propagation, 151, 115–120.CrossRef Chiou, M. H., & Hsu, K. Y. J. (2006). A new wideband modeling technique for spiral inductors. IET Microwave, Antennas, and Propagation, 151, 115–120.CrossRef
10.
Zurück zum Zitat Lu, H.-C., Chan, T. B., Chen, C. C. P., & Liu, C. M. (2010). Spiral inductor synthesis and optimization with measurement. IEEE Transactions on Advanced Packaging, 33. Lu, H.-C., Chan, T. B., Chen, C. C. P., & Liu, C. M. (2010). Spiral inductor synthesis and optimization with measurement. IEEE Transactions on Advanced Packaging, 33.
11.
Zurück zum Zitat Talwalkar, N. A., Yue, C. P., & Wong, S. S. (2005). Analysis and synthesis of on-chip spiral inductors. IEEE Transactions on Electron Devices, 52, 176–182.CrossRef Talwalkar, N. A., Yue, C. P., & Wong, S. S. (2005). Analysis and synthesis of on-chip spiral inductors. IEEE Transactions on Electron Devices, 52, 176–182.CrossRef
12.
Zurück zum Zitat Mukherjee, S., Mutnury, S., Dalmia, S., & Swaminathan, M. (2005). Layout-level synthesis of RF inductors and filters in LCP substrate for Wi-fi applications. IEEE Transactions on Microwave Theory and Technology, 53, 2196–2210.CrossRef Mukherjee, S., Mutnury, S., Dalmia, S., & Swaminathan, M. (2005). Layout-level synthesis of RF inductors and filters in LCP substrate for Wi-fi applications. IEEE Transactions on Microwave Theory and Technology, 53, 2196–2210.CrossRef
13.
Zurück zum Zitat Kulkarni, J. P., Augustine, C., Jung, C., & Roy, K. (2010). Nano spiral inductors for low-power digital spintronic circuits. IEEE Trans. on Magnetics, 46, 1898–1901.CrossRef Kulkarni, J. P., Augustine, C., Jung, C., & Roy, K. (2010). Nano spiral inductors for low-power digital spintronic circuits. IEEE Trans. on Magnetics, 46, 1898–1901.CrossRef
14.
Zurück zum Zitat Greenhouse, H. M. (1974). Design of planar rectangular microelectronic inductors. IEEE Transactions on Parts, Hybrids and Packaging, 10, 101–109.CrossRef Greenhouse, H. M. (1974). Design of planar rectangular microelectronic inductors. IEEE Transactions on Parts, Hybrids and Packaging, 10, 101–109.CrossRef
16.
Zurück zum Zitat Jenei, S., Nauwelaers, B. K. J. C., & Decoutere, S. (2002). Physics-based closed-form inductance expression for compact modeling of integrated spiral inductors. IEEE Journal of Solid-State Circuits, 37, 77–80.CrossRef Jenei, S., Nauwelaers, B. K. J. C., & Decoutere, S. (2002). Physics-based closed-form inductance expression for compact modeling of integrated spiral inductors. IEEE Journal of Solid-State Circuits, 37, 77–80.CrossRef
17.
Zurück zum Zitat Asgaran, S. (2002). New accurate physics-based closed-form expressions for compact modeling and design of on-chip spiral inductors. Proceedings of the 14th International Conference on Microelectronics, 247–250. Asgaran, S. (2002). New accurate physics-based closed-form expressions for compact modeling and design of on-chip spiral inductors. Proceedings of the 14th International Conference on Microelectronics, 247–250.
18.
Zurück zum Zitat Mohan, S. S., Hershenson, M. M., Boyd, S. P., & Lee, T. H. (1999). Simple accurate expressions for planar spiral inductance. IEEE Journal of Solid-State Circuits, 34, 1419–1424.CrossRef Mohan, S. S., Hershenson, M. M., Boyd, S. P., & Lee, T. H. (1999). Simple accurate expressions for planar spiral inductance. IEEE Journal of Solid-State Circuits, 34, 1419–1424.CrossRef
19.
Zurück zum Zitat Chen, C. C., Huang, J. K., & Cheng, Y. T. (2005). A closed-form integral model of spiral inductor using the Kramers-Kronig relations. IEEE Microwave and Wireless Components Letters, 15. Chen, C. C., Huang, J. K., & Cheng, Y. T. (2005). A closed-form integral model of spiral inductor using the Kramers-Kronig relations. IEEE Microwave and Wireless Components Letters, 15.
20.
Zurück zum Zitat Sieiro, J., Lopez-Villegas, J. M., Cabanillas, J., Osorio, J. A., & Samitier, J. (2002). A physical frequency-dependent compact model for RF integrated inductors. IEEE Transactions on Microwave Theory and Technology, 50, 384–392.CrossRef Sieiro, J., Lopez-Villegas, J. M., Cabanillas, J., Osorio, J. A., & Samitier, J. (2002). A physical frequency-dependent compact model for RF integrated inductors. IEEE Transactions on Microwave Theory and Technology, 50, 384–392.CrossRef
21.
Zurück zum Zitat Sun, H., Liu, Z., Zhao, J., Wang, L., & Zhu, J. (2008). The enhancement of Q-factor of planar spiral inductor with low-temperature annealing. IEEE Transactions on Electron Devices, 55, 931–936.CrossRef Sun, H., Liu, Z., Zhao, J., Wang, L., & Zhu, J. (2008). The enhancement of Q-factor of planar spiral inductor with low-temperature annealing. IEEE Transactions on Electron Devices, 55, 931–936.CrossRef
22.
Zurück zum Zitat Tsai, H. S., Lin, L., Frye, R. C., Tai, K. L., Lau, M. Y., Kossives, D., Hrycenko, F., & Chen, Y. K. (1997). Investigation of current crowding effect on spiral inductors. IEEE MTT-S Symposium on Technologies to Wireless Applications, 139–142. Tsai, H. S., Lin, L., Frye, R. C., Tai, K. L., Lau, M. Y., Kossives, D., Hrycenko, F., & Chen, Y. K. (1997). Investigation of current crowding effect on spiral inductors. IEEE MTT-S Symposium on Technologies to Wireless Applications, 139–142.
23.
Zurück zum Zitat Bushyager, N., Davis, M., Dalton, E., Laskar, J., & Tentzeris, M. (2002). Q-factor and optimization of multilayer inductors for RF packaging microsystems using time domain techniques. Electronic Components and Technology Conference, 1718–1721. Bushyager, N., Davis, M., Dalton, E., Laskar, J., & Tentzeris, M. (2002). Q-factor and optimization of multilayer inductors for RF packaging microsystems using time domain techniques. Electronic Components and Technology Conference, 1718–1721.
24.
Zurück zum Zitat Eroglu, A., & Lee, J. K. (2008). The complete design of microstrip directional couplers using the synthesis technique. IEEE Transactions on Instrumentation and Measurement, 12, 2756–2761.CrossRef Eroglu, A., & Lee, J. K. (2008). The complete design of microstrip directional couplers using the synthesis technique. IEEE Transactions on Instrumentation and Measurement, 12, 2756–2761.CrossRef
25.
Zurück zum Zitat Costa, E. M. M. (2009). Parasitic capacitances on planar coil. Journal of Electromagnetic Waves and Applications, 23(17–18), 2339–2350.CrossRef Costa, E. M. M. (2009). Parasitic capacitances on planar coil. Journal of Electromagnetic Waves and Applications, 23(17–18), 2339–2350.CrossRef
26.
Zurück zum Zitat Nguyen, N. M., & Meyer, R. G. (1990). Si IC-compatible inductors and LC passive filter. IEEE Journal of Solid-State Circuits, 27(10), 1028–1031.CrossRef Nguyen, N. M., & Meyer, R. G. (1990). Si IC-compatible inductors and LC passive filter. IEEE Journal of Solid-State Circuits, 27(10), 1028–1031.CrossRef
27.
Zurück zum Zitat Zu, L., Lu, Y., Frye, R. C., Law, Y., Chen, S., Kossiva, D., Lin, J., & Tai, K. L. (1996). High Q-factor inductors integrated on MCM Si substrates. IEEE Transactions on Components. Packaging and Manufacturing Technology, Part B: Advanced Packaging, 19(3), 635–643. Zu, L., Lu, Y., Frye, R. C., Law, Y., Chen, S., Kossiva, D., Lin, J., & Tai, K. L. (1996). High Q-factor inductors integrated on MCM Si substrates. IEEE Transactions on Components. Packaging and Manufacturing Technology, Part B: Advanced Packaging, 19(3), 635–643.
28.
Zurück zum Zitat Burghartz, J. N., Soyuer, M., & Jenkins, K. (1996). Microwave inductors and capacitors in standard multilevel interconnect silicon technology. IEEE Transactions on Microwave Theory and Technology, 44(1), 100–103.CrossRef Burghartz, J. N., Soyuer, M., & Jenkins, K. (1996). Microwave inductors and capacitors in standard multilevel interconnect silicon technology. IEEE Transactions on Microwave Theory and Technology, 44(1), 100–103.CrossRef
29.
Zurück zum Zitat Merrill, R. B., Lee, T. W., You, H., Rasmussen, R., & Moberly, L. A. (1995). Optimization of high Q integrated inductors for multi-level metal CMOS. IEDM, 38.7.1–38.7.3. Merrill, R. B., Lee, T. W., You, H., Rasmussen, R., & Moberly, L. A. (1995). Optimization of high Q integrated inductors for multi-level metal CMOS. IEDM, 38.7.1–38.7.3.
30.
Zurück zum Zitat Chang, J. Y. C., & Abidi, A. A. (1993). Large suspended inductors on silicon and their use in a 2 μm CMOS RF amplifier. IEEE Electron Device Letters, 14(5), 246–248.CrossRef Chang, J. Y. C., & Abidi, A. A. (1993). Large suspended inductors on silicon and their use in a 2 μm CMOS RF amplifier. IEEE Electron Device Letters, 14(5), 246–248.CrossRef
31.
Zurück zum Zitat Craninckx, J., & Steyaert, M. (1997). A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors. IEEE Journal of Solid-State Circuits, 32(5), 736–745.CrossRef Craninckx, J., & Steyaert, M. (1997). A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors. IEEE Journal of Solid-State Circuits, 32(5), 736–745.CrossRef
32.
Zurück zum Zitat Lovelace, D., & Camilleri, N. (1994). Silicon MMIC inductor modeling for high volume, low cost applications. Microwave Journal, 60–71. Lovelace, D., & Camilleri, N. (1994). Silicon MMIC inductor modeling for high volume, low cost applications. Microwave Journal, 60–71.
33.
Zurück zum Zitat Kamon, M., Tsulk, M. J., & White, J. K. (1994). FASTHENRY a multipole accelerated 3-D inductance extraction program. IEEE Transactions on Microwave Theory and Technology, 42(9), 1750–1757.CrossRef Kamon, M., Tsulk, M. J., & White, J. K. (1994). FASTHENRY a multipole accelerated 3-D inductance extraction program. IEEE Transactions on Microwave Theory and Technology, 42(9), 1750–1757.CrossRef
34.
Zurück zum Zitat Pettenpaul, E., Kapusta, H., .Weisgerber, A., Mampe, H., Luginsland, J., Wolff, I. (1988). CAD models of lumped elements on GaAs up to 18 GHz, IEEE Transactions of Microwave Theory and Technology, 36(2) 294–304.CrossRef Pettenpaul, E., Kapusta, H., .Weisgerber, A., Mampe, H., Luginsland, J., Wolff, I. (1988). CAD models of lumped elements on GaAs up to 18 GHz, IEEE Transactions of Microwave Theory and Technology, 36(2) 294–304.CrossRef
35.
Zurück zum Zitat Howard, G. E., Yang, J. J., & Chow, Y. L. (1992). A multipipe model of general strip transmission lines for rapid convergence of integral equation singularities. IEEE Transactions on Microwave Theory Technology, 40(4), 628–636.CrossRef Howard, G. E., Yang, J. J., & Chow, Y. L. (1992). A multipipe model of general strip transmission lines for rapid convergence of integral equation singularities. IEEE Transactions on Microwave Theory Technology, 40(4), 628–636.CrossRef
36.
Zurück zum Zitat Gharpurey, R. Modeling and Analysis of Substrate Coupling in Integrated Circuits Doctoral. Thesis, University of California. Gharpurey, R. Modeling and Analysis of Substrate Coupling in Integrated Circuits Doctoral. Thesis, University of California.
37.
Zurück zum Zitat Stetzler, T., Post, I., Havens, J., & Koyama, M. (1995). A 2.7V to 4.5V single-chip GSM transceiver RF integrated circuit. IEEE International Solid-State Circuits Conference, 150–151. Stetzler, T., Post, I., Havens, J., & Koyama, M. (1995). A 2.7V to 4.5V single-chip GSM transceiver RF integrated circuit. IEEE International Solid-State Circuits Conference, 150–151.
38.
Zurück zum Zitat Kim, B. K., Ko, B. K., Lee, K., Jeong, J. W., Lee, K.-S., & Kim, S. C. (1995). Monolithic planar RF inductor and waveguide structures on silicon with performance comparable to those in GaAs MMIC. IEDM, 29.4.1–29.4.4. Kim, B. K., Ko, B. K., Lee, K., Jeong, J. W., Lee, K.-S., & Kim, S. C. (1995). Monolithic planar RF inductor and waveguide structures on silicon with performance comparable to those in GaAs MMIC. IEDM, 29.4.1–29.4.4.
39.
Zurück zum Zitat Krafesik, D., & Dawson, D. (1986). A closed-form expression for representing the distributed nature of the spiral inductor. Proceedings of the IEEE-MTT Monolithic Circuits Symposium, 87–91. Krafesik, D., & Dawson, D. (1986). A closed-form expression for representing the distributed nature of the spiral inductor. Proceedings of the IEEE-MTT Monolithic Circuits Symposium, 87–91.
40.
Zurück zum Zitat Kuhn, W. B., Elshabini-Riad, A., & Stephenson, F. W. (1995). Centre-tapped spiral inductors for monolithic bandpass filters. Electronics Letters, 31(8), 625–626.CrossRef Kuhn, W. B., Elshabini-Riad, A., & Stephenson, F. W. (1995). Centre-tapped spiral inductors for monolithic bandpass filters. Electronics Letters, 31(8), 625–626.CrossRef
43.
Zurück zum Zitat Mohri, K., Uchitama, T., Panina, L. V., Yamamoto, M., & Bushida, K. Recent Advances of Amorphous Wire CMOS IC Magneto-Impedance Sensors: Innovative High-Performance Micromagnetic Sensor Chip Copyright © 2015 Kaneo Mohri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided that it is properly cited. Mohri, K., Uchitama, T., Panina, L. V., Yamamoto, M., & Bushida, K. Recent Advances of Amorphous Wire CMOS IC Magneto-Impedance Sensors: Innovative High-Performance Micromagnetic Sensor Chip Copyright © 2015 Kaneo Mohri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided that it is properly cited.
44.
Zurück zum Zitat Kurup, H. B., Dinesh, S., Ramesh, M., & Rodrigues, M. (2020). Low profile dual-frequency shorted patch antenna. International Journal of recent Technology and Engineering, 8(5), 2277–3878. Kurup, H. B., Dinesh, S., Ramesh, M., & Rodrigues, M. (2020). Low profile dual-frequency shorted patch antenna. International Journal of recent Technology and Engineering, 8(5), 2277–3878.
45.
Zurück zum Zitat Mishra, A., Singh, P., Yadav, N. P., Ansari, J. A., & Viswakarma, B. R. (2009). Compact shorted microstrip patch antenna for dual band operation. Progress In Electromagnetics Research C, 9, 171–182.CrossRef Mishra, A., Singh, P., Yadav, N. P., Ansari, J. A., & Viswakarma, B. R. (2009). Compact shorted microstrip patch antenna for dual band operation. Progress In Electromagnetics Research C, 9, 171–182.CrossRef
46.
Zurück zum Zitat Ansari, J. A., Singh, P., Yadav, N. P., & Viswakarma, B. R. (2009). Analysis of shorting pin loaded half disk patch antenna for wideband operation. Progress in Electromagnetics Research C, 6, 179–192.CrossRef Ansari, J. A., Singh, P., Yadav, N. P., & Viswakarma, B. R. (2009). Analysis of shorting pin loaded half disk patch antenna for wideband operation. Progress in Electromagnetics Research C, 6, 179–192.CrossRef
49.
Zurück zum Zitat Tripathi, A. K., Bhatt, P. K., & Pandey, A. K. (2012). A comparative study of rectangular and triangular patch antenna using HFSS and CADFEKO. International Journal of Computer Science and Information Technologies, 3(6), 5356–5358. Tripathi, A. K., Bhatt, P. K., & Pandey, A. K. (2012). A comparative study of rectangular and triangular patch antenna using HFSS and CADFEKO. International Journal of Computer Science and Information Technologies, 3(6), 5356–5358.
50.
Zurück zum Zitat Li, R. L., Wu, T., Pan, B., Lim, K., Laskar, J., & Tentzeris, M. M. (2009). Equivalent circuit analysis of a broadband printed dipole with adjusted integrated balun and array for base station applications. IEEE Transactions on Antennas and Propagation, 57(7). Li, R. L., Wu, T., Pan, B., Lim, K., Laskar, J., & Tentzeris, M. M. (2009). Equivalent circuit analysis of a broadband printed dipole with adjusted integrated balun and array for base station applications. IEEE Transactions on Antennas and Propagation, 57(7).
51.
Zurück zum Zitat Application Note 639 Design of Printed Trace Differential Loop Antennas Copyright 2021 Silicon Laboratories Inc. Application Note 639 Design of Printed Trace Differential Loop Antennas Copyright 2021 Silicon Laboratories Inc.
53.
Zurück zum Zitat Balanis, C. A. (2016). Antenna theory analysis and design fourth edition. Wiley. Library of Congress Cataloging-in-Publication Data:ISBN 978-1-118-642060-1 (cloth) 1. Antennas (Electronics) I. Title.TK7871.6.B354 2016 621.382. Balanis, C. A. (2016). Antenna theory analysis and design fourth edition. Wiley. Library of Congress Cataloging-in-Publication Data:ISBN 978-1-118-642060-1 (cloth) 1. Antennas (Electronics) I. Title.TK7871.6.B354 2016 621.382.
Metadaten
Titel
Fundamental Physics of Planar Inductors, Embedded Planar Transformers, and Planar (Patch) Antennas
verfasst von
Amal Banerjee
Copyright-Jahr
2023
DOI
https://doi.org/10.1007/978-3-031-08778-3_2

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