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Method of Edge Currents for Calculating Mutual External Inductance in a Microstrip Structure
Marina Y. Koledintseva;James L. Drewniak;Thomas P. Van Doren;David J. Pommerenke;Matteo Cocchini;David M. Hockanson
PIER , 2008, DOI: 10.2528/PIER07101504
Abstract: Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequencyindependent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.
Mutual Inductance for an Explicitly Finite Number of Turns
John Thomas Conway
PIER B , 2011, DOI: 10.2528/PIERB10110103
Abstract: Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared out over the solenoid windings is explored.
Inductance of Circuit Structures for MIT LL Superconductor Electronics Fabrication Process with 8 Niobium Layers  [PDF]
Sergey K. Tolpygo,Vladimir Bolkhovsky,T. J. Weir,C. J. Galbraith,Leonard M. Johnson,Mark A. Gouker,Vasili K. Semenov
Physics , 2014, DOI: 10.1109/TASC.2014.2369213
Abstract: Inductance of superconducting thin-film inductors and structures with linewidth down to 250 nm has been experimentally evaluated. The inductors include various striplines and microstrips, their 90-degree bends and meanders, interlayer vias, etc., typically used in superconducting digital circuits. The circuits have been fabricated by a fully planarized process with 8 niobium layers, developed at MIT Lincoln Laboratory for very-large-scale superconducting integrated circuits. Excellent run-to-run reproducibility and inductance uniformity of better than 1% across 200-mm wafers have been found. It has been found that the inductance per unit length of stripline and microstrip line inductors continues to grow as the inductor linewidth is reduced deep into the submicron range to the widths comparable to the film thickness and magnetic field penetration depth. It is shown that the linewidth reduction does not lead to widening of the parameter spread due to diminishing sensitivity of the inductance to the linewidth and dielectric thickness. The experimental results were compared with numeric inductance extraction using commercial software and freeware, and a good agreement was found for 3-D inductance extractors. Methods of further miniaturization of circuit inductors for achieving circuit densities > 10^6 Josephson junctions per cm^2 are discussed.
Mutual Inductance and Force Exerted Between Thick Coils
Romain Ravaud;Guy Lemarquand;Valerie Lemarquand;Slobodan I. Babic;Cevdet Akyel
PIER , 2010, DOI: 10.2528/PIER10012806
Abstract: We present exact three-dimensional semi-analytical expressions of the force exerted between two coaxial thick coils with rectangular cross-sections. Then, we present a semi-analytical formulation of their mutual inductance. For this purpose, we have to calculate six and seven integrations for calculating the force and the mutual inductance respectively. After mathematical manipulations, we can obtain semi-analytical formulations based on only two integrations. It is to be noted that such integrals can be evaluated numerically as they are smooth and derivable. Then, we compare our results with the filament and the finite element methods. All the results are in excellent agreement.
Full-Wave Modeling of Stripline Structures in Multilayer Dielectrics
Konstantinos Nikellis;Nikolaos K. Uzunoglu;Yorgos Koutsoyannopoulos;Sotiris Bantas
PIER , 2006, DOI: 10.2528/PIER05071302
Abstract: A novel computational method based on full-wave analysis of stripline planar structures with vertical interconnects in multilayer dielectric media is presented. The method is based on the electric-field integral-equation solved with the Method of Moments (MoM). The special characteristics of stripline structures facilitate the extensive use of semi-analytical techniques to analyze the multilayer structures, limiting significantly the use of purely numerical techniques. The accuracy of the proposed modeling method is examined thoroughly with extensive numerical tests and the results are compared with results generated by commercial simulators for simple stripline structures.
Calculation of the Mutual Inductance and the Magnetic Force Between a Thick Circular Coil of the Rectangular Cross Section and a Thin Wall Solenoid (Integro-Differential Approach)
Slobodan I. Babic;Cevdet Akyel;Frederic Sirois;Guy Lemarquand;Romain Ravaud;Valerie Lemarquand
PIER B , 2011, DOI: 10.2528/PIERB11062111
Abstract: Systems that employ stimulating and implantable monitoring devices utilize inductive links, such as external and implanted coils. The calculation of the mutual inductance and the magnetic force between these coils is important for optimizing power transfer. This paper deals with an efficient and new approach for determining the mutual inductance and the magnetic force between two coaxial coils in air. The setup is comprised of a thick circular coil of the rectangular cross section and a thin wall solenoid. We use an integro-differential approach to calculate these electrical parameters. The mutual inductance and the magnetic force are obtained using the complete elliptic integrals of the first and second kind, Heuman's Lambda function and one term that has to be solved numerically. All possible regular and singular cases were solved. The results of the presented work have been verified with the filament method and previously published data. The advantage of these proposed formulas for mutual inductance or for the magnetic force is that they give the solution in the analytical and the semi-analytical form either for regular cases or singular cases. It is not case with already known methods in which it is necessary to take particular care of these cases of consideration.
Progress and Research on Interconnects Crosstalk in Deep Submicron Technology

Cai Yici,Zhao Xin,Hong Xianlong,

半导体学报 , 2003,
Abstract: As develops in deep sub micron designs,the interconnect crosstalk becomes much more serious.Espe cially, the coupling inductance can not be ignored in gigahertz designs.So shield insertion is an efficient technique to reduce the inductive noise.In this paper,the characteristics of on chip mutual inductance (as well as self) for coplanar,micro stripline and stripline structures are introduced first.Then base on the coplanar interconnect structures,the effective coupling K eff model and the RLC explicit noise model are proposed respectively.The results of experiments show that these two models both have high fidelity.
Intermode Dephasing in a Superconducting Stripline Resonator  [PDF]
Oren Suchoi,Baleegh Abdo,Eran Segev,Oleg Shtempluck,M. P. Blencowe,Eyal Buks
Physics , 2009,
Abstract: We study superconducting stripline resonator (SSR) made of Niobium, which is integrated with a superconducting interference device (SQUID). The large nonlinear inductance of the SQUID gives rise to strong Kerr nonlinearity in the response of the SSR, which in turn results in strong coupling between different modes of the SSR. We experimentally demonstrate that such intermode coupling gives rise to dephasing of microwave photons. The dephasing rate depends periodically on the external magnetic flux applied to the SQUID, where the largest rate is obtained at half integer values (in units of the flux quantum). To account for our result we compare our findings with theory and find good agreement. Supplementary info at arXiv:0901.3133 .
Validity Check of Mutual Inductance Formulas for Circular Filaments with Lateral and Angular Misalignments
Slobodan I. Babic;Frederic Sirois;Cevdet Akyel
PIER M , 2009, DOI: 10.2528/PIERM09060105
Abstract: In this paper we derived the formula for calculating the mutual inductance between circular filaments with lateral and angular misalignment by using the approach of the magnetic vector potential. The results obtained correspond to those of F. W. Grover, although the latter used the general formula given by the Neumann integral instead of a vector potential approach. However, the major purpose of this paper is to clarify some confusion introduced in previous works regarding the mutual inductance calculation between thin filamentary circular coils with parallel axes in air. This problem has been solved by Kim et al. (1997) using the magnetic vector potential, but unfortunately it leads to erroneous results, even for slight misalignments of the coils' center axes. This is why we chose to use the approach of the magnetic vector potential to show that, when properly derived, the results must indeed reduce to the well known F.W. Grover's formulas.
Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance

MENG Xiang-Guo,WANG Ji-Suo,ZHAI Yun,FAN Hong-Yi,

中国物理快报 , 2008,
Abstract: For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenbergequation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coefficient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.
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