Method of Edge Currents for Calculating Mutual External Inductance in a Microstrip Structure

Abstract

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.

Inductance Comparison of the Solenoidal Coil of Modular Toroidal Coils Using the Analytical and Finite Element Method

“…Furthermore, the relation between θ and ϕ for the ith ring and the differential of ϕ, using Fig. 4, can be expressed as Equations (8) and (9). The dependency of the presented …”

“…Therefore, in the equations of mutual inductance between two rings, misalignments have to be taken into consideration. Many contributions have been made in the literature to the problem of mutual inductance calculation for coaxial circular coils [5][6][7][8][9][10][11]. These contributions have been based on the application of Maxwell's formula, Neumann's formula, and the Biot-Savart law.…”

Mutual Inductance Calculation for Non-Coaxial Circular Air Coils With Parallel Axes

“…Many contributions to the problem of mutual inductance calculation for circular coils have been made in the literature [3][4][5][6]. Many contributions have been based on the application of Maxwell's formula, Neumann's formula and the Biot-Savart law [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The mutual inductance of circular coils can be obtained in analytical or semi-analytical forms expressed over elliptic integrals of the first, second and third kind, Heuman's Lambda function, Bessel functions, and Legendre functions.…”

Mutual Inductance and Force Exerted Between Thick Coils

“…The calculation of mutual inductance for circular coils has been studied by many authors [3][4][5][6][7][8][9][10][11][12]. These papers are generally based on the application of Maxwell's formula, Neumann's formula and the Biot Savart law.…”