Inductance of perfectly conducting foils including spiral inductors

Abstract

layer will be studied in a subsequent paper. This paper has only studied the simpler lossless second layer, so that the ranges of application formula (14) can be checked for extensive variations of dielectric constants of both the first and second layer of the substrate. As seen from the above results, the ranges are indeed large.The capacitance formula of one layer substrate of Eq. (5) is simple as opposed to the "a little more complicated" formula of two layers of Eq. (14) in this paper. This is expected when there is one extra layer. However, since both are derived from the same synthetic asymptote technique (as pointed out at the end of subsection 3.3), the formula of two layers readily reduces to that of one layer of Eq. (5) , the impedance bandwidth of a patch antenna can be enhanced to over 30%. It is low in cost and simple in structure. However, this technique has the disadvantage of high cross-polarization, which is contributed by the portion of the probe normal to the ground plane. Using the phase-cancellation technique can effectively suppress the cross-polarized radiation of a single element antenna [3,4] or an array antenna [5][6][7]. However, the power divider increases the complexity of the antenna, which increases the antenna's fabrication cost. Recently, a suspended probe-fed plate antenna [8] and a meandering probe-fed patch antenna [9] were suggested for suppressing the cross-polarization level and increasing the impedance bandwidth of a probe-fed patch antennas. Even though the suspended probe and the meandering-shaped probe are easy to design and fabricate; one end is connected to the patch and the other is connected to a SMA connector. The fabricating process could be simpler if the connection point between the feeding probe and the patch was removed. Based on the concept of a meandering probe and an L-shaped probe, a modified L-shaped probe feed for the patch antenna is proposed in this paper. The antenna has characteristics of wide impedance bandwidth and low cross-polarization level. The experimental results show good agreement with the numerical simulations. ANTENNA STRUCTUREThe geometry of the modified L-shaped probe fed patch antenna is shown in Figure 1. For operation at 1.72 GHz as the center frequency, a 1-mm-thick rectangular aluminum patch, which has a width W ϭ 70 mm (0.4 0 ), a length L ϭ 60 mm (0.344 0 ), is selected. The patch locates at a height of H ϭ 17.5 mm (0.1 0 ) and is supported by plastic posts. The modified L-shaped probe is a combination of three horizontal parts and three vertical parts. It is connected to the inner conductor of a 50⍀ SMA launcher. The three vertical parts are related to the two gaps, g 1 and g 2 , which are both equal to 1.5 mm (0.0086 0 ); therefore, the lengths of the RESULTS AND DISCUSSIONAll results shown in this paper were obtained using Zeland IE3D version 9.35. The measured and simulated SWR and gain of the proposed antenna have been obtained and are shown in Figure 2. It shows that the simulated impedance bandwidth of the antenna is 21% ...

Numerical Solution of an Integro-Differential Equation for a Sheet Current

“…A numerical method for the computation of inductances of ideal infinitely thin conductors was suggested in [14]. It is based on triangular grids but is not a finite-element method, does not use the current function, and is based on physical arguments and a simple but very accurate approximation to the equations of magnetostatics.…”

“…Then relation (14) implies the simple estimate |b ij | ≤ Mh/m 3 ij . Therefore, the matrix entries are rapidly decreasing as m ij grows, which corresponds to the growth of the distance between the supports of finite elements.…”

CAD formula for inductance calculation of double‐level square spiral inductors

“…The other two brackets of the denominator are the mutual potentials from the quarter-spirals in different plane, where the terms in the second bracket of the denominator come from the mutual potential of two parallel plates [10][11][12]. Usually the power p in [1] can be set to 1. However, the maximum error of the inductance may reach up to 10%.…”

“…Microstrip antennas have found considerable interest since they are low-profile, inexpensive to manufacture, and compatible with monolithic microwave integrated circuit (MMIC) designs [1,2]. Although they are very popular, microstrip antennas suffer from low efficiency and narrow impedance bandwidth (BW).…”

“…Many authors have treated the spiral inductors with different analyses. Most of these approaches were based on numerical techniques [1,2], curve fitting, or empirical formulas [3].…”