THE EQUIVALENT SELF-INDUCTANCE OF <I>N</I> COUPLED PARALLEL COILS

Abstract

Abstract-Based on Faraday's law of electromagnetic induction and the existence condition of nontrivial solution to a homogeneous and linear differential system of equations, the equivalent selfinductance of N coupled parallel coils has been derived by using some algebraic techniques. It can be expressed as the ratio of the determinants of two matrices, with ranks of N and N − 1, respectively, and constructed with the self and mutual inductance of those coils. In addition, special conclusions are deduced and/or discussed in detail for three particular cases: 1. the completely uncoupled case, 2. the identical and symmetrical case, and 3. the completely coupled case, which are coincident with the existing results in the references.

Numerical Evaluation and Experimental Test on a New Giant Magnetostrictive Transducer with Low Heat Loss Design

“…The geometric feature of parallel wiring harness is that each layer of coil in the skeleton is a layer of nested helix, thus it meets the inductive coupling model, as shown in Figure 6. Since the magnetic field direction of the two parallel coils is similar, assume the inductance of the single coil is L , and the inductance after coupling is ' L , then it should satisfy the following equation [21],…”

“…where K is the coupling coefficient of mutual inductance coil and M is mutual inductance coil. By introducing Equation (4) into Equation (3), we get the following result, Since the magnetic field direction of the two parallel coils is similar, assume the inductance of the single coil is L, and the inductance after coupling is L , then it should satisfy the following equation [21],…”

Analysis and Optimal Design of Induction Heating Cookers

“…where V P is input supply voltage and I * P is the conjugate of primary winding current I P which can be obtained from (9). The power delivered to the secondary winding can be calculated as in (12).…”

“…The combined equation in the form of impedance matrices for the elements of secondary winding is given as in (8), [9]. .…”

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“…Note that in this symmetric discharge circuit the current introduced by each of the two units is the same (I C1 =I C2 =I C /2). Furthermore, in the case of N C identical CLIQ units connected symmetrically across 2N C coil sections with the same self-and mutual inductances, the equivalent inductance per unit length is decreased proportionally to N 2 C [106,121]. The total capacitance of the system is increased by a factor N C , and its equivalent resistance reduced by a factor N C , since the units are also in parallel.…”