Coils exposed to eddy current and hysteresis losses are conventionally described by an inductance with equivalent core-loss resistance connected in parallel. The value of the equivalent core-loss resistance depends on the working frequency and the external wiring. Thus the model is less than satisfactory. The authors propose to describe loss inductance using fractional derivatives containing both a loss term and a storage term.After introducing the theory of fractional derivatives, the operating mode of the fractional coil model is explained by the example of an RLC oscillating circuit. Subsequent measurements of a series resonant circuit with a lossy coil impressively confirm the theoretical model with regard to both the frequency and time domains.

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This article describes the preparation of composite thick films via inkjet printing in one process step. A novel ceramic/polymer ink is developed, suitable for the fabrication of homogeneous dielectric composite thick films. Therefore, a barium strontium titanate (BST) dispersion is prepared and combined with a highly loaded polymer solution afterwards. Ba 0.6 Sr 0.4 TiO 3 is synthesized by a sol-gel method and dispersed in butyl diglycol using a stirred media mill. A poly(methyl methacrylate) (PMMA) solution is prepared in butanone and mixed with the BST dispersion to obtain an ink with a 50:50 volume ratio of BST and PMMA. The ink characteristics and printability are investigated, in particular the drying behavior of the ink at different temperatures and the morphology of the composite thick films.The drying behavior of low viscosity particle suspensions is often influenced by the coffee stain effect. However, for the developed composite ink no coffee stain effect is observed and homogeneous composite thick films are achieved. Afterwards, all-inkjet-printed capacitors are fabricated, using the developed composite ink. Finally, the relative permittivity e r and loss tangent tan d of the composite thick films are determined.