Impedance formulas problems

The deductive knowledge is represented as a taxonomy of production rules that implements the knowledge relevant to the applicable electrical laws and formulae, such as Ohm law, Kirchhoff laws, equivalent impedance formulae, etc. The system uses the symbolic method (electrical quantities represented as complex numbers) in its problem solving activity. 

Problems with Existing Impedance Formulas Used in Circuit Theory-Based Approaches... 

ABSTRACT Eddy current sensors are well-established in industrial appheations, such as in hot testing of rolled rods. However, the eddy current sensors currently in use are not able to detect longitudinal cracks in hod rolled rods. This paper introduces a 3D eddy current model which allows an investigation of this particular problem. Generally, 3D eddy current Finite Element Analysis (FEA) are time consuming due to the fine mesh as a result of the small penetration depth of the currents. The introduced 3D FEA model calculates the complex coil impedance of a detection coil affected by a rod with cracks using the current sheet approximation with additional correction formulas. 

These relations offer the possibility to examine measured transfer functions (impedance spectra) on errors caused by time instability or time drift. However, KK-checking techniques have fundamental problems in their application to practical measurements. Therefore many attempts have been made to overcome these limitations by means of different interpolation procedures. An attempt is the Z-HIT approximation, applied by Schiller et al. [2001], Agarwal et al. [1995], and Ehm et al. [2000], an approximation formula for the calculation of the impedance modulus course from the phase angle by integration. 

Once these substitutions are made, the electrical formulas and intuition can be applied to thermal problems. Ohm s law, voltage dividers, parallel and series impedances and conductances, and capacitors charging through a resistor all have thermal analogs. 

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