Lumped-circuit technique

As already mentioned, the lumped-circuit technique is the most widely used by the research community [16]. The dielectric response is measured in parallel-plate or coaxial geometry as an association of resistances (R) and capacitances (C) in parallel or series. In a.c. measurements only, the parallel and series electrical circuits can be forced to be equivalent [20] giving for the admittance, T((d) and impedance Z(co), the following equations ... 

Filters are combinations of microwave passive elements designed to have a specified frequency response. Typically, a topology of a filter is chosen based on established lumped element filter design theory. Then computer-aided design techniques are used to optimize the response of the circuit to the desired response. 

ABSTRACT State determination of Li-ion cells is often accomplished with Electrochemical Impedance Spectroscopy (EIS). The measurement results are in frequency domain and used to describe the state of a Li-ion cell by parameterizing impedance-based models. Since EIS is a costly measurement method, an alternative method for the parameterization of impedance-based models with time-domain data easier to record is presented in this work. For this purpose the model equations from the impedance-based models are transformed from frequency domain into time domain. As an excitation signal a current step is applied. The resulting voltage step responses are the model equations in time domain. They are presented for lumped and derived for distributed electrical circuit elements, i.e. Warburg impedance, Constant Phase Element and RCPE. A resulting technique is the determination of the inner resistance from an impedance spectrum which is performed on measurement data. 

Averaging methods. Equivalent resistance calculations in simple electric circuits is based on appropriate use of lumped or averaged properties. Similar results are desired in petroleum engineering, but in three widely used simulators we evaluated, averaging techniques are systematically abused. Formulas that are derived for linear (vs. cylindrical or spherical) flow under constant density, single-phase, identical-block-size assumptions are indiscriminately employed to process intermediate results in compressible, multiphase, variable grid block runs, leading to questionable results. 

Ametani, A. 1973. Modified traveling-wave techniques to solve electrical transients on lumped and distributed constant circuits Refraction-coefficient method. Proc. lEE 120(2) 497-504. 

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