This paper describes the equivalent-circuit model of a metamaterial composed of conducting spheres and wires. This model involves electromagnetic coupling between the conductors, with retardation. The lumped-parameter equivalent circuit, which imports retardation to the electromagnetic coupling, is developed in this paper from Maxwell's equation. Using the equivalent-circuit model, we clarify the relationship between the retardation and radiation loss; we theoretically demonstrate that the electromagnetic retardation in the near-field represents the radiation loss of the meta-atom in the far-field. Furthermore, this paper focuses on the retarded electromagnetic coupling between two meta-atoms; we estimate the changes in the resonant frequencies and the losses due to the distance between the two coupled meta-atoms. It is established that the dependence characteristics are significantly affected by electromagnetic retardation.

The impedance expansion method (IEM), which was previously proposed by the authors, is a circuit-modeling technique for electrically-very-small devices. The equivalent circuits derived by the IEM include dependent voltage sources proportional to the powers of the frequency. However, the previous report did not describe how circuit simulators could realize such dependent voltage sources. This paper shows how this can be achieved by approximating the equivalent circuit using only passive elements.

To extract extrinsic resistances, conventional cold-FET methods require additional DC measurements or channel technological parameters. Additionally, the methods need at least two sets of cold-FET S-parameters measured at different cold-FET bias conditions in order to completely determine gate and drain pad capacitance as well as extrinsic gate, source and drain inductance and their resistances. One set of S-parameters handles the extraction of extrinsic inductances, and the other set extracts the gate and drain pad capacitance. To be free from additional DC measurement or channel technological parameters and reduce the number of sets of cold-FET S-parameters, we propose a cold-FET method that can extract all the extrinsic elements including the gate and drain capacitance, using only one set of cold-FET S-parameters. The method has shown excellent agreement between modeled and measured S-parameters up to 62 GHz at 56 different normal operating bias points.

We propose a new technique that is able to extract the small-signal equivalent-circuit elements of high electron mobility transistors (HEMTs) without causing any gate degradation. For the determination of extrinsic resistance values, unlike other conventional techniques, the proposed technique does not require an additional relationship for the resistances. For the extraction of extrinsic inductance values, the technique uses the R-estimate, which is known to be more robust relative to the measurement errors than the commonly used least-squares regression. Additionally, we suggest an improved cold HEMT model that seems to be more general than conventional cold HEMT models. With the use of the improved cold HEMT model, the proposed technique extracts the extrinsic resistance and inductance values.