A completed model of the probabilistic distribution of the drain current’s random variation of the nanometer multiple input floating gate MOSFET (MIFGMOSFET) is proposed in this work. The modelling process has taken the dominant physical level causes of the drain current’s variations into account. Unlike its predecessor, the proposed model considers both N-type and P-type nanometer MIFGMOSFET. Moreover, the formerly neglected parasitic coupling capacitances have also been taken into account. The obtained modelling results, which are based on the derived drain current’s equations of nanometer MIFGMOSFET, are very accurate. They can predict the probabilistic distributions of the candidate N-type and P-type nanometer MIFGMOSFETs obtained by using Monte-Carlo simulations with 99% confidence and higher accuracy than that of the previous work. We also perform a comparative robustness study of the nanometer MIFGMOSFET of both types and demonstrate various interesting applications of our modelling results

An extensive s-domain multilinear algebraic model of the transformer has been proposed. This model is alternatively a tensor algebraic model because the multilinear algebra is alternatively the tensor algebra. Unlike the traditional matrix-vector approach, which relies on conventional linear algebra, this model, which in turn uses the multilinear algebra that is of higher dimension and is thus more generic, is applicable to those recently often cited transformers which often have unconventional characteristics such as frequency variant parameters, time variant parameters, and fractional impedance. Examples of such transformers are on-chip monolithic transformers, dynamic transformers, and transformers with fractional impedances. The imperfect coupling has been considered, and a multiple winding transformer has also been assumed. Applications of the proposed model to the chosen recent transformers with unconventional characteristics is presented. The effects of failure of Kron's postulate on power invariant and validity of duality invariant, which pertain to the mentioned issues, are also discussed. The proposed extensive model is more inclusive and up to date than the matrix-vector based model and previous algebraic models. However, it is more complicated.

In this research, the analysis of the active fractional circuits has been performed by using the fractional differential equation approach. Both voltage and current mode circuits have been taken into account. The fractional time component parameters have been included in the derivative terms within the fractional differential equations. This is because the consistency in time dimension between the fractional derivative and the conventional one, which is also related to the physical measurability, is concerned. The fractional derivatives have been interpreted in the Caputo sense. The resulting analytical solutions of the time dimensional consistency aware fractional differential equations have been determined. We have found that the dimensional consistency between both sides of the equations of the solutions, which cannot be achieved in the previous works, can be obtained. By applying different source terms to the obtained analytical solutions, the response of both voltage and current mode circuits have been determined and the behaviours of the circuits have been analysed. The fractional time constant and pole locations in the Fplane of these circuits have been determined. Their dynamic behaviours and stabilities have been analysed. Moreover, the discussion on circuit realizations with a fractional capacitor has also been made.