In this brief we prove that both forms of Middlebrook's formula for the transfer impedance T of a two-port can be seen as particular instances of the more general expression T = T* (p_nq_3 + q_np_3)/(p_d q_3 + q_d p_3) , which involves a generic reference immittance, not necessarily an open-circuit or a short-circuit. The p-and q-parameters arising above owe to the use of a homogeneous description of the extra element and of the double null and the single injection immittances. The formula holds under minimal regularity assumptions.

This paper discusses a new modeling framework for switched circuits. The core idea is to avoid the distinction between the topologies defined by the short-and open-circuits corresponding to the on-and off-states of each ideal switch. We treat both cases in a uniform manner by describing Ohm's law in terms of a single variable u, via the relations i = pu, v = qu. The parameters p and q describe the state of the switch, either ideal or nonideal. An ideal switch is described by the values p = pon = 1, q = qon = 0 in the on-state and p = poff = 0, q = qoff = 1 in the off-state, whereas nonideal switches are described by nonzero values of qon and/or p off. Regardless of the number of switches, all working states of a given circuit can be described by means of a single model which, in essence, may be set up by conventional methods. This avoids the need to draw different schematics and write down a variety of models depending on the state of each switch, as it is almost invariably done when modeling switched circuits. We use this framework to address the state-space formulation problem for switched circuits. The results are then applied to the analysis of several DC-DC power converters and a multilevel inverter.

This paper discusses an analytical framework to model one-and two-ports in a way which avoids prioritizing either the voltage or the current as model variables. This approach allows for a truly general symbolic treatment of such circuits, avoiding the need to perform repetitive analyses in different working scenarios, and also displays a number of benefits from a theoretical point of view. The key ingredient is a homogeneous version of the Thévenin-Norton theorem for one-ports which possibly include controlled sources and coupling effects. This paves the way for the introduction of a comprehensive form for the transfer functions and the driving point immitances of two-ports, accounting for all possible impedance/admittance descriptions of the devices connected at the ports and also of the internal devices. Our framework allows e.g. for a universal definition of reciprocity but also for a straightforward derivation of Middlebrook's formulae in the context of the extra element theorem. Several examples illustrate the results.

The homogeneous description of a linear, uncoupled circuit is based on the assignment to each device of a triad $(p: q: s)$, where the parameters are defined up to a nonzero multiplicative constant and characterize a voltage-current relation of the form $pv-qi=s$. Given a one-port, the open-circuit and short-circuit network determinants, to be denoted as $p_e$ and $q_e$, are polynomial functions of the $p$- and $q$-parameters of the individual devices. With this formalism, we may state the Thévenin-Norton theorem in a uniform manner by saying that, for any given set of parameter values, if at least one of the functions $p_e$ and $q_e$ does not vanish then the voltage-current behavior at the port is characterized by a homogeneous triad $(p_e: q_e: s_e)$. In particular, the assumptions $p_e \neq 0$ and $q_e \neq 0$, respectively, characterize the existence of the Thévenin and the Norton equivalents, but the formulation proposed above avoids the need to make an a priori distinction between one form and another. We also show that the excitation parameter $s_e$ can be computed by inserting any admissible load at the port, but also analytically, in terms of the topology of the underlying digraph. The results hold without the need to specify whether each circuit element is a source or a passive device, much less to assume whether they are voltage- or current-controlled.