Universal Approach of the Modified Nodal Analysis for Nonlinear Lumped Circuits in Transient Behavior

Envelope-Domain Analysis and Modeling of Super-Regenerative Oscillators

“…As an additional comment, both (11) and (30) are LTV transfer functions, but they are conceptually very different. The function (11), used for the stability analysis, is obtained by linearizing the SRO about the non-oscillatory periodic solution () q Xt , forced by the quench signal.…”

“…Otherwise unstable poles might be numerically cancelled with RHS zeroes. Instead, function (30) is obtained linearizing the SRO about the oscillatory solution () o Xt . The input considered in (30) is a small-signal sinusoidal source vin(t), introduced at the location of the input signal to be amplified.…”

“…The modified-nodal analysis (MNA) of a given nonlinear circuit is based on the application to this circuit of Kirchoff's laws [17], [26] taking into account the constitutive relationships of its elements or components. This provides the following general system of differential equations, in vector form [27]- [30]:…”

“…x is the vector containing the node voltages and branch currents that cannot be expressed in terms of node voltages and/or their first order derivatives [30], f is the vector of containing the linear and nonlinear resistive terms, q is the vector of linear and nonlinear charges and fluxes, [] d is a matrix containing the impulsive responses of the distributed elements, and () gt are the input generators. In circuits containing two different time scales, system (1) can be efficiently solved using the envelope-transient method [14]- [20].…”

“…The stability of the solution () q Xt is analyzed by introducing into the circuit a small-signal sinusoidal current source ip(t) at the frequency  [29]- [30]. In the presence of this small-signal source, the vector of state variables is expressed as [31]:…”