An analytical representation of operation principles of boost-type quasi-Z-source (QZS) dc-dc converter is obtained by determining of commutation intervals (where semiconductor switches keep their fixed states) inside a single operation period. An analytical model of converter is obtained by composing of nodal admittance matrix (NAM) by using of Kirchhoff’s voltage law and written-up in Laplace-domain by using of operational calculus method applied for each commutation interval. Finding the inverse nodal admittance matrix with subsequent inverse Laplace transform in symbolic form allows obtaining a set of time-domain analytical equations for applied voltages and circulating currents inside converter at each commutation interval in a steady-state mode. A set of borderline conditions, allows determining a switching moment from one commutation interval to another, and an interval switching sequence depending on load impedance and control signal parameters, is formulated. Two above milestones together allow obtaining of converter operation laws as a set of piecewise functions for voltages and currents at the whole operation period. Analytic form allows evaluating the influence of parasitic parameter onto converter operation, analytically justifying the connection topology and impedance character of various snubber and gain-enhanced networks, and, moreover, opens up opportunities for analytically constructing the optimal control loops and control correction networks for stability improvement and operation range extension.