This paper presents a new family of the integrated boost-buck DC/AC converters – voltage-fed quasi-impedance (quasi-Z) source inverters (qZSI) with continuous input current. Paper unveils the design and operating principle of the qZSI and discusses further optimization possibility of it by the introduction of the cascaded quasi-Z-source network (qZS-network). The paper is generally concentrating on the static models of the cascaded qZSI converter. Static models were elaborated and analyzed for the continuous (CCM) and discontinuous (DCM) conduction modes of the converter. Finally, the static model with losses is presented and discussed.