Z-source inverters are suited for applications which require a large range of gain, such as in renewable energy. Recently proposed Trans-Z-source inverters (TZSIs) and T-source inverters (TSIs) characterize improved voltage gain thanks to the application of coupled inductors with turns ratio higher than one. The present paper extends the concept of Trans-Z-source (T-source) inverters. Two novel impedance networks: the LCCT (inductor-capacitor-capacitor-transformer) Z-source impedance network and the LCCT-qZ-source impedance network are presented. The former contains two built-in DC-current-blocking capacitors connected in series with transformer windings and therefore prevent the transformer core from saturation while the latter contains one built-in DC-current-blocking capacitor and combines the features of qZ-source and T-source impedance networks. The novel topologies of LCCT-impedance-source inverters: LCCT-Z-source inverter (LCCT-ZSI) and LCCT-quasi-Z-source inverter (LCCT-qZSI) proposed in the paper characterize available continuous input current which is the advantage compared to TZSIs and TSIs. Simulations and experimental results are provided to verify the analysis of two proposed topologies.