This paper presents a class of high step-up impedance source inverters. The proposed topologies utilize an optimized coupled transformer with unique structure to reach high voltage boost capability with small turns ratio. In other words, high voltage boost ability is gained by decreasing the turns ratio to 1 which leads to lower cost and volume. The absorbing circuits are exploited to clamp dc-link voltage to reduce the effect of the leakage inductance. So, huge spikes across the inverter bridge are removed effectively. Input inductor and input dc-source are connected in series. It results in continuous input current with low start-up inrush current which is appropriate for renewable energy sources such as fuel cell and photovoltaic (PV). In addition, high output voltage is obtained with small shoot-through (ST) duty ratio and high modulation ratio which causes semiconductor voltage stress reduction and better quality of the output voltage. The simulation results confirm the operation of the introduced inverters. The paper also extracts the mathematical equations of the proposed inverter.