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Interleaving techniques in DC-DC converters enhance the operational redundancy and reduce the current ripple. However, the phase-shifted operation of the interleaved branches results in different mathematical models for high and low values of duty ratio. In applications such as renewable energy integration where wide variations in duty ratios are bound to occur due to the dynamic nature of the source, a single mathematical model cannot represent the interleaved converter for the entire duty ratio range. This is due to the fact that when the duty ratio increases beyond a threshold the conduction period of the interleaved phases overlap, resulting in a different set of operating modes of the converter. Existing literature has not investigated this effect while formulating the mathematical model as it becomes evident only when the parasitic circuit elements are accounted for in the model. Firstly, this paper presents an extensive small-signal of a two-phase interleaved boost converter considering all the internal voltage drops due to parasitic circuit elements. Secondly, this work investigates the variations in the mathematical model due to the presence of parasitic circuit elements, when the interleaved converter operates in phase-shifted mode over a wide range of duty ratio. The proposed model is tested by simulation in MATLAB/Simulink® and validated with a 300W hardware prototype. [ABSTRACT FROM AUTHOR]