Inhomogeneous radomes, characterized by stacked layers of continuously varying dielectric parameters, are potential in yielding excellent electromagnetic (EM) performance. This two-part sequence of papers presents a study on the EM performance of inhomogeneous airborne radomes based on impedance match, including comparison with the conventional constant thickness radomes and variable thickness radomes (VTRs). In this paper, study on the phase distortion of antenna aperture field caused by inhomogeneous radomes gives a physical insight into the cause of radome boresight error (BSE), and explains why the substantial decrease of insertion phase delay (IPD) of inhomogeneous radomes, instead of leading to BSE improvement, increases the BSE. Based on the study, a method is proposed to estimate the IPD distribution which can be used to predict the BSE. The results reveal the EM characteristics of inhomogeneous radomes which is potential in realizing high-performance airborne radomes superior to traditional VTRs. The second part of the paper studies the bandwidth performance and the effect of radome coating, thickness errors, and layer number in order to acquire an overall understanding of the performance of inhomogeneous radomes.