The secret key rate of a continuous variables quantum key distribution system (CV-QKD) depends highly on the loss and excess noise of the quantum channel. A proper modelling of the quantum channel is essential to detect and prevent an eavesdropping attack. In CVQKD, homodyne detection is widely used to measure the quadratures of the modulated optical signal. Nevertheless, the homodyne detector (HD) can be a source of noise for the CV-QKD system. In this paper, a HD is modelled considering intrinsic imperfections. Moreover, an improved method is proposed to obtain mean, variance and auto-covariance functions for estimation of the HD performance, considering ideal and unbalanced HD operation modes with ideal and non-ideal local oscillator pulse intensity functions being compared. The imbalance of the HD leads to non-zero mean output and a quadratic relation of voltage variance. Despite that, the rebalance of the system was attained with the cost of lowering the system voltage output intensity.