Quantum random number generators (QRNGs) are currently in high demand across a
large number of cryptographic applications as secure sources of true randomness. In this work, we
characterize the conditions from which randomness can be extracted in a QRNG based on homodyne
measurements of vacuum fluctuations by assessing the impact of experimental limitations, such as
the digitizer resolution or the presence of excess local oscillator (LO) noise due to an unbalanced
detection. Moreover, we propose an estimation method to quantify the excess entropy contribution
introduced by an unbalanced detection and analyze the implementation of the post-processing
algorithm. Finally, we submitted the generated numbers to a set of statistical tests to assess the
quality of its output randomness and verified that it passes the standard libraries.