CONCERTO is a millimeter-wave imaging instrument that operated on the Atacama Pathfinder Experiment (APEX) telescope from April 2021 to May 2023. Its primary scientific objectives include the study of galaxy clusters through the Sunyaev-Zel'dovich (SZ) effects, the observation of Galactic star-forming regions, and the first measurements constraining the power spectrum of dusty star-forming galaxies. The instrument consists of two detector arrays, each comprising 2400 Microwave Kinetic Inductance Detectors (MKIDs). Each of the two arrays comprises six feed-lines and is read out by six KID_READOUT electronic boards, each capable of reading out one feed-line coupled to 400 frequency-multiplexed MKIDs. As the demand for higher-resolution millimeter-wave imaging continues to grow, future instruments aim to significantly increase the pixel count, with more than 800 detectors per feed-line. However, the MKID readout electronics chain is inherently complex, making it difficult to fully understand its performance limits and optimization margins. To address this challenge, we initiated a modeling effort that first focused on the digital section of KID\_READOUT. In this phase, we developed a digital twin of the FPGA-based signal processing chain, which led to substantial performance improvements. The present paper extends this modeling strategy to the analog readout chain. It presents the characterization and behavioral modeling of all analog components, allowing us to identify the elements that limit the frequency multiplexing factor, determine the dominant noise contributors, and highlight areas for improvement in signal conditioning for the future-generation board. Together, these developments establish, to the best of our knowledge, the first consolidated digital-and-analog behavioral framework of an MKID readout architecture, implemented in a unified Python-based modeling environment.