Abstract The problem of design and analysis of synchronization control circuits is a challenging task for many applications: satellite navigation, digital communication, wireless networks, and others. In this article the Charge-Pump Phase-Locked Loop (CP-PLL) electronic circuit, which is used for frequency synthesis and clock generation in computer architectures, is studied. Analysis of CP-PLL is not trivial: full mathematical model, rigorous definitions, and analysis still remain open issues in many respects. This article is devoted to development of a mathematical model, taking into account engineering aspects of the circuit, interpretation of core engineering problems, definition in relation to mathematical model, and rigorous analysis.