Cryogenic classical electronics for the control of qubits can be placed near quantum processors for a more compact system, ultimately enabling a highly scalable one. However, cryogenic operation poses very strict power requirements on electronics, in addition to heavy constraints on precision in both amplitude and phase, as well as noise, so as to achieve the necessary fidelity. To test all the trade-offs that arise from these requirements, detailed simulations based on the physics of qubits and on the effects that circuits may have on them are needed. This paper focuses on the models and the simulation framework needed for quantum processors that can be efficiently executed on classical hardware. These models allow circuit design and specification derivation at all levels of the design. The suitability of the approach is demonstrated with superconducting qubit platforms and their control and characterization.