Multirate Circuit - EM - Device Simulation

Radio frequency (RF) integrated circuits are at the core of modern mobile communication. They basically comprise the analog front-end, the analog-to-digital and vice versa the digital-to-analog conversion, and the digital signal processing. These days, both the analog and digital parts, are integrated on the same die. The analog front-end mainly performs amplification, filtering and mixing to or vice versa from the RF regime to baseband. The waveforms of voltages and currents of such an IC are described by a system of ordinary Differential-Algebraic Equations (DAEs) resulting from the well-known Modified Nodal Analysis (MNA). Standard solvers for initial value problems, also referred to as transient analysis, are however prohibitively slow, since the time step or vice versa its inverse the sampling rate, are limited by Shannon’s sampling theorem. The sampling theorem predicates that the sampling rate must be at least twice as high as the highest relevant frequency components of the spectra of all waveforms of the circuit. Since modern RF integrated circuits operate in the GHz range, solving the initial value problem of these DAEs is extremely slow. This chapter addresses the simulation problem of RF circuits by generalizing the method of the Equivalent Complex Baseband (ECB) for circuits and systems described by nonlinear DAEs.