**Hybrid Time-Frequency Numerical Simulation of Electronic Radio Frequency Systems**

Jorge F. Oliveira

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64152

#### **Abstract**

This chapter is devoted to the discussion of a hybrid frequency-time CAD tool especially designed for the efficient numerical simulation of nonlinear electronic radio frequen‐ cy circuits operating in an aperiodic slow time scale and a periodic fast time scale. Circuits driven by envelope-modulated signals, in which the baseband signal (the information) is aperiodic and has a spectral content of much lower frequency than the periodic carrier, are typical examples of practical interest involving such time evolu‐ tion rates. The discussed method is tailored to take advantage of the circuits and signals heterogeneity and so will benefit from the time-domain latency of some state varia‐ bles in the circuits. Because the aperiodic slowly varying state variables are treated only in time domain, the proposed method can be seen as a hybrid scheme combining multitime envelope transient harmonic balance based on a multivariate formulation, with a purely time-step integration scheme.

**Keywords:** partial differential equations, numerical simulation, radio frequency cir‐ cuits, time-frequency analysis
