**1. Introduction**

In the last two decades, radio frequency (RF) and microwave system design has been found as a significant part of the electronic semiconductor industry's portfolio. Over the years, the necessity of continuously providing new wireless systems' functionalities and higher trans‐ mission rates, as also the need to improve transmitters' efficiency, has been gradually reshap‐ ing wireless architectures. Heterogeneous circuits combining baseband blocks, digital blocks, and RF blocks, in the same substrate, are commonly found today. Hence, RF and microwave

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circuit simulation has been conducted to an increasingly challenging scenario of heterogene‐ ous broadband and strongly nonlinear wireless communication circuits, presenting a wide variety of slowly varying and fast changing state variables (node voltages and branch cur‐ rents). Thus, RF and microwave design has been an important booster for numerical simula‐ tion and device modeling development.

In general, waveforms processed by wireless communication systems can be expressed by a high-frequency RF carrier modulated by some kind of slowly varying baseband aperiodic signal (the information signal). Therefore, the evaluation of any relevant information time window requires the computation of thousands or millions of time instants of the composite modulated signal, turning any conventional numerical time-step integration of the circuits' systems of differential algebraic equations highly inefficient. However, if the waveforms do not require too many harmonic components for a convenient frequency-domain representa‐ tion, this category of circuits can be efficiently simulated with hybrid time-frequency techni‐ ques. Handling the response to the slowly varying baseband information signal in the conventional time step by time step basis, but representing the reaction to the periodic RF carrier as a small set of Fourier components (a harmonic balance algorithm for computing the steady-state response to the carrier), hybrid time-frequency techniques are playing an impor‐ tant role in RF and microwave circuit simulation.

Beyond overcoming the signals' time-scale disparity, the partitioned time-frequency technique discussed in Section 3.2 is also able to efficiently simulate highly heterogeneous RF networks, by splitting the circuits into different subsets (blocks) and computing their state variables with distinct numerical schemes.
