**1. Introduction**

The design and simulation of integrated circuits (IC) are assisted by compact MOSFET models, which started to be developed in the 1960s [1] for long-channel devices. The technological progress promoted the down-scaling of semiconductor devices, giving rise to short-channel effects and their interference in circuit performance; thereby, these shortchannel effects were incorporated into the existing long-channel based models to improve circuit-design efficiency.

Although BSIM [2,3] has been broadly used as the main MOSFET model to simulate MOS circuits in EDA tools, the complexity of its calculations and numerous parameters have opened a gap between circuit simulations and designs by hand [4,5], which has complicated the understandings of how the main MOSFET parameters relate to simulation results. Therefore, it is in designers' interest to have models founded on physics available in the simulator, such as those based on the inversion charge.

In the fast expanding ultra-low-voltage domain [6], some short-channel effects, such as velocity saturation, are not relevant; thus, a simplified MOSFET model can be satisfactory for circuit design. Targeting the increasing number of ultra-low-voltage designs [7–12], this work proposes a four-parameter model (4PM) based on the all-region advanced compact MOSFET model (ACM) [13].

In this work, the 4PM was carried out with the description language Verilog-A to easily simulate circuits in the commercial Cadence Virtuoso simulator, which implements BSIM 4.5 through a private propriety interface [14]. Hardware description languages

**Citation:** Adornes, C.M.; Alves Neto, D.G.; Schneider, M.C.; Galup-Montoro, C. Bridging the Gap between Design and Simulation of Low-Voltage CMOS Circuits. *J. Low Power Electron. Appl.* **2022**, *12*, 34. https://doi.org/10.3390/ jlpea12020034

Academic Editors: Orazio Aiello and Andrea Acquaviva

Received: 16 February 2022 Accepted: 5 May 2022 Published: 16 June 2022

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(HDLs), such as Verilog-A, are interchangeable with different simulators and assist designers in describing circuits and systems in a variety of behavioral modeling levels. We chose Verilog-A because it combines simplicity, functionality and portability [14].

The paper is structured as described in the following lines. Section 2 briefly introduces the four-parameter model (4PM). Section 3 describes the methods employed to extract the model's parameters and describes the extraction results of the parameters with temperature and process variations. Section 4 describes how to carry out the 4PM in Verilog-A for its inclusion in Cadence. Section 5 presents the results of the simulations carried out by using BSIM or the 4PM in Verilog-A. Four circuits designed according to the ACM model were simulated: a CMOS inverter, a ring oscillator, a self-biased current source and a common source amplifier. Conclusions are drawn in Section 6.
