**1. Introduction**

Presently, energy harvesting appears as a promising reliable technology that can prolong the lifetime of batteries and power wireless sensor networks (WSNs) for environmental monitoring [1]. However, in these WSN applications, ambient vibrations are unpredictable, time-varying, and low amplitude, which restricts the available power of the energy harvesting system [2]. To overcome these drawbacks, research groups have been focusing on using piezoelectric harvesters due to their high power density and capability to integrate MEMS and CMOS technology, making it possible to develop all the systems (energy harvester and electronic system) in a single chip [3–5]. Thus, to maximize the amount of energy transferred under different ambient conditions, a power managemen<sup>t</sup> circuit (PMC) is crucial in order to extract, convert, store, regulate, and manage the scavenged energy from the piezoelectric device [6,7].

Because the vibrational energy sources produce AC signals, scavenging such energy requires a full-wave rectifier as a key circuit inside the PMC, which allows the AC/DC

**Citation:** Godinho, A.; Yang, Z.; Dong, T.; Gonçalves, L.; Mendes, P.; Wen, Y.; Li, P.; Jiang, Z. A Dynamic Threshold Cancellation Technique for a High-Power Conversion Efficiency CMOS Rectifier. *Sensors* **2021**, *21*, 6883. https://doi.org/10.3390/s21206883

Academic Editors: Jong-Ryul Yang and Seong-Tae Han

Received: 24 September 2021 Accepted: 13 October 2021 Published: 17 October 2021

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conversion to properly power the WSNs. However, because the output power of the vibrational energy harvester is low [4], the high forward voltage required by standard full-wave diode bridges and Schottky diode rectifiers limits their use on these low power restrict applications [8]. To surpass these limitations, diode-connected MOS transistors have been widely used because they present similar I-V characteristics to the standard diodes. Thus, designing the rectifier in CMOS technology is highly desirable to decrease the device's form factor and easily integrate with the energy harvester while exploring new dynamic techniques to reduce the power consumption, achieve high PCE, and minimize leakage current [9,10].

Recent work has been developing dynamic threshold techniques to reduce the threshold voltage effect [11]. Addressing these techniques allows for the reduction of total voltage drop and mitigation of the reverse leakage current in the active stage. By attending to these concerns during the design of the circuit, it is possible to minimize the circuit's overall power and leakage current consumption. Thus, all these conditions were carefully considered during the design of the proposed high-power efficiency CMOS rectifier to attend to the demands of this application.

In this work, a new CMOS rectifier structure for piezoelectric energy harvesters is presented. It combines a passive stage negative voltage converter (NVC) with an active diode controlled by a dynamic threshold cancellation circuit to build a new architecture that can reduce its total voltage drop. With this configuration, a voltage drop lower than 2 mV can be achieved in the second stage, which consequently enhances features such as VCE and PCE, as well as reduces the reverse leakage current that flows from the load.

## **2. CMOS Rectifiers**

## *2.1. Passive Rectifiers*

The CMOS gate cross coupled can replace the conventional full-wave bridge rectifier to overcome the high forward voltage drop because it allows a minimum input voltage to operate [10,12,13]. However, this topology still lacks efficiency due to the threshold voltage (*VTH*) drop across the diode connected in each conduction path [13].

The fully cross-coupled rectifier intends to fulfill the gap of the previous configuration by eliminating all *VTH* drops, which reduces the voltage drop across this stage [13]. Consequently, this topology improves both PCE and VCE of the circuit [13]. However, the reverse leakage current appears to be the main disadvantage of using this single configuration, which affects the power transferred from the circuit to the load [10]. Thus, an extra circuit must be added to overcome this issue.
