**1. Introduction**

The Internet of Things (IoT) currently is attracting researchers' attention, which is a system for the interaction of information from things such as sensing edge devices to the cloud and servers via the Internet and vice versa [1]. The maintenance costs to replace batteries can be a large portion of the costs of edge devices. Therefore, it is expected that sensing devices should be battery free based on the energy transducer generating electric power from environmental energy such as sunlight and vibration kinetic energy. A thermoelectric generator (TEG) extracts power from a temperature gradient. The opencircuit voltage *VOC* of the TEG increases in proportion to the temperature difference between hot and cold heat sources [2]. Bulk-type TEGs [3] have a low output impedance (*RTEG*) of the order of Ω and are in production together with boost converters. Flexible-type thin film TEGs [4] are expected to have various applications because they can be placed on curved surfaces. A drawback of the flexible-type TEG is the high-output impedance of the order of 10–100 Ω, especially in the case of a small form-factor. Even worse, a low-cost small form-factor TEG generates *VOC* as low as a few hundred mV. To operate sensor ICs, boost converters are required [5–7]. In this research, the design of boost charge pump circuits (CPs) is proposed for a flexible-type TEG with high-output impedance, as illustrated in Figure 1. Such a system is used for heat pipes [8] and wrist watches [9].

To design systems with TEGs and integrated CPs, the circuit area and power conversion efficiency (PCE) are key figures of merit. Table 1 summarizes the key features of existing designs and this work. In [10], the design of low-voltage CPs was developed to strike a balance between the circuit area and power efficiency under the conditions of a given output voltage and current. In this design, CPs are driven by voltage sources with zero impedance, while TEGs have a finite output impedance. In [11], both TEGs and CPs were optimally designed to minimize their areas when CPs were driven by TEGs. However, design constraints such as temperature differences and the number of TEG units connected

**Citation:** Koketsu, K.; Tanzawa, T. Design of a Charge Pump Circuit and System with Input Impedance Modulation for a Flexible-Type Thermoelectric Generator with High-Output Impedance. *Electronics* **2021**, *10*, 1212. https://doi.org/ 10.3390/electronics10101212

Academic Editors: Shailendra Rajput, Moshe Averbukh and Noel Rodriguez

Received: 2 April 2021 Accepted: 13 May 2021 Published: 19 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

in parallel and in series were not taken into consideration. A design methodology was proposed when *VOC* and *RTEG* were given in [12,13]. In [12], an optimum design was provided to determine the dimensions of switching devices and the clock frequency to maximize the output power of the CP when the number of stages *N* and stage capacitors *C* of the CP and the *VOC* and *RTEG* of TEG were given. However, the output voltage of the CP was not given, whereas the input voltage of the load circuit must be controlled with a specific voltage. In [13], how the input voltage of the CP or the output voltage of the TEG is determined theoretically was discussed when the circuit area of the CP was minimized or, in other words, when the output power of the CP was maximized with a given CP circuit area to generate a target output current at a specific output voltage, as shown in Figure 2a, which is the same target design of this work. However, the minimum operation voltage of circuits was not considered in [13], but it was assumed that the input voltage of the CP can be set at any voltage. Furthermore, no control circuit was disclosed to control the input voltage of the CP in [13]. In this work, the minimum operating voltage of the circuits was taken into consideration in the design, as shown in Figure 2b. This can be a key design point especially for TEGs with a high-output impedance, which have a potentially large IR drop at *VDD*.

**Figure 1.** Block diagram of the energy harvesting system based on the TEG and CP.



This paper is an extended version of a conference paper [14] to describe its details. A control circuit to operate the CP was proposed to meet the demand that the output current be generated as high as the target current at a specific voltage while the input voltage of the CP is controlled at a voltage higher than the minimum operating voltage. The designs of the CP system and building blocks are presented in Sections 2.1 and 2.2, respectively, to discuss how the circuits can be optimally designed. The entire system was fabricated in 65 nm CMOS. Experimental results are shown in Section 2.3, and Section 3 gives a summary of this work.

**Figure 2.** Operating points of [8] (**a**) and of this work (**b**).
