**1. Introduction**

With the rapid development of wearable electronics and IoT (Internet of things), the demand of an on-chip and low-power oscillator has received much attention in the research. Low power consumption is especially important for IoT devices because of the real-time clock which has to stay awake all the time, even when other circuits are in sleep mode [1]. Although the crystal oscillator can provide an accurate signal with high stability, it is relatively expensive and occupies a large area with high current consumption [2]. For small size, the on-chip oscillators, such as ring oscillators and relaxation oscillators (ROSC), are widely used. Regarding to the ring oscillator, despite its simple architecture and low-power consumption under low oscillation frequency, the circuit is sensitive to process, supply, and temperature (PVT) variation [3]. This leads to a significant variation in the output frequency. Although other ring oscillators [4–6] can achieve relatively low sensitivity for output frequency, the power consumption is large. Hence, it may not be suitable for providing a stable clock using the standalone ring oscillator topology. Several reported works [7–11] have shown that the relaxation oscillator can provide a good tradeoff between frequency stability, temperature variation, and supply variation while occupying at reasonably small area. Thus, the relaxation oscillator is preferred as on-chip oscillator for those applications that require good stability with low cost and moderate precision. For example, the switchedcapacitor based sensor interfaces [12,13] usually employ a low-frequency clock to control the sampling and charge transfer action in the circuits. Moreover, for the design of an instrumentation amplifier, ROSC can be applied for chopping amplifiers [14,15] to provide

**Citation:** Liao, Y.; Chan, P.K. A 1.1 V 25 ppm/◦C Relaxation Oscillator with 0.045%/V Line Sensitivity for Low Power Applications. *J. Low Power Electron. Appl.* **2023**, *13*, 15. https://doi.org/10.3390/jlpea13010015

Academic Editor: Orazio Aiello

Received: 11 November 2022 Revised: 16 January 2023 Accepted: 19 January 2023 Published: 7 February 2023

**Copyright:** © 2023 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/).

School of EEE, Nanyang Technological University, Singapore 639798, Singapore

the chopping signal for modulating the signal to high frequency for amplification and translating it back to baseband for analog signal processing.

Figure 1 depicts the plot of the T.C. and line sensitivity of representative relaxation oscillators against the power consumption. As can be seen, it shows a tradeoff relationship among the performance parameters in context of the frequency stability and the power consumption [16]. The same goes for line sensitivity. In order to realize a lower T.C., one previous work [17] adopted the error feedback to achieve temperature-dependent delay cancellation, while another one [18] utilized the second-order compensation with a charge pump and filter. However, these complex designs led to avoidable high power consumption. Although other designs [16,19] reduced the power to a relatively small value, their thermal stability is slightly weakened due to the timing error and the temperature-sensitive current reference, respectively. Regarding the line sensitivity, there are works [8,10] utilizing highgain operational amplifiers to minimize the effect from the supply variation, but at the cost of higher current consumption. Although other works [9,20] employed lowered the supply voltage as well as the bias current to reduce power, the circuit topologies were subject to higher supply sensitivity. Therefore, it is challenging to achieve a good stability of output frequency with relatively low power consumption in the ROSC design.

**Figure 1.** Tradeoff performance of reported relaxation oscillators: (**a**) T.C. versus power; (**b**) line sensitivity versus power.

In this paper, an improved relaxation oscillator with simple circuit topology is presented. As illustrated in Figure 1, the proposed ROSC features excellent stability against temperature and supply variation while achieving relatively low power consumption. This is achieved by using a simple delay drift compensation technique to enhance the thermal stability, in conjunction with the design of a simple V-I converter, which is based on two-transistor-type circuit topology to provide good immunity against the fluctuation of supply voltage change. Section 1 provides the introduction. Several representative prior-art relaxation oscillator designs are described in Section 2. Section 3 describes the design and implementation of the proposed relaxation oscillator. Section 4 presents the results and discussions. This is followed by the conclusion in Section 5.
