RC Frequency References Based on Pulse-Density Trimmed Resistors

Kyu Sang Park, Pavan Kumar Hanumolu

Research output: Chapter in Book/Report/Conference proceedingChapter


Stable frequency references serve many essential purposes, such as timekeeping for calendar functions and reference clocks for radios and microcontrollers. While quartz crystal-based references can achieve the desired performance, they are bulky and expensive and suffer from a long start-up time. Hence, techniques for implementing power-efficient frequency references that can be fully integrated in standard CMOS technology and achieve excellent frequency stability across a wide temperature and voltage range are needed. Highly stable on-chip RC frequency references offer the possibility of replacing crystal oscillators in many cost- and form factor-constrained applications. However, achieving good frequency stability in a power-efficient manner across process, voltage, and temperature variations poses many design challenges. In this paper, we describe these challenges and present methods for improving the frequency accuracy of RC oscillators by overcoming them. We show that the impact of the resistor temperature coefficient on the output frequency accuracy can be mitigated by using a parallel combination of switched resistors digitally controlled by pulse-density modulated sequences. Finally, we present experimental results obtained from prototype oscillators fabricated in a 65 nm CMOS process and use them to illustrate that reducing the inaccuracy to better than ±140 ppm over -40 °C to 95 °C (2.1 ppm/°C) is feasible without compromising long-term stability (1.3 ppm Allan deviation) and power efficiency (1 µW/MHz).

Original languageEnglish (US)
Title of host publicationBiomedical Electronics, Noise Shaping ADCs, and Frequency References
Subtitle of host publicationAdvances in Analog Circuit Design 2022
Number of pages20
ISBN (Electronic)9783031289125
ISBN (Print)9783031289118
StatePublished - Jan 1 2023


  • Composite resistor
  • Crystal oscillator
  • Finite capacitance
  • Finite off resistance
  • Frequency reference
  • Frequency-locked loop (FLL)
  • Integrator
  • Offset
  • Open loop
  • Pulse density
  • RC
  • Relaxation oscillator
  • Switched resistor
  • Switched-capacitor resistor (SCR)
  • Temperature coefficient (TC)
  • Temperature compensation
  • Temperature-compensated oscillator (TCO)
  • Trimmed resistor
  • Trimming
  • Voltage-controlled oscillator (VCO)

ASJC Scopus subject areas

  • General Engineering
  • General Biochemistry, Genetics and Molecular Biology


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