Frequency References Based on the Thermal Properties of Silicon

  • S. Mahdi Kashmiri
  • Kofi A. A. Makinwa
Part of the Analog Circuits and Signal Processing book series (ACSP)


This chapter introduces the concept of on-chip frequency generation based on the thermal properties of silicon. Thermal-diffusivity of silicon, D, will be introduced as the rate at which heat diffuses through a silicon substrate. It will be described how an electrothermal filter (ETF) harnesses this physical property in order to produce accurate on-chip delays. The design of a practical ETF within standard CMOS processes will be described. It will be shown that an ETF behaves like a low-pass filter with a defined phase shift, which is a combined function of its geometry and D. Furthermore, a method of frequency generation based on an electrothermal frequency-locked loop (FLL) will be introduced. Such loop locks the output frequency of a variable oscillator to the phase shift of an ETF.


Thermal Noise Output Frequency Synchronous Demodulator Loop Bandwidth Noise Bandwidth 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. Mahdi Kashmiri
    • 1
  • Kofi A. A. Makinwa
    • 2
  1. 1.Texas Instruments, Inc.DelftThe Netherlands
  2. 2.Delft University of TechnologyDelftThe Netherlands

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