A Thermal-Diffusivity-Based Frequency Reference in Standard CMOS With an Absolute Inaccuracy of $\pm $0.1% From $-$55 $^{\circ}$C to 125 $^{\circ}$C

Abstract

An on-chip frequency reference exploiting the well-defined thermal-diffusivity (TD) of IC-grade silicon has been realized in a standard 0.7 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\mu{\hbox{m}}$</tex></formula> CMOS process. A frequency-locked loop (FLL) locks the frequency of a digitally controlled oscillator (DCO) to the process-insensitive phase shift of an electrothermal filter (ETF). The ETF's phase shift is determined by its geometry and by the thermal diffusivity of bulk silicon ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$D$</tex> </formula> ). The temperature dependence of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$D$</tex></formula> is compensated for with the help of die-temperature information obtained by an on-chip band-gap temperature sensor. The resulting TD frequency reference has a nominal output frequency of 1.6 MHz and dissipates 7.8 mW from a 5 V supply. Measurements on 16 devices show that it has an absolute inaccuracy of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\pm $</tex></formula> 0.1% ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sigma= \pm $</tex></formula> 0.05%) over the military temperature range ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$-$</tex></formula> 55 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$^{\circ}{\hbox{C}}$</tex></formula> to 125 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$^{\circ}{\hbox{C}}$</tex></formula> ), with a worst case temperature coefficient of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\pm \hbox{11.2~ppm}/^{\circ}{\hbox{C}}$</tex></formula> .