A 1.9–3.8 GHz $\Delta \Sigma$ Fractional-N PLL Frequency Synthesizer With Fast Auto-Calibration of Loop Bandwidth and VCO Frequency (2012)

A fast and high-precision all-digital automatic calibration circuit that is highly suited for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta \Sigma$</tex></formula> fractional-N synthesizers is designed to achieve a constant loop bandwidth and fast lock time over an octave tuning range. A high-speed frequency-to-digital converter (FDC) measures VCO frequency on-chip with a sub- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f_{\rm REF}$</tex> </formula> frequency resolution of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f_{\rm REF}/k$</tex></formula> in a time period of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$k\cdot T_{\rm REF}$</tex></formula> . The on-chip detected VCO frequency is then used for calibrating the loop bandwidth and the VCO frequency. The loop bandwidth calibration circuit measures the VCO gain <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$K_{\rm VCO}$</tex></formula> and uses it to precisely control the charge pump current, hence making the loop bandwidth constant. For the VCO frequency calibration, a minimum error code finding block significantly enhances the calibration accuracy by finding the truly closest code to the target frequency. Moreover, this method does not need to activate <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta \Sigma$</tex></formula> modulator to achieve sub- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$f_{\rm REF}$</tex></formula> calibration resolution, which makes this technique much accurate and faster than the conventional ones. A 1.9–3.8 GHz <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\Delta \Sigma$</tex></formula> fractional-N synthesizer is implemented in 0.13 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> m CMOS, demonstrating that the loop bandwidth calibration is completed in 1.1–6.0 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> s with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\pm}2\hbox{\%}$</tex></formula> accuracy and the VCO frequency calibration is completed in 1.225–4.025 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> s, all across the entire octave tuning range.