Analysis and Design of a 21.2-to-25.5-GHz Triple-Coil Transformer-Coupled QVCO

This paper reports a triple-coil transformer-coupled quadrature voltage-controlled oscillator (TC-QVCO), which inherently provides the quadrature signal without using the noisy active-coupling transistors. The determinate correlation of tank voltages is verified by utilizing the initial state to facilitate the oscillation state analysis. Thus, the TC-QVCO would operate without the oscillation mode ambiguity. Additionally, thanks to the triple-coil transformer coupling, a large source coil <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{S}$ </tex-math></inline-formula> aids in achieving in-phase coupling for phase noise (PN) improvement, and the intensified coupling factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{gd}$ </tex-math></inline-formula> benefits reducing the PN and the quadrature phase error simultaneously. Therefore, our TC-QVCO would alleviate the tradeoff between PN and quadrature phase accuracy via using a large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{S}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{gd}$ </tex-math></inline-formula>. The proposed QVCO prototyped in 65-nm CMOS exhibits a superior FoM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\text {@10MHz}}$ </tex-math></inline-formula> (180.1 to 182.2 dBc/Hz) over a 18.2% frequency tuning range (21.2 to 25.5 GHz), and the estimated quadrature phase error <0.8°.