A Novel Design Method for CML Frequency Divider Based on <i>C</i>/<i>I_d </i> and <i>G</i>/<i>I_d </i> and Application for Quadrature-Injection CML Frequency Dividers

A novel design method for current-mode-logic (CML) frequency divider based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C/I} _{\boldsymbol {d}}$ </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">${G/I} _{\boldsymbol {d}}$ </tex-math></inline-formula> is proposed. The design method proposes using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C/I} _{\boldsymbol {d}}$ </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">${G/I} _{\boldsymbol {d}}$ </tex-math></inline-formula> as independent design parameters, where C and G are the equivalent capacitance and conductance of coupling pair (C cell) and negative-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {g}_{\boldsymbol {m}}$ </tex-math></inline-formula> pair (N cell) in CML frequency dividers. Different from the traditional design method optimizing the maximum operating frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {f}_{\textit {in,max} }$ </tex-math></inline-formula>) by adjusting the self-resonant frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {f}_{\textit {SR} }$ </tex-math></inline-formula>), the proposed design method directly targets <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {f}_{\textit {in,max} }$ </tex-math></inline-formula> and output amplitude (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {V}_{\textit {out} }$ </tex-math></inline-formula>) to obtain the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${C/I} _{\boldsymbol {d}}$ </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">${G/I} _{\boldsymbol {d}}$ </tex-math></inline-formula> and solve the size and bias current of C and N cells, which realizes efficient design. Based on the proposed design method, several design examples are provided showing less than 3% error between the simulation results and design goals, and the proposed quadrature-injection CML (QI-CML) frequency divider is implemented and proven to have an improved sensitivity curve (SC). To validate the efficacy of our proposal, a frequency divider that can switch between differential-injection (DI) and QI is designed and fabricated in 110-nm CMOS process. For QI mode, the measured locking range (LR) is 141% (5-29 GHz) while consuming 5.47 mW. The achieved two figure of merits FOM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\textbf {Pdc}}$ </tex-math></inline-formula> and FOM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\textbf {A}}$ </tex-math></inline-formula> are 24.1 dB and 52.8 dB, respectively, which are superior to most published works.