Abstract
This paper presents an in-depth analysis of a recently proposed frequency divider by two, which is based on a parallel connection of varactor-inductor cells, in a differential operation at the subharmonic frequency. The analytical study of a single-cell divider enables the derivation of a real equation governing the circuit at the frequency-division threshold. This equation is used for a detailed investigation of the impact of the circuit elements on the input-amplitude threshold and the frequency bandwidth. Insight provided by the analytical formulation enables the derivation of a thorough synthesis methodology for multiple-cell dividers, usable in harmonic balance with an auxiliary generator at the divided frequency. Two different applications of this topology are demonstrated: a dual-phase divider and a dual-band frequency divider. The former is obtained by using Marchand balun to deliver 180 $^{\circ}$ phase-shifted signals to the two dividers. On the other hand, the dual-band divider is based on a novel configuration which combines cells with parallel varactors and cells with series varactors. Departing from the optimization procedure of the single-band divider, a simple synthesis method is presented to center the two division bands at the desired values. The techniques have been applied to three prototypes at 2.15 GHz, 1.85 GHz, and 1.75 GHz/3.95 GHz, respectively.
Highlights
T HE works [1]−[2] propose a frequency divider topology based on the use of two parallel nonlinear transmission lines (NLTL) connected through back to back diodes [Fig. 1(a)]
The analysis demonstrates the coupling between the two dividers since the amplitude in Divider A varies with this bias voltage
The method derives from an initial analytical study of a single−cell divider, which provides insight into the impact of the various circuit elements on the input−amplitude threshold and the frequency bandwidth
Summary
T HE works [1]−[2] propose a frequency divider topology based on the use of two parallel nonlinear transmission lines (NLTL) connected through back to back diodes [Fig. 1(a)]. The circuit total admittance is calculated at the node located between the first inductor and the rest of the varactor−inductor structure, at the subharmonic frequency ω This provides the following recursive equation: frequency ωin,c will depend on the number of cells and should be optimized for each N.
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