Analysis of high-order sub-harmonically injection-locked oscillators

Abstract

High-order subharmonically injection-locked oscillators have recently been proposed for low phase-noise frequency generation, with carrier-selection capabilities. This work focuses on the analysis of this frequency-synthesis procedure, with emphasis on the oscillator capability to discriminate the input tones, under the variation of a tuning voltage. The oscillator is described with an analytical envelopedomain formulation, leading to an expression for the oscillator phase shift with respect to the input source. The average of this phase shift is shown to evolve in a continuous manner in the distinct synchronization bands obtained versus the tuning voltage. Then, the subsynchronized operation at a high frequency ratio (N = 30) is considered, showing the applicability of envelopedomain simulations under various Fourier decompositions and sampling rates. The synchronization bands are obtained through the phase averaging technique. The analysis has been applied to a prototype at 2.7 GHz that has been manufactured and measured.

Analysis of high-order sub-harmonically injection-locked oscillators

“…In this section, the case of an oscillator injected with multiple input tones about the oscillation frequency will be studied [15], which is conceptually simpler than the one of sub-harmonic injection-locked oscillators under a high order N, considered in the section "Sub-harmonic injection-locked operation". This will allow an understanding of the oscillator behavior when driven by multiple tones and an evaluation of its frequency-selection capabilities.…”

“…On the other hand, though harmonic balance (HB) [8][9][10][11][12] can deal at present with a high number of harmonic terms, in injection-locked oscillators it converges by default to the non-oscillatory solution that generally coexists with the oscillatory one. In the non-oscillatory solution, the circuit just responds to the input forcing in a non-autonomous manner [13][14][15]. To consider the selfoscillation in commercial HB, one should impose the oscillation condition using an auxiliary generator (AG) [13][14][15].…”

“…In the non-oscillatory solution, the circuit just responds to the input forcing in a non-autonomous manner [13][14][15]. To consider the selfoscillation in commercial HB, one should impose the oscillation condition using an auxiliary generator (AG) [13][14][15]. The AG amplitude and its phase-shift with respect to the input source are optimized to obtain a zero value of the AG total admittance function.…”

“…The AG amplitude and its phase-shift with respect to the input source are optimized to obtain a zero value of the AG total admittance function. In the case of a sub-harmonic injection locking of a high order N, the convergence of this optimization procedure is demanding [15] due to the need of a high number NH of harmonic terms, involving multiples of the high order N. For instance, the consideration of three harmonic components of the oscillation frequency f o , requires NH = 3N = 90.…”

“…This work is an extension of [15], presenting an envelopedomain analysis [16][17][18][19] of the sub-harmonic injection-locked oscillator is presented, using a Fourier-series description of the circuit variables, with time-varying harmonic terms X k (t), where k is the frequency index. This will require a proper initialization of the oscillation frequency to avoid the system convergence to a non-oscillatory steady-state solution [20].…”