Abstract
AbstractHigh-order sub-harmonically injection-locked oscillators have recently been proposed for low phase-noise frequency generation, with carrier-selection capabilities. Though excellent experimental behavior has been demonstrated, the analysis/simulation of these circuits is demanding, due to the high ratio between the oscillation frequency and the frequency of the input source. This work provides an analysis methodology that covers the main aspects of the circuit behavior, including the detection of the locking bands and the prediction of the phase-noise spectral density. Initially, the oscillator in the presence of a multi-harmonic input source is described with a reduced-order envelope-domain formulation, at the oscillation frequency, based on an oscillator-admittance function extracted from harmonic-balance simulations. This allows deriving an expression for the oscillation phase shift with respect to the input source, and the average of this phase shift is shown to evolve continuously in the distinct synchronization bands obtained when varying a tuning voltage. This property can be used to detect the locking bands in circuit-level envelope-domain simulations, which, as shown here, can be done through different Fourier decompositions and sampling rates. The phase noise of the high-order sub-harmonic injection-locked oscillator under an arbitrary periodic input waveform is investigated in detail. The frequency response to the noise sources is described with a semi-analytical formulation, relying on the oscillator-admittance function in injection-locked conditions. The input noise is derived from the timing jitter of the injection source and the phase-noise response is shown to exhibit a low-pass characteristic, which initially follows the up-converted input noise and then the oscillator own noise sources. A method is proposed to identify the key parameters of the derived phase-noise spectrum from envelope-domain simulations. The various analysis methodologies have been applied to a prototype at 2.7 GHz at the sub-harmonic order N = 30 which has been manufactured and measured.
Highlights
The recent works [1]-[7] have demonstrated a novel frequency-synthesis methodology, based on the high-order subharmonic injection-locking of a high frequency oscillator, at a frequency fo, by an independent source at a much lower frequency fin
As demonstrated in [4], the phase-noise spectral density of the higher-frequency oscillator can be lower than the one resulting from lower subharmonic ratios
The oscillator is described with the aid of a semi-analytical formulation, based on the modelling of this oscillator with an outer-tier admittance function extracted from harmonic-balance simulations
Summary
The recent works [1]-[7] have demonstrated a novel frequency-synthesis methodology, based on the high-order subharmonic injection-locking of a high frequency oscillator, at a frequency fo, by an independent source at a much lower frequency fin. This work is an extension of [15], presenting an envelope-domain analysis [16]-[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]. In the solution of the subharmonic injection-locked oscillator there will be a high number of spectral lines at multiples of the low injection-locking frequency fin This can be achieved through pulse forming plus oscillator switching, as in [1]-[3], or using of a multi-harmonic input source, as in this work.
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