Phase-Noise Analysis of Injection-Locked Oscillators and Analog Frequency Dividers

In-depth investigation of the phase-noise behavior of injection-locked oscillators and analog frequency dividers is presented. An analytical formulation has been obtained, which allows a better understanding of the shape of the output phase-noise spectrum of these circuits. The simplicity of this formulation is also helpful for circuit design. Approximate expressions for the corner frequencies of the spectrum are determined, identifying the most influential magnitudes and deriving design criteria. In particular, a technique has been developed to shift the frequency of the first corner of the phase-noise spectrum, up to which the output phase noise follows the input one. The expressions for the corner frequencies can be introduced in either in-house or commercial harmonic-balance software, thus allowing an agile design, as no separate phase-noise analysis is required. The validity of the analytical techniques is verified with the conversion-matrix approach and with measurements using two field-effect-transistor-based circuits: a 4.9-GHz injection-locked oscillator and a frequency divider by 2 with 9.8-GHz input frequency.

I. Introduction

Injection-Locked oscillators are used at microwave frequencies for oscillator stabilization, amplification, phase shifting, quadrature generation, frequency division, and other applications [1]–[11]. In a fundamentally synchronized oscillator, the output phase noise copies that of the synchronizing source up to a certain offset frequency [12]. From that offset frequency, the output phase-noise spectrum is different from the input one, typically with higher power. Similar behavior is obtained in the case of a frequency divider: the output phase noise is a sub-multiple of that of the input source, up to a certain offset frequency. When using harmonic balance (harmonic balance), the conversion matrix approach [13]–[15] enables an accurate prediction of the oscillator phase noise. However, this numerical technique provides little insight into the parameters and magnitudes that give the output phase-noise spectrum of the oscillator or divider its particular shape. This knowledge would be useful from a design point of view, as strategies could be devised in order to reduce the output phase noise. This phase-noise reduction can be achieved by increasing the offset-frequency range for which the oscillator circuit behaves like a low-pass filter with respect to the input phase noise.