Oscillator AM-to-FM noise conversion due to the dynamic frequency-drive sensitivity of the crystal resonator

Abstract

An analysis has been made of the potential effects of AM-to-FM noise conversion in quartz crystal oscillators as a result of the dynamic frequency-drive sensitivity of the crystal resonator. The analysis indicates that it is quite possible for the FM noise resulting from AM-to-FM conversion in the crystal resonator to equal or exceed that due to the conversion of oscillator open loop phase noise to closed loop frequency noise. This is especially true in oscillators designed to exhibit low white phase noise (floor) levels by operating the crystal resonator at relatively high drive level. In addition, the analysis indicates that, for the same drive sensitivity, the relative degradation in FM noise level due to this effect is more severe at lower relative oscillator operating frequencies.

Noise minimization techniques for voltage controlled crystal oscillator (VCXO) circuits

“…Figure (5) shows the typical oscillator phase noise plot for low and high resonator Q factor. For f 0 /(2Q L f) >>1, the value of k d that results in the equal levels of oscillator closed PM noise level due to AM noise and open loop PM noise can be described by [5] ⎥ ⎦ …”

“…where f m is the modulation frequency, the spectral density of the oscillator output signal phase fluctuation S φ(f) and amplitude fluctuation S a(f) can be described by [5] …”

“…The dynamic coefficient of the crystal frequency-drive sensitivity in terms of the fractional change induced as a function of the square current can be described by [5] …”

“…The phenomenon of phase noise generation in VCXO circuit has been the main focus of important research efforts, and it is still an open issue despite significant gains in practical experience and modern CAD tools for design. Recent analysis indicates that oscillator dynamic noise factor and resonator dynamic frequency drive sensitivity contribute phase noise significantly, and, the relative degradation in FM noise due to this effect is more severe at relative low operating frequencies [5]. Therefore, designing low phase noise VCXO circuit is challenging for a given, noise factor, frequency-drive sensitivity, Q-factor, cost, size, and power-consumptions, and these objectives have been accomplished using empirical rules, therefore, predictive power of the VCXO model is limited [4].…”

Highly Sensitive Dual Quartz Reactance-to-Frequency Transducer

“…Another important factor of great importance is high dynamic stability during temperature changes in the extended operating range. The use of switching circuits in many instances improves electrical circuit characteristics and/or compensates certain influences [23][24][25][26][27][28][29][30].…”