When a local oscillator signal generation system is based on an LC oscillator and a frequency multiplier, the question of determining the optimal multiplication factor is a key issue. In this paper, the problem is addressed in order to minimize the 1∕f 2 phase noise within a tuning range constraint. The analysis, with a practical graphical representation, reveals the oscillator phase noise dependence on the oscillating frequency in the transition from two different regimes, named the inductor-limited quality factor and the capacitor-limited quality factor. The results obtained enable the evaluation of the phase noise performance of systems based on a sub-harmonic and super-harmonic oscillators and how they compare with an oscillator in the fundamental mode. Crucial questions like the phase noise improvement that these systems can achieve are analytically answered. A design methodology is thus proposed and verified through measurements on a frequency source at 31 GHz, composed by a sub-harmonic voltage-controlled oscillator followed by an injection-locked frequency tripler, dedicated to backhauling applications, designed on a BiCMOS process technology. The tuning range is 10%, and the phase noise at a 1-MHz offset is −112 dBc/Hz. D. CABRERA, ET AL. ¶ While Q L increases with the frequency, Q C decreases asymptotically. ‖ Note that the phase noise is an increasing function even when the resonator quality factor increases with frequency. Figure 9. Improvement in the phase noise at 1-MHz offset by using a system composed of a sub-harmonic oscillator and an ideal frequency multiplier-by-n over a fundamental oscillator at 31 GHz.A simplified view of the gm cell used in [5] for the VCO is presented in Figure 12. A DC-decoupling network composed of C f and r f is used to allow a differential amplitude of 1.4 V while keeping at 0 V the maximum forward voltage of the base-collector junction of each transistor, hence keeping the transistors out of the saturation region. The bias voltage is Vb1 = 995 mV. Considering the signal magnitudes involved in the cross-coupled pair and its voltage/currentdependent capacitances, a large signal analysis should be followed to determine G ; however, an