Minimum phase noise of an LC oscillator: Determination of the optimal operating point of the active part

Abstract

In this paper, we describe an original method for determining the optimal operating point of the active part (transistor) of an LC oscillator leading to the minimum phase noise for given specifications in terms of power consumption, oscillation frequency and for given devices (i.e., transistor and resonator). The key point of the proposed method is based on the use of a proper LC oscillator architecture providing a fixed loaded quality factor for different operating points of the active part within the oscillator. The feedback network of this architecture is made of an LC resonator with coupling transformers. In these conditions, we show that it is possible to easily change the operating point of the amplifier, through the determination of the turns ratio of those transformers, and observe its effect on phase noise without modifying the loaded quality factor of the resonator. The optimal operating point for minimum phase noise is then extracted from nonlinear simulations. Once this optimal behaviour of the active part known and by associating the previous LC resonator, a design of an LC oscillator or VCO with an optimal phase noise becomes possible. The conclusions of the presented simulation results have been widely used to design and implement a fully integrated, LC differential VCO on a 0.35 µm BiCMOS SiGe process.

Analysis and design of an array of two differential oscillators coupled through a resistive network

“…A tail capacitor C T is used to attenuate both the high-frequency noise component of the tail current and the voltage variations on the tail node. This latter effect results in more symmetric waveforms and smaller harmonic distortion in LC-VCO outputs [9].…”

Electronic Tunability and Cancellation of Serial Losses in Wire Coils

“…We tried to compare typical narrow-band solutions of LC oscillators intended for high-frequency purposes with our design. The proposed solution seems to be slightly complex but the intended application bandwidths (kHz, MHz) do not allow us to implement the method used in the published solutions (see Table 2 and circuits in [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]). This is because of the values and physical realization of integrated inductors (unsuitable for low frequencies due to values in nH and also their implementation).…”

“…Wider tunability (e.g., from 3 up to 5 GHz) supposes the switching of LC banks (“LC tanks”) by additional control logic. The driving voltage range seems to be also very large [ 38 , 42 ], while the gained frequency ranges of tunability are very low. On the other hand, these systems do not need precise amplitude stabilization and low waveform purity due to different application purposes (communications) and have also very good phase noise (>80 dBc/Hz) in comparison with low-frequency solutions (typically between 40 and 80 dBc/Hz).…”

“…The electronic tunability of the oscillation frequency by the inductance value (as presented in our case) has not been tested in recently published works because it has certain limitations, especially at high frequencies (extensive active circuitries), but can be used without issues in kHz and MHz bands with significant advantages (wideband tuning). The wideband tunability of the frequency with almost constant output levels and low THD requires the implementation of a circuit for amplitude stabilization, which is standardly not used in LC oscillators (including the Colpitts type) because of their narrowband tunability [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ].…”

Graphical method for the phase noise optimization applied to a 6-GHz fully integrated NMOS differential LC VCO

“…The tail current source is a simple NMOS current mirror. In these conditions, the width and the length of the NMOS tail transistor must be increased to reduce the flicker noise which lowers significantly the close-in phase noise of the VCO [3]. A tail capacitor C T is used to attenuate both the high-frequency noise component of the tail current and the voltage variations on the tail node.…”