The tuning curve of an LC-tuned voltage-controlled oscillator (VCO) substantially deviates from the ideal curve 1//spl radic/(LC(V)) when a varactor with an abrupt C(V) characteristic is adopted and the full oscillator swing is applied directly across the varactor. The tuning curve becomes strongly dependent on the oscillator bias current. As a result, the practical tuning range is reduced and the upconverted flicker noise of the bias current dominates the 1/f/sup 3/ close-in phase noise, even if the waveform symmetry has been assured. A first-order estimation of the tuning curve for MOS-varactor-tuned VCOs is provided. Based on this result, a simplified phase-noise model for double cross-coupled VCOs is derived. This model can be easily adapted to cover other LC-tuned oscillator topologies. The theoretical analyses are experimentally validated with a 0.25 /spl mu/m CMOS fully integrated VCO for 5 GHz wireless LAN receivers. By eliminating the bias current generator in a second oscillator, the close-in phase noise improves by 10 dB and features -70 dBc/Hz at 10 kHz offset. The 1/f/sup 2/ noise is -132 dBc/Hz at 3 MHz offset. The tuning range spans from 4.6 to 5.7 GHz (21%) and the current consumption is 2.9 mA.

It has been noted that the power spectrum of intracortical local field potential (LFP) often scales as 1/f⁻². It is thought that LFP mostly represents the spiking-related neuronal activity such as synaptic currents and spikes in the vicinity of the recording electrode, but no 1/f² scaling is detected in the spike power. Although tissue filtering or modulation of spiking activity by UP and DOWN states could account for the observed LFP scaling, there is no consensus as to how it arises. We addressed this question by recording simultaneously LFP and single neurons (“single units”) from multiple sites in somatosensory cortex of anesthetized rats. Single-unit data revealed the presence of periods of high activity, presumably corresponding to the “UP” states when the neuronal membrane potential is depolarized, and periods of no activity, the putative “DOWN” states when the membrane potential is close to resting. As expected, the LFP power scaled as 1/f² but no such scaling was found in the power spectrum of spiking activity. Our analysis showed that 1/f² scaling in the LFP power spectrum was largely generated by the steplike transitions between UP and DOWN states. The shape of the LFP signal during these transitions, but not the transition timing, was crucial to obtain the observed scaling. These transitions were probably induced by synchronous changes in the membrane potential across neurons. We conclude that a 1/f² scaling in the LFP power indicates the presence of steplike transitions in the LFP trace and says little about the statistical properties of the associated neuronal firing.

Flicker noise up-conversion in voltage-biased oscillators can be effectively suppressed by inserting resistances in series to the drain of the transconductor MOSFETs. This solution avoids the degradation of the start-up margin and the adoption of area-demanding resonant filters with proper tuning. This paper presents a detailed theoretical analysis of 1/f noise up-conversion and quantitatively addresses the impact of two major contributions, namely the Groszkowski effect and the loop delay caused by stray capacitances at the drain node of the transistors. A simple flow for the design of an oscillator with suppressed flicker noise up-conversion is presented which is based on first-order closed-form formulas. Finally , theoretical estimates are compared to experimental results on a 65-nm CMOS VCO covering the 3.0-3.6 GHz band.

This paper reports the developments toward an integrated, tri-axial, frequency-modulated, consumergrade, and microelectromechanical system (MEMS) gyroscope. A custom low-power (160 μA), low-phase-noise integrated circuit is designed specifically for frequencymodulated operation. Both yawand pitch-rate sensing systems are demonstrated by coupling the circuit with two novel micromachined structures fabricated with a 24-μmthick industrial process. In operation, both gyroscopes show a repeatable and stable scale factor, with less than 0.55% of part-to-part variability, obtained with no any calibration, and 35 ppm/°C of variability over a 25-70 °C temperature range.

This paper proposes a complete analysis of quadrature-coupled LC oscillators. These oscillators operate off-resonance and for this reason, their phase noise worsens at increasing coupling strength. Since the coupling transistors raise the total power consumption, the noise-power product degrades further with respect to a stand-alone oscillator. On the other hand, at high coupling factors component mismatches affect less the phase accuracy of the quadrature outputs. Closed-form expressions for phase noise and phase accuracy are derived which are verified against circuit simulations.

Harmonic content modulation of the oscillator output voltage can contribute to flicker noise up-conversion in LC-tuned oscillators. The paper reports a quantitative analysis of the effect in Van der Pol oscillators using the framework of the impulse sensitivity function (ISF). It is shown that most of the up-conversion efficiency results from the first harmonic of the ISF, which is not perfectly in quadrature to the output voltage waveform, and from the first harmonic of the transistor current, which is slightly lagging the voltage waveform. A closed-form expression of 1/f³ phase noise in voltage-limited LC-tuned oscillator is derived that is in good agreement with circuit simulations. The paper also shows that the values of both phase shifts are determined by the non-linearity of the active element and are linked to the relevant oscillator parameters, i.e., excess gain and tank quality factor.