Sergio Sancho

SAMPLING TECHNIQUES FOR THE ESTIMATION OF THE ANNUAL EQUIVALENT NOISE LEVEL UNDER URBAN TRAFFIC CONDITIONS

Abstract This paper summarises 5 years of continuous noise measurements carried out at one of the most important squares in Valencia (Spain). The chosen square is a clear hotspot for traffic noise in a large city. The aim of this study is to determine the appropriate measuring time in order to obtain a 24-h noise level suitable to represent the annual equivalent level. Our findings allow us to reach a number of conclusions in terms of the most suitable urban traffic noise measurement techniques. A random day strategy for sampling is found to give a more accurate representation than a consecutive days strategy. If the sampling strategy involves measurements on randomly-chosen days, then at least 6 days should be used.

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.

Analytical comparison between time- and frequency-domain techniques for phase-noise analysis

In the literature, different techniques have been presented for the phase-noise analysis of free-running oscillator circuits. In order to give some insight into the relationships existing between them, an analytical comparison is carried out in this paper between three different approaches. Two of them are time-domain approaches, based on Floquets theory and the impulse sensitivity function, respectively, and the third one is the carrier modulation approach, in frequency domain. The application of Floquets theory enables the calculation of periodic sensitivity functions to the noise perturbations. Here, the possibility to determine these functions through harmonic balance is demonstrated. This allows applying the whole stochastic characterization of phase noise, obtained from time-domain analysis, to circuits simulated through harmonic balance. For illustration, calculations in a cubic-nonlinearity oscillator are presented.

Analysis of noise effects on the nonlinear dynamics of synchronized oscillators

The higher sensitivity to noise of nonlinear systems near the onset of instability is analyzed here. The analysis is particularized to synchronized oscillators, studying the influence of the proximity to Hopf and Saddle-Node bifurcations. The calculations are compared with former scaling relationships and with results from time-domain integration. The average shift of bifurcation points due to noise perturbations is also analyzed. Two examples are shown: a cubic-nonlinearity oscillator and a 5 GHz hybrid oscillator, for experimental verifications.

General envelope-transient formulation of phase-locked loops using three time scales

In this paper, a novel time-frequency method for the analysis of phase-locked loops (PLLs) has been developed. It enables an efficient and realistic simulation, taking into account the spurious frequency components generated at the phase detectors and intrinsic to their nonlinear performance. The variables of the loop equations are expanded in a Fourier series, at these spurious frequencies, with time-varying phasors. This generalizes the envelope-transient analysis to loops containing three different time scales, provided by the frequency of the voltage-controlled oscillator, external signals, and noise or modulations, respectively. The new technique substantially reduces the computational cost in the simulation of transients and acquisition times in the common case of a narrow-band loop. It also allows considering low-frequency noise perturbations, while taking into account the spurious frequency components. In the absence of modulation, the harmonic-balance (HB) formulation of the loop equations enables an efficient analysis of the variation of the PLL solution versus any parameter of interest. In addition, the conversion matrix approach, based on this HB formulation, can be used to determine the output noise spectrum from frequency-domain descriptions of the input noise sources, while taking the spurious content into account. To show the generality of application of the techniques, two different PLLs have been considered here: a frequency synthesizer with a tri-state comparator and charge pump, and an automatic frequency-control loop. In each case, the results have been successfully compared with time-domain simulations and measurements.

Phase and Amplitude Noise Analysis in Microwave Oscillators Using Nodal Harmonic Balance

In this paper, a nodal harmonic balance (HB) formulation is presented for the phase and amplitude noise analysis of free-running oscillators. The implications of using different constraints in the resolution of the perturbed-oscillator equations are studied. The obtained formulation allows the prediction of the possible spectrum resonances without ill conditioning at low frequency offset from the carrier. The noise spectrum is meaningfully expressed in terms of the eigenvalues of a newly defined matrix, obtained from the linearization of the nodal HB system about the steady-state solution. The cases of real or complex-conjugate dominant eigenvalues are distinguished. The developed phase-noise formulation is extended to a system of two coupled oscillators. The phase and amplitude noise analyses have been applied to a push-push oscillator at 18 GHz, a bipolar oscillator at 1 GHz, and a coupled system of two field-effect transistor oscillators at 6 GHz.

Envelope transient analysis of self-oscillating mixers

In this paper, the envelope-transient method is applied to the analysis of intermodulation distortion in self-oscillating mixers (SOM). A two-tone Fourier-series expansion of the circuit variables with time-varying harmonic components is used with a new initialization technique of the oscillation to avoid convergence toward unstable forced solutions. The two cases of an autonomous oscillation and a sub-synchronized oscillation are studied and compared. In the sub-synchronized SOM, the ranges of sub-synchronized operation in terms of the sub-synchronization generator power and frequency are determined through harmonic balance. The techniques are applied to a SOM with 5.5-GHz input frequency and 0.5-GHz IF. In the case of an autonomous oscillation, two different values of the quality factor of the load circuit are considered. For sub-synchronized operation, a generator is introduced at approximately one-third the self-oscillation frequency. In order to validate the analysis techniques, the circuit has been experimentally characterized in both autonomous and sub-synchronized operation, obtaining very good agreement with the simulation results.

Analysis of Near-Carrier Phase-Noise Spectrum in Free-Running Oscillators in the Presence of White and Colored Noise Sources

This paper presents the stochastic characterization of the phase-noise spectrum of free-running oscillators in the envelope domain. The flicker-noise sources are modeled as an infinite summation of Ornstein-Uhlenbeck processes. Inputs of the formulation are parameters extracted with harmonic balance (HB) by means of the carrier-modulation approach. These parameters can be easily identified with commercial software packages without user access to the Jacobian matrix of the HB system. The presented envelope-domain formulation significantly reduces the complexity of the stochastic analysis in comparison with time-domain techniques. The phase-noise spectrum depends on the measurement time interval, instead of estimated cutoff frequencies for the colored noise sources. With the new formulation it has been possible to investigate the influence of the measurement time interval on the near-carrier phase-noise spectrum. The formulation will show that provided the measurement time fulfills some nonstrict mathematical conditions, typically accomplished in any practical measurement, the full phase-noise spectrum will be nearly the same, whatever the measurement time interval. Analytical expressions are provided for the full phase-noise spectrum. All the obtained expressions have been exhaustively validated by means of Monte Carlo simulations. In order to verify the generality of the results, the analysis method has been applied to various oscillator configurations. The simulated and measured phase-noise spectra have been compared, obtaining very good agreement in all cases.

Stability and Noise Analysis of Coupled-Oscillator Systems

We present a simplified closed-form formulation for the optimized design of coupled-oscillator systems. It is based on admittance models for the oscillator elements, extracted from HB simulations. The formulation relates explicitly the coupled-system oscillation frequency and amplitude and phase distributions with the parameters of the coupling network and the oscillator elements. It allows anticipating and understanding the form of variation of the system variables and can be used for an insightful design. With a perturbation analysis based on the new formulation, we will generalize existing stability criteria to more complete oscillator models. A combined amplitude- and phase-noise formulation will enable the prediction of the phase-noise spectrum flattening near oscillator carrier, while taking into account the system resonances that affect the spectrum shape. The techniques have been successfully applied to a coupled-oscillator system at 5.2 GHz.

Nonlinear dynamics of microwave synthesizers-stability and noise

The nonlinear dynamics of microwave synthesizers based on type-II third-order loops is analyzed in this paper. Instead of using standard simplified models, realistic models are considered for the loop filter, phase detector (PD), and voltage-controlled oscillator based on experimental characterization. The new models enable the simulation of incidental frequency modulation and the accurate prediction of the synthesizer operation ranges, including possible hysteresis phenomena. The stability of phase-locked solutions is analyzed, enabling the prediction of possible chaotic behavior. For an accurate determination of the output spectrum, a phase-noise simulation is also carried out, considering the noise contributions from the loop elements. The sidebands inherent to the synthesizer solution are taken into account for this analysis. The analysis strategy has been applied to a microwave synthesizer, operating in the 2-3 GHz band, with very good results. Two types of PDs are considered: the JK flip-flop PD and frequency mixer, comparing the resulting loop performance in terms of stability and phase noise.