Phase Noise and Frequency Stability of the Red-Pitaya Internal PLL

partially_open5sìIn field-programmable gate array platforms, the main clock is generally a low-cost quartz oscillator whose stability is of the order of 10-9 to 10-10 in the short term and 10-7 to 10-8 in the medium term, with the uncertainty of tens of ppm. Better stability is achieved by feeding an external reference into the internal phase-locked loop (PLL). We report the noise characterization of the internal PLL of Red-Pitaya platform, an open-source embedded system architected around the Zynq 7010 System on Chip, with analog-to-digital and digital-to-analog converters. Our experiments show that, providing an external 10-MHz reference, the PLL exhibits a residual frequency stability of 1.2×10-12 at 1 s and 1.3×10-15 at 4000 s, Allan deviation in 5-Hz bandwidth. These results help to predict the PLL stability as a function of frequency and power of the external reference, and provide guidelines for the design of precision instrumentation, chiefly intended for time and frequency metrology.partially_openCardenas Olaya, Andrea Carolina; Calosso, Claudio Eligio; Friedt, Jean-Michel; Micalizio, Salvatore; Rubiola, EnricoCardenas Olaya, Andrea Carolina; Calosso, Claudio Eligio; Friedt, Jean-Michel; Micalizio, Salvatore; Rubiola, Enric

Spectral Weighting Functions for Single-symbol Phase-noise Specifications in OFDM Systems

For the specification of phase-noise requirements for the front-end of a HiperLAN/2 system we investigated available literature on the subject. Literature differed in several aspects. One aspect is in the type of phase-noise used (Wiener phase-noise or small-angle phase noise). A Wiener phase-noise based analysis leads to contradictions with the type of analysis normally used in the solid state oscillator literature. However, a phase-noise spectrum with a Wiener phase-noise shape can be used provided that the small-angle approximation is satisfied. An other aspect is whether a Fourier Series or DFT based approach is used. The approaches use weighting functions to relate phase-noise power spectral densities to phase-noise power. The two types of analysis are presented in a unified fashion that allows easy comparison of the weighting functions involved. It can be shown that for practical purposes results are identical. Finally phase-noise specifications for the Hiper-LAN/2 case are presented

Virtual damping and Einstein relation in oscillators

This paper presents a new physical theory of oscillator phase noise. Built around the concept of phase diffusion, this work bridges the fundamental physics of noise and existing oscillator phase-noise theories. The virtual damping of an ensemble of oscillators is introduced as a measure of phase noise. The explanation of linewidth compression through virtual damping provides a unified view of resonators and oscillators. The direct correspondence between phase noise and the Einstein relation is demonstrated, which reveals the underlying physics of phase noise. The validity of the new approach is confirmed by consistent experimental agreement

Jitter and phase noise in ring oscillators

A companion analysis of clock jitter and phase noise of single-ended and differential ring oscillators is presented. The impulse sensitivity functions are used to derive expressions for the jitter and phase noise of ring oscillators. The effect of the number of stages, power dissipation, frequency of oscillation, and short-channel effects on the jitter and phase noise of ring oscillators is analyzed. Jitter and phase noise due to substrate and supply noise is discussed, and the effect of symmetry on the upconversion of 1/f noise is demonstrated. Several new design insights are given for low jitter/phase-noise design. Good agreement between theory and measurements is observed

Phase Noise Modeling of Opto-Mechanical Oscillators

We build upon and derive a precise far from carrier phase noise model for radiation pressure driven opto-mechanical oscillators and show that calculations based on our model accurately match published phase noise data for such oscillators. Furthermore, we derive insights based on the equations presented and calculate phase noise for an array of coupled disk resonators, showing that it is possible to achieve phase noise as low as -80 dBc/Hz at 1 kHz offset for a 54 MHz opto-mechanical oscillator

Constrained Phase Noise Estimation in OFDM Using Scattered Pilots Without Decision Feedback

In this paper, we consider an OFDM radio link corrupted by oscillator phase noise in the receiver, namely the problem of estimating and compensating for the impairment. To lessen the computational burden and delay incurred onto the receiver, we estimate phase noise using only scattered pilot subcarriers, i.e., no tentative symbol decisions are used in obtaining and improving the phase noise estimate. In particular, the phase noise estimation problem is posed as an unconstrained optimization problem whose minimizer suffers from the so-called amplitude and phase estimation error. These errors arise due to receiver noise, estimation from limited scattered pilot subcarriers and estimation using a dimensionality reduction model. It is empirically shown that, at high signal-to-noise-ratios, the phase estimation error is small. To reduce the amplitude estimation error, we restrict the minimizer to be drawn from the so-called phase noise geometry set when minimizing the cost function. The resulting optimization problem is a non-convex program. However, using the S-procedure for quadratic equalities, we show that the optimal solution can be obtained by solving the convex dual problem. We also consider a less complex heuristic scheme that achieves the same objective of restricting the minimizer to the phase noise geometry set. Through simulations, we demonstrate improved coded bit-error-rate and phase noise estimation error performance when enforcing the phase noise geometry. For example, at high signal-to-noise-ratios, the probability density function of the phase noise estimation error exhibits thinner tails which results in lower bit-error-rate

Oscillator Phase Noise and Small-Scale Channel Fading in Higher Frequency Bands

This paper investigates the effect of oscillator phase noise and channel variations due to fading on the performance of communication systems at frequency bands higher than 10GHz. Phase noise and channel models are reviewed and technology-dependent bounds on the phase noise quality of radio oscillators are presented. Our study shows that, in general, both channel variations and phase noise can have severe effects on the system performance at high frequencies. Importantly, their relative severity depends on the application scenario and system parameters such as center frequency and bandwidth. Channel variations are seen to be more severe than phase noise when the relative velocity between the transmitter and receiver is high. On the other hand, performance degradation due to phase noise can be more severe when the center frequency is increased and the bandwidth is kept a constant, or when oscillators based on low power CMOS technology are used, as opposed to high power GaN HEMT based oscillators.Comment: IEEE Global Telecommun. Conf. (GLOBECOM), Austin, TX, Dec. 201