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75
1.156GHz SelfAligned Vibrating Micromechanical Disk Resonator
, 2004
"... A new fabrication methodology that allows selfalignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radialcontour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q’s at this frequency>2,650 in both ..."
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Cited by 19 (2 self)
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A new fabrication methodology that allows selfalignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radialcontour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q’s at this frequency>2,650 in both vacuum and air. In addition, a 734.6MHz version has been demonstrated with Q’s of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, selfalignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.
Virtual Damping and Einstein Relation in Oscillators
 IEEE Journal of SolidState Circuits
, 2003
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A selfsustaining ultrahighfrequency nanoelectromechanical oscillator
 Nature Nanotech., 3:342 – 346
, 2008
"... Sensors based on nanoelectromechanical systems vibrating at high and ultrahigh frequencies1 are capable of levels of performance that surpass those of larger sensors. Nanoelectromechanical devices have achieved unprecedented sensitivity in the detection of displacement2, mass3, force4 and charge5. T ..."
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Cited by 12 (0 self)
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Sensors based on nanoelectromechanical systems vibrating at high and ultrahigh frequencies1 are capable of levels of performance that surpass those of larger sensors. Nanoelectromechanical devices have achieved unprecedented sensitivity in the detection of displacement2, mass3, force4 and charge5. To date, these milestones have been achieved with passive devices that require external periodic or impulsive stimuli to excite them into resonance. Here, we demonstrate an autonomous and selfsustaining nanoelectromechanical oscillator that generates continuous ultrahighfrequency signals when powered by a steady d.c. source. The frequencydetermining element in the oscillator is a 428 MHz nanoelectromechanical resonator that is embedded within a tunable electrical feedback network to generate active and stable selfoscillation. Our prototype nanoelectromechanical
Compensation of Phase Noise in OFDM Wireless Systems
"... Abstract—Phase noise causes significant degradation in the performance of orthogonal frequency division multiplexing (OFDM)based wireless communication systems. The presence of phase noise can reduce the effective signaltonoise ratio (SNR) at the receiver, and consequently, limit the bit error ra ..."
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Abstract—Phase noise causes significant degradation in the performance of orthogonal frequency division multiplexing (OFDM)based wireless communication systems. The presence of phase noise can reduce the effective signaltonoise ratio (SNR) at the receiver, and consequently, limit the bit error rate (BER) and data rate. In this paper, the effect of phase noise on OFDM wireless systems is studied, and a compensation scheme is proposed to mitigate the common phase error and intercarrier interference (ICI) caused by phase noise. In the proposed scheme, the communication between the transmitter and receiver blocks consists of two stages. In the first stage, blocktype pilot symbols are transmitted and the channel coefficients are jointly estimated with the phase noise in the time domain. In the second stage, combtype OFDM symbols are transmitted such that the receiver can jointly estimate the data symbols and the phase noise. It is shown both by theory and computer simulations that the proposed scheme can effectively mitigate the ICI caused by phase noise and improve the BER of OFDM systems. Another benefit of the proposed scheme is that the sensitivity of OFDM receivers to phase noise can be significantly lowered, which helps simplify the oscillator and circuitry design in terms of implementation cost and power consumption. Index Terms—Common phase error, compensation scheme, equalization, intercarrier interference (ICI), orthogonal frequency division multiplexing (OFDM), performance analysis, phaselocked loop (PLL), phase noise. I.
On the Difference Between Two Widely Publicized Methods for Analyzing Oscillator Phase Behavior
 In Proc. IEEE/ACM ICCAD, Session 4A
, 2002
"... This paper describes the similarities and differences between two widely publicized methods for analyzing oscillator phase behavior. The methods were presented in [3] and [6]. It is pointed out that both methods are almost alike. While the one in [3] can be shown to be, mathematically, more exact, ..."
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This paper describes the similarities and differences between two widely publicized methods for analyzing oscillator phase behavior. The methods were presented in [3] and [6]. It is pointed out that both methods are almost alike. While the one in [3] can be shown to be, mathematically, more exact, the approximate method in [6] is somewhat simpler, facilitating its use for purposes of analysis and design. In this paper, we show that, for stationary input noise sources, both methods produce equal results for the oscillator’s phase noise behavior. However, when considering injection locking, it is shown that both methods yield different results, with the approximation in [6] being unable to predict the locking behavior. In general, when the input signal causing the oscillator phase perturbations is nonstationary, the exact model produces the correct results while results obtained using approximate model break down. 1.
An analytical formulation of phase noise of signals with Gaussian distribution jitter,” unpublished
"... Abstract—The output of many oscillatory systems can be approximated by a stochastic squarewave signal with noisefree amplitude and Gaussiandistributed jitter. We present an analytical treatment of the phase noise of this signal with white and Lorentzian jitter spectra. With a white jitter spectru ..."
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Abstract—The output of many oscillatory systems can be approximated by a stochastic squarewave signal with noisefree amplitude and Gaussiandistributed jitter. We present an analytical treatment of the phase noise of this signal with white and Lorentzian jitter spectra. With a white jitter spectrum, the phase noise is nearly Lorentzian around each harmonic. With a Lorentzian jitter spectrum, it is a sum of several Lorentzian spectra, a summation that has a I R shape at farout frequencies. With a combination of the two, it has I R and I P shapes at closein and farout frequencies, respectively. In all cases, the phase noise at the center frequency and the total signal power are both finite. These findings will improve our understanding of phase noise and will facilitate the calculation of phase noise using time domain jitter analysis. Index Terms—Analytical formulation, frequency stability, oscillator noise, phase jitter, phase noise. I.
On the estimation of nonrandom signal coefficients from jittered samples
 IEEE TRANS. SIGNAL PROCESS
, 2011
"... This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive, independent identically distributed (i.i.d.) Gaussian noise, where the signal lies in the span of a finite basis. For the presented classical est ..."
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Cited by 4 (2 self)
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This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive, independent identically distributed (i.i.d.) Gaussian noise, where the signal lies in the span of a finite basis. For the presented classical estimation problem, the Cramér–Rao lower bound (CRB) is computed, and an ExpectationMaximization (EM) algorithm approximating the maximum likelihood (ML) estimator is developed. Simulations are performed to study the convergence properties of the EM algorithm and compare the performance both against the CRB and a basic linear estimator. These simulations demonstrate that by postprocessing the jittered samples with the proposed EM algorithm, greater jitter can be tolerated, potentially reducing onchip ADC power consumption substantially.
Minimum Phase Noise of an LC oscillator: Determination of the optimal operating point of the active part
, 2012
"... 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 r ..."
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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.
Clock Jitter Estimation based on PM Noise Measurements∗ by
"... ABSTRACT “Jitter ” is the noise modulation due to random time shifts on an otherwise ideal, or perfectly ontime, signal transition. In the absence of ultrahighspeed jitter analyzers, spectrum analysis is an alternate noise measurement for timing jitter. Conventionally, jitter has been defined a ..."
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Cited by 3 (1 self)
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ABSTRACT “Jitter ” is the noise modulation due to random time shifts on an otherwise ideal, or perfectly ontime, signal transition. In the absence of ultrahighspeed jitter analyzers, spectrum analysis is an alternate noise measurement for timing jitter. Conventionally, jitter has been defined as a the integral of the phase noise. This paper presents a modified way of calculating timing jitter using phasemodulation (PM) noise measurements of highspeed digital clocks, which considers the frequency response of the jitter analyzer, providing a more accurate map. Measurements of phase noise are typically much more sensitive to phase (or time) fluctuations than a jitter analyzer. A summary table is provided for mapping the results of these measurements in the Fourier frequency domain to jitter in the τ domain for various random (specifically, powerlaw) noise types, spurs, vibration, and powersupply ripple. In general, one cannot unambiguously map back, that is, translate from jitter measurements to phase noise. 1.
Singleended to differential converter for multiplestage singleended ring oscillators
 IEEE Journal of SolidState Circuits
, 2003
"... Abstract—This paper presents an improved technique for singleended to differential conversion that allows for the use of singleended CMOS ring oscillators in an otherwise fully differential integrated circuit environment. An interpolating resistor network is used to derive a fully differential rep ..."
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Abstract—This paper presents an improved technique for singleended to differential conversion that allows for the use of singleended CMOS ring oscillators in an otherwise fully differential integrated circuit environment. An interpolating resistor network is used to derive a fully differential representation of the singleended voltagecontrolledoscillator (VCO) signal. The technique preserves the fundamental noise performance of singleended ring oscillators in the presence of supply and substrate interference. Experimental results in a 0.35 m CMOS process show the applicability of this technique at the VCO speeds of up to 1.3 GHz. Index Terms—Jitter, phase noise, powersupply interference, powersupply noise, singleended to differential conversion, substrate noise, voltagecontrolled oscillator. I.