Dynamic range expansion for optical frequency shift detection based on multiple harmonics

Sensors based on optical resonators often have their measurement range limited by their cavity linewidth,particularly in the measurement of time-varying signals.This paper introduces a method for optical frequency shift detection using multiple harmonics to expand the dynamic range of sensors based on optical resonators.The proposed method expands the measurement range of optical frequency shift beyond the cavity linewidth while maintaining measurement accuracy.The theoretical derivation of this method is carried out based on the equation of motion for an optical resonator and the recursive relationship of the Bessel function.Experimental results show that the dynamic range is expanded to 4 times greater than the conventional first harmonic method while still maintaining accuracy.Furthermore,we present an objective analysis of the correlation between the expansion factor of the method and the linewidth and free spectrum of the optical resonator.

Some Implications of the Gessel Identity

We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.

The frequency estimation of harmonic signals embedded in multiplicative and additive noise

A method to separate a harmonic signal from multiplicative and additive noises is proposed. The method is to square the signal x(t), which consists of a harmonic signal embedded in multiplicative and additive noises, to form another signal y(t) = x2(t)-E[x2(t)]. After y(t) having been gotten, the Fourier transform is imposed on it. Because the information of x(t) (especially about frequency) is included in y(t), the frequency of x(t) can be estimated from the power spectrum of y(t). According to the simulation, under the condition where frequencies divided by resolution dω are integer, the maximum relative error of estimated frequencies is less than 0.4% when the signal-to-noise ratio (SNR) is greater than -23 dB. If frequencies divided by resolution dω are not integer, the maximum relative error will be less than 2.9%. But it is still small in terms of engineering.

Magnets Shifting Design of Dual PM Excited Vernier Machine for High-torque Application

In this study,a novel dual permanent magnet excited vernier machine(DPMEVM)with magnets shifting in stator is proposed.Compared with the conventional permanent magnet synchronous machine(PMSM),the DPMEVM based on the bidirectional field modulation effect can operate in a wider torque range.However,the torque ripple of a conventional DPMEVM is high because of the superposition of the torque generated by the stator-side and rotor-side PMs.Consequently,a novel DPMEVM with magnets shifting is proposed to further reduce the torque ripple.First,the topologies and working principles of the baseline machine and proposed machines are introduced.Second,the torque-contribution harmonics are analyzed and calculated using the Maxwell tensor method.The calculation results reveal that the DPMEVM,benefiting from multiple working harmonics,can offer an enhanced torque capability compared to the PMSM.In addition,the torque ripple characteristics of the proposed machines are analyzed.It is verified that the torque ripple can be significantly reduced through magnets shifting.Third,the performances of the baseline machine and proposed machines are analyzed and compared in terms of flux density,open-circuit back-EMF,and torque characteristics.In addition,the proposed principle can be extended to machines with the same unit motor.Finally,a 120s-110p prototype machine is manufactured for validation.