Frequency-modulated Mode Research Articles

Noise analysis and modeling for a digital control architecture for Lissajous frequency-modulated MEMS gyroscope with amplitude-modulated readout

We report a digital control architecture that demodulates both amplitude-modulated (AM) and frequency-modulated (FM) rate information simultaneously from a gyroscope working in Lissajous frequency-modulated (LFM) mode. The angular rate information is derived from both quadrature (X and Y) resonance modes of the gyroscope simultaneously. A noise model for the AM signal processing channel of the LFM gyroscope is built, analyzed and compared with that of a conventional AM gyroscope, which shows that methods to improve the performance of the conventional AM gyroscope can also be applied to the AM signal processing channel of the LFM gyroscope. The angular rate output obtained from the AM information of the LFM gyroscope has better noise characteristics, which therefore supplements the low precision inadequacy of the FM signal channel of the LFM mode. Tests on the same gyroscope working in different control architectures are conducted. The angle random walk (ARW) and bias instability (BI) of the AM channel of the proposed architecture are 0.51 deg √h−1 and 1.8 deg h−1, respectively, which are better than the results obtained from the FM channel in the same architecture, with values of 0.99 deg √h−1 and 4.3 deg h−1, respectively. Also ARW amd BI of the same gyroscope working in conventional AM mode is 0.50 deg √h−1 and 5.2 deg h−1, respectively.

A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> and 2 °/h, respectively.

A Non-Destructive Health Evaluation Method for Wooden Utility Poles with Frequency-Modulated Empirical Mode Decomposition and Laplace Wavelet Correlation Filtering.

Wooden utility poles are one of the most commonly used utility carriers in North America. Even though they are given different protection treatments, wooden utility poles are prone to have defects that are mainly caused by temperature, oxygen, moisture, and high potential hydrogen levels after decades of being exposed in open-air areas. In order to meet the growing demand regarding their maintenance and replacement, an effective health evaluation technology for wooden utility poles is essential to ensure normal power supply and safety. However, the commonly used hole-drilling inspection method always causes extra damage to wooden utility poles and the precision of health evaluation highly relies on technician experience at present. Therefore, a non-destructive health evaluation method with frequency-modulated empirical mode decomposition (FM-EMD) and Laplace wavelet correlation filtering based on dynamic responses of wooden utility poles was proposed in this work. Specifically, FM-EMD was used to separate multiple confusing closely-spaced vibration modes due to nonlinear properties of wooden utility poles into several single modes. The instantaneous frequency and damping factor of the decomposed signal of each single mode of the dynamic response of a wooden utility pole could be determined using Laplace wavelet correlation filtering with high precision. The health status of a wooden utility pole could then be estimated according to the extracted instantaneous frequency and damping factor of the decomposed signal of each single mode. The proposed non-destructive health evaluation method for wooden utility poles was tested in the field and achieved successful results.

Optical frequency comb generation from a 1.65 µm single-section quantum well laser.

Optical frequency combs (OFCs) in the 1.65 µm wavelength band are promising for methane sensing and extended high-capacity optical communications. In this work, a frequency-modulated (FM) OFC is generated from a 1.65 µm single-section quantum well laser. This is characterized by a 1 kHz-wide beatnote signal at ∼19.4 GHz. Typical FM optical spectra are shown and optical linewidth of the OFC narrows through the mutual injection locking process in the comb formation. No distinct pulse train is observed on oscilloscope, which conforms with the FM operation. Furthermore, to add further evidence that four-wave mixing (FWM) is the driving mechanism of the comb formation, FWM frequency conversion characterization is conducted on a semiconductor optical amplifier (SOA) fabricated together with the tested laser. An efficiency of ∼-30 dB confirms the capability of FM mode locking.

Toward robust and practical interband cascade laser frequency combs: A perspective

Multimode emission from a semiconductor laser can sometimes take the form of a low-noise frequency comb with equidistant separation between the modes. Two general types of “passive” comb operation have been explored experimentally: (1) the periodic short-pulse mode achieved by intracavity mode locking, usually obtained by incorporating a saturable absorber section into the cavity, and (2) the so-called frequency-modulated (FM) mode in which the output intensity can vary within wide bounds but does not completely turn off between pulses, and the instantaneous frequency is linearly chirped over a round trip. The FM mode sometimes manifests as a “sparse” harmonic state, with individual modes spaced by multiples of the cavity free spectral range. This Perspective reviews the current understanding of these modes, along with the conditions under which they may arise in practical devices. We then consider in detail the case of type-II mid-infrared interband cascade laser (ICL) frequency combs. Our simulations clarify the roles of carrier dynamics and group velocity dispersion and identify design modifications that may substantially improve the device performance. We find no fundamental roadblocks to the development of practical mode-locked ICL frequency combs that emit short pulses with broad spectral bandwidth for dual comb spectroscopy and other applications, alongside the FM combs that have already been demonstrated experimentally.

Vital-SAR-Imaging With a Drone-Based Hybrid Radar System

Full-coverage synthetic-aperture radar (SAR) imaging and human target identification in complex scenes are very important for security and rescue applications. In this paper, a drone-based vital-SAR-imaging hybrid radar system is proposed to realize targets’ imaging and human identification simultaneously. Carried by an operational custom-built drone with a designed S-shaped trajectory, 2-D SAR images of the entire region could be obtained through the frequency-modulated continuous-wave mode, and the “vital Doppler” effect of human target can be searched through the Doppler mode. Then, the vital-SAR-imaging could be achieved. Several experiments including cart-based SAR imaging with three trajectories, cart-based vital-SAR-imaging, and drone-based multitrajectory vital-SAR-imaging were carried out to reveal the capability and distinct operational features of the proposed system. Experimental results demonstrate that the system has the ability to obtain SAR imaging results in different scenes with multiple trajectories, and the human target could be effectively distinguished from other stationary objects. The results show that the lowest human target location error is 0.06 m in a $4\,\,\text {m} \times 9$ m indoor region, which illustrates the great potential for search and rescue applications.

Analyses of EEG Oscillatory Activities during Slow and Fast Repetitive Movements using Holo-Hilbert Spectral Analysis.

Neural oscillatory activities existing in multiple fre-quency bands usually represent different levels of neurophysiolog-ical meanings, from micro-scale to macro-scale organizations. In this study, we adopted Holo-Hilbert spectral analysis (HHSA) to study the amplitude-modulated (AM) and frequency-modulated (FM) components in sensorimotor Mu rhythm, induced by slow- and fast-rate repetitive movements. The HHSA-based approach is a two-layer empirical mode decomposition (EMD) architecture, which firstly decomposes the EEG signal into a series of frequency-modulated intrinsic mode functions (IMF) and then decomposes each frequency-modulated IMF into a set of amplitude-modulated IMFs. With the HHSA, the FM and AM components were incor-porated with their instantaneous power to achieve full-informa-tional spectral analysis. We observed that the instantaneous power induced by slow-rate movements was significantly higher than that induced by fast-rate movements (p < 0.01, Wilcoxon signed rank test). The alpha-band AM frequencies induced by slow-rate movements were higher than those induced by fast-rate move-ments, while no statistical difference was found in beta-band AM frequencies. In addition, to study the functional coupling between the primary sensorimotor area and other brain regions, spectral coherence was applied and statistical difference was found in frontal area in slow-rate versus fast-rate movements. The discrep-ancy between slow- and fast-rate movements might be owing to the change of motor functional modes from default mode network (DMN) to automatic timing with the increase of movement rates. The use of HHSA for oscillatory activity analysis can be an effi-cient tool to provide informative interaction among different fre-quency bands.

A gearbox fault diagnosis method based on frequency-modulated empirical mode decomposition and support vector machine

During the operation process of a gearbox, the vibration signals can reflect the dynamic states of the gearbox. The feature extraction of the vibration signal will directly influence the accuracy and effectiveness of fault diagnosis. One major challenge associated with the extraction process is the mode mixing, especially under such circumstance of intensive frequency. A novel fault diagnosis method based on frequency-modulated empirical mode decomposition is proposed in this paper. Firstly, several stationary intrinsic mode functions can be obtained after the initial vibration signal is processed using frequency-modulated empirical mode decomposition method. Using the method, the vibration signal feature can be extracted in unworkable region of the empirical mode decomposition. The method has the ability to separate such close frequency components, which overcomes the major drawback of the conventional methods. Numerical simulation results showed the validity of the developed signal processing method. Secondly, energy entropy was calculated to reflect the changes in vibration signals in relation to faults. At last, the energy distribution could serve as eigenvector of support vector machine to recognize the dynamic state and fault type of the gearbox. The analysis results from the gearbox signals demonstrate the effectiveness and veracity of the diagnosis approach.

Towards Three-Dimensional Millimeter-Wave Radar With the Bistatic Fast-Factorized Back-Projection Algorithm—Potential and Limitations

In this paper, we report on a time-domain approach for 3-D synthetic image reconstruction at stand-off distances called the bistatic fast-factorized back-projection (BiFFBP) algorithm. Although the algorithm is suited for multiple purposes, it is applied in this paper to a millimeter-wave radar system that operates in a frequency-modulated continuous-wave mode between 234 and 306 GHz. After initially mapping the bistatic to a quasi-monostatic configuration, the algorithm recursively factorizes both, the aperture positions and the target area. Three-dimensional reconstructions are shown for a simulated point-target in order to evaluate the point-spread-function of the system. In addition, 2-D-imaging is performed on real objects at stand-off distances using a scanner system that consists of 8 transmitters and 16 receivers. Reconstructions with the BiFFBP-algorithm are compared with the global back-projection (GBP) algorithm that serves as a benchmark. The results show that the BiFFBP-approach yields similar results to the GBP with respect to dynamic range in the image and the overall image quality. It is also shown that a resolution of 2 cm can be achieved with relatively few elements, no scanning, and over a large field-of-view.

Cavity quantum electrodynamics of a two-level atom with modulated fields

We present a numerical study of the interaction of a two-level atom with a frequency-modulated cavity mode described by the Jaynes-Cummings Hamiltonian. In particular, we explore how the population of the atomic levels changes for monochromatic and bichromatic modulations of the cavity field. The primary goal is to find sets of boundary conditions for which the evolution of the system exhibits nonlinear dynamic behavior, by solving the equations of motion of the atomic system using embedded and semi-implicit numerical algorithms. We find that the system shows quasiperiodicity when the monochromatic frequencies or ratio of the bichromatic frequencies of the field are irrational (incommensurate) numbers. In addition, when the modulated frequencies are overtones of the Rabi frequency a nearly single dominant frequency becomes apparent for the evolution of the atomic level population of the system.

Generation of a 64-GHz, 33-ps transform-limited pulse train from a fiber laser employing higher-order frequency-modulated mode locking

We demonstrate the generation of optical pulses at a repetition rate of 64 GHz directly from a frequency-modulated (FM) mode-locked fiber laser. This is achieved by phase modulation at 16 GHz and by initiating of higher-order FM mode locking by use of an intracavity Fabry-Perot filter with a free spectral range of 64 GHz. This process yielded transform-limited pulses with a width of 3.3 ps. We investigated the operating characteristics of the laser and compared them with the characteristics that were predicted theoretically.

AM and high-harmonic FM laser mode locking

We demonstrate a new technique of active mode locking that combines amplitude-modulated (AM) mode locking at the cavity fundamental repetition rate with frequency-modulated (FM) mode locking at a high harmonic. This method combines the advantages of pulse shortening by high-harmonic mode locking while preserving the higher peak powers available at the fundamental repetition rate. We demonstrate this technique using a Nd:YAG laser that is simultaneously AM mode locked at 80 MHz and FM mode locked at the 22nd harmonic (1.76 GHz). Pulses as short as 16 ps with a peak power of 6.25 kW were measured.

Modification of a vacuum Rabi splitting via a frequency-modulated cavity mode.

The spectrum radiated by an initially excited two-level atom in a very-high-Q cavity is studied. We consider the situation where the frequency of the vacuum field cavity mode is varied time-dependently during Rabi cycles. Under the resonance condition where the modulation frequency is the same as the vacuum Rabi frequency, we show that the vacuum Rabi splitting can be further split into two doublets. The relative heights of spectral peaks are shown to depend on the modulation phase. Furthermore, we show that the interference between different spectral peaks can break the symmetry of the spectrum.

Use of chlorpyrifos as an evaluation standard for gas chromatographic detectors

The performance of a range of element-selective detectors was studied using chlorpyrifos (O,O-diethyl-O-3,5,6-trichloro-2-pyridyl phosphorothioate) as a standard. It involved determination of the minimum detectable amount and linearity of the response of the flame photometric, alkali flame ionization, Hall electrolytic conductivity and electron capture detectors. The minimum detectable amount varied with both the model and type of detector, with the electron capture detector (frequency-modulated mode) being the most sensitive and the flame photometric detector (S-mode) the least. A study of various models of electron capture detector demonstrated the superior performance of the frequency-modulated type to the d.c. or d.c. pulse mode in both sensitivity and linearity. The responses of various types of alkali flame ionization detector were similar and ca. 10 times more sensitive than the flame photometric detector (P-mode). The N/P response of the alkali flame ionization detector was dependent on the hydrogen flow-rate. The multi-element response of the detector is suppressed by using a flame energized source. The response of the flame photometric detector to chlorpyrifos analogues showed a variation in the minimum detectable amout of 2.1–4.5 for the PO/PS ratio, which indicated it to be a detector effect. The results obtained warrant the consideration of chlorpyrifos as a common evaluation standard for the sensitivity and linearity data of gas chromatographic detectors used in pesticide residue analysis.

Volume Reverberation as a Function of Single Frequency Pulse Lengths and FM Sweep Rates

Volume-reverberation tests were conducted with a vertically directional transducer at a frequency of 15.4 kHz. For each of two source levels, the system was capable of transmitting single frequency (SF) pulses of 10-, 50-, 100-, 300-, and 1000-msec duration and 1000-msec frequency-modulated (FM) pulses swept 100, 200, and 400 cycles. The relationship between volume reverberation level and pulse length is investigated. The data show a less than linear dependence of volume reverberation on pulse length and a linear dependence on source level. Reverberation levels for FM and SF pulses of 1000-msec duration are discussed. Although the amplitudes of the deviations from the mean reverberation are lower in the FM mode than the SF mode, no significant difference in mean levels is observed.

X-Band Diode Limiting (Correspondence)

Broad-band, matched, low power, instantaneous, passive, X--band diode limiting has been demonstrated. The limiter, which uses standard microwave components, is an outgrowth of point contact germanium diode microwave switch research. In fact, the hybrid-tee switch makes a very good narrow-band limiter under the condition of zero bias voltage on the crystals (biasing terminals short circuited). The output power under these conditions is limited to 0.5 mw² for incident power up to 30 mw, deduced from Fig. 9 of Garver, et al. However, the bandwidth of the hybrid-tee switch when used as a limiter is insufficient for many applications such as limiting the amplitude of a 0.2-µsec magnetron pulse or flattening a frequency-modulated klystron mode.