Dual-frequency Oscillations Research Articles

Compact and low phase-noise dual-frequency oscillator based on dual-band filter with multiple coupling technique

This paper presents a switchable feedback dual-frequency oscillator with ultra low phase-noise based on dual-band filter for the first time. The application of multiple coupling technique in dual-band filter such as direct coupling, indirect coupling, self-coupling and source-load coupling not only reduces the circuit size significantly but also obtains high group delay that the ultra low phase-noise can be achieved. Due to the auxiliary oscillating network, two different oscillation frequencies are switched independently without inter-modulation. For demonstration, a physical prototype was fabricated and measured. The measured results show that the proposed dual-frequency oscillator can oscillate at 887 MHz or 2.446 GHz by controlling four PIN diode switches and the phase-noise keeps better than −139 dBc/Hz and −136.1 dBc/Hz at 1 MHz frequency offset. And the output power of 887 MHz and 2.446 GHz are 5.94 dBm and 5.08 dBm respectively.

A Low Phase-Noise Dual-Frequency Oscillator Based on Filter Switching Technique

This letter presents a parallel-feedback dual-frequency oscillator (DFO) with low phase noise. It is achieved based on the filter switching technique. By using four switches to control two oscillator loops with a common active device, the oscillation frequency of the proposed DFO can be switched from one to another. Due to the high isolation level of the employed switches, the two oscillator loops almost operate independently. Thus, there is no intermodulation (IM) spurs generated in the output spectrum of the proposed DFO. In the meantime, to improve the phase noise performance of the DFO, each oscillator loop utilizes a high frequency-selectivity bandpass filter with high group delay (GD) as a frequency selective element. In this way, the low phase-noise DFO is developed. For demonstration, the DFO is designed, fabricated, and tested. As seen from the measurement results, the oscillator can oscillate at 2.04 or 3.092 GHz by controlling the four switches. At 100 kHz and 1 MHz frequency offset from the carrier frequency, the phase noises are −108.5 and −129.7 dBc/Hz for 2.04 GHz, while −112.7 and −135.7 dBc/Hz for 3.092 GHz.

Analytical method of the modal damping ratio of the beam with distributed dissipative oscillators and application in broadband vibration mitigation

Distributed dissipative oscillators are considered effective measures to broaden the vibration mitigation bandwidth of structures. However, the existing calculation methods are mainly based on parameter analysis, which is not convenient for engineering applications. Modal damping ratio can be used to evaluate the frequency band and degree of vibration attenuation quickly. Therefore, the explicit analytical formulas of modal damping ratio for the beam distributed with single-frequency and dual-frequency oscillators are derived and verified by comparing with FEM results. And the influence of mode order, boundary conditions, the mass ratio, and frequency ratio of the oscillators on modal damping ratio is also discussed. As an application of the presented equations, the optimized frequencies of single-frequency or dual-frequency oscillators satisfying the Minimax optimization (maximize the minimum damping in a target frequency band) are obtained. The frequency response of the beam with optimized oscillators is compared with modal damping ratio curves to discuss the influence of mass ratio and loss factor on vibration suppression and the adaptability of modal damping to design. The results show that the presented formulas have satisfied accuracy and can be used for broadband mitigation design.

Neuronal Switching between Single- and Dual-Network Activity via Modulation of Intrinsic Membrane Properties.

Oscillatory networks underlie rhythmic behaviors (e.g., walking, chewing) and complex behaviors (e.g., memory formation, decision-making). Flexibility of oscillatory networks includes neurons switching between single- and dual-network participation, even generating oscillations at two distinct frequencies. Modulation of synaptic strength can underlie this neuronal switching. Here we ask whether switching into dual-frequency oscillations can also result from modulation of intrinsic neuronal properties. The isolated stomatogastric nervous system of male Cancer borealis crabs contains two well-characterized rhythmic feeding-related networks (pyloric, ∼1 Hz; gastric mill, ∼0.1 Hz). The identified modulatory projection neuron MCN5 causes the pyloric-only lateral posterior gastric (LPG) neuron to switch to dual pyloric/gastric mill bursting. Bath applying the MCN5 neuropeptide transmitter Gly1-SIFamide only partly mimics the LPG switch to dual activity because of continued LP neuron inhibition of LPG. Here, we find that MCN5 uses a cotransmitter, glutamate, to inhibit LP, unlike Gly1-SIFamide excitation of LP. Thus, we modeled the MCN5-elicited LPG switching with Gly1-SIFamide application and LP photoinactivation. Using hyperpolarization of pyloric pacemaker neurons and gastric mill network neurons, we found that LPG pyloric-timed oscillations require rhythmic electrical synaptic input. However, LPG gastric mill-timed oscillations do not require any pyloric/gastric mill synaptic input and are voltage-dependent. Thus, we identify modulation of intrinsic properties as an additional mechanism for switching a neuron into dual-frequency activity. Instead of synaptic modulation switching a neuron into a second network as a passive follower, modulation of intrinsic properties could enable a switching neuron to become an active contributor to rhythm generation in the second network.SIGNIFICANCE STATEMENT Neuromodulation of oscillatory networks can enable network neurons to switch from single- to dual-network participation, even when two networks oscillate at distinct frequencies. We used small, well-characterized networks to determine whether modulation of synaptic strength, an identified mechanism for switching, is necessary for dual-network recruitment. We demonstrate that rhythmic electrical synaptic input is required for continued linkage with a "home" network, whereas modulation of intrinsic properties enables a neuron to generate oscillations at a second frequency. Neuromodulator-induced switches in neuronal participation between networks occur in motor, cognitive, and sensory networks. Our study highlights the importance of considering intrinsic properties as a pivotal target for enabling parallel participation of a neuron in two oscillatory networks.

Experimental investigations of equivalence ratio effect on nonlinear dynamics features in premixed swirl-stabilized combustor

In this work, the dynamics of the pressure oscillations and flame behaviors in a premixed swirl-stabilized combustor were experimentally investigated. As equivalence ratio Φ varied between 0.55 and 1.35, five combustion states were distinguished based on the characteristics of the acoustic pressures and flame dynamics. The permutation entropy (PE) and proper orthogonal decomposition (POD) were used to analyze the fluctuating pressure signal complexities and spatial CH⁎ chemiluminescence images, respectively. The results showed that the magnitude of the PE was at a differentiable level. In addition, the POD modes exhibited distinguishable features when the system was in different combustion states. Further analyses of the state transitions indicated that the system underwent a supercritical Hopf bifurcation and a pair of fold bifurcations when Φ was in the lean condition. The state transition from quasi-periodic oscillation to limit-cycle oscillation was attributed to the movement of the flame location, which enhanced the coupling of the acoustics and combustion by reducing the phase difference between the pressure oscillations and heat release fluctuations. In addition, a hysteresis phenomenon was observed for the trajectory of the fluctuating pressure root-mean-square (RMS) value in the forward and backward processes of the equivalence ratio under the lean condition. A low-order model was used to capture the bifurcations; the theoretical results agreed well with the experimental data. As for the rich condition, a supercritical Hopf bifurcation was captured when the system switched between the dual-frequency oscillation mode and the rich stable state. Furthermore, the influence of combustion chamber length Lc on the combustion stability in relation to Φ was investigated. Parameter Lc was divided into steady and unsteady regions depending on whether the combustion system could reach limit-cycle oscillation. The PE was demonstrated to be effective in distinguishing the stable state and limit-cycle oscillation even for combustors of different lengths. Understanding the nonlinear dynamics by analyzing experimental data could be critical to developing models for the prediction and suppression of thermoacoustic instabilities.

A 3π Band-Edge Dual Frequency Oscillator Based on a Novel Folded Waveguide Structure

In this article, a $3\pi $ band-edge dual frequency oscillator using a novel half-period staggered folded waveguide (FWG) is proposed. Simulation results from CST Particle Studio show that the half-period staggered FWG could form a stopband at $3\pi $ phase shift with a high coupling impedance, enabling the device operating at two frequencies. A prototype oscillator was then designed and fabricated. The experimental results showed that it was capable of operating at both 89.2 and 94.5 GHz with the maximum output power 148 and 65W, respectively. The testing results are also compared with the simulation.

Analysis of the Transient Dynamics of Microwave Oscillators

A semianalytical method for the global prediction and understanding of the transient dynamics of oscillator circuits is presented. It covers both the linear and nonlinear transient stages, which are related with the circuit generalized eigenvalues, here introduced for the first time. The transient model relies on the application of the implicit function theorem to the harmonic-balance (HB) system, in order to derive a reduced-order nonlinear differential equation from a given observation node. This requires the extraction of a nonlinear admittance function, depending on the voltage excitation and oscillation frequency, which is done with a forcing auxiliary generator (AG). The linearization of this admittance function for each excitation amplitude provides a sequence of linear ordinary differential equations (ODEs), describing the system dynamics in the vicinity of each point of the transient trajectory, which can be reconstructed from the expression of the solution increment at each time step. The sequence of differential equations provides a set of generalized eigenvalues, responsible for the acceleration or deceleration of the oscillation growth and capable to detect spurious transient frequencies. The concept of escape time, or time required by the transient trajectory to go through a certain interval of amplitude values, is also introduced, for the first time to our knowledge. The method has been successfully applied to analyze the transient dynamics of several FET oscillators, including dual-frequency oscillators and switched oscillators.

SIW-Based Self-Oscillating Concurrent Dual-Frequency Active Integrated Antenna

In this letter, a self-oscillating concurrent dual-frequency active integrated antenna (DFAIA) is proposed. The proposed circuit is designed based on substrate-integrated waveguide technology, where the concurrent dual-frequency feature is realized by the use of a miniaturized self-oscillating/self-diplexing antenna. The feedback paths on either side of the diplexing antenna, comprising a main port and an auxiliary port, are employed to design the concurrent dual-frequency oscillator. The proposed DFAIA transmits 7.97 and 8.9 GHz signals simultaneously, having effective isotropic radiated power level of 5.3 and 6.41 dBm for the 7.97 and 8.9 GHz signals, respectively. The measured phase noise is approximately −90 and −110 dBc/Hz at 100 kHz and 1 MHz offset, respectively for both the lower and the higher frequencies. The overall circuit footprint is $\mathbf {\text{1.33}\lambda _{g}\times \text{2.26}\lambda _{g}}$ at the mean frequency of 8.4 GHz.

Experimental study into rotational-oscillatory vibrations of a vibration machine platform excited by the ball auto-balancer

We have experimentally investigated the rotational-oscillatory vibrations of vibratory machine platform excited by the ball auto-balancer. The law of change in the vibration accelerations at a platform was studied using the accelerometer sensors, a board of the analog-to-digital converter with an USB interface and a PC. The amplitude of rapid and slow vibratory displacements of the platform was investigated employing a laser beam. It was established that the resonance frequency (frequency of natural oscillations) of the platform is: 62.006 rad/s for the platform with a mass of 2,000 gm; 58.644 rad/s ‒ of 2,180 gm; 55.755 rad/s ‒ of 2,360 gm. An error in determining the frequencies does not exceed 0.2 %. The ball auto-balancer excites almost perfect dual-frequency vibrations of a vibratory machine platform. Slow frequency corresponds to the rotational speed of the center of balls around the longitudinal axis of the shaft, while the fast one ‒ to the shaft rotation speed, with the unbalanced mass attached to it. A dual-frequency mode occurs in a wide range of change in the parameters and it is possible to alter its basic characteristics by changing the mass of balls and the unbalanced mass, the angular velocity of shaft rotation. It has been established experimentally that the balls get stuck at a frequency that is approximately 1 % lower than the resonance frequency of platform oscillations. Assuming the platform executes the dual frequency oscillations, we employed the software package for statistical analysis Statistica to select coefficients for the respective law. It was found that: – the process for determining the magnitudes of coefficients is steady (robust); coefficients almost do no change when altering the time interval for measuring the law of a platform motion; – the amplitude of accelerations due to the low oscillations is directly proportional to the total mass of the balls and the square of the frequency at which balls get stuck; – the amplitude of rapid oscillations is directly proportional to the unbalanced mass at the auto-balancer's casing and to the square of angular velocity of shaft rotation. The discrepancy between the law of motion, obtained experimentally, and the law, obtained using the methods of statistical analysis, is less than 3 %. The results obtained add relevance to both the analytical studies into dynamics of the examined vibratory machine and to the creation of the prototype a vibratory machine.

Dual frequency MEMS resonator through mixed electrical and mechanical coupling scheme

Miniaturised transceivers are essential in multiband wireless communication systems for higher data rates and low power consumption. Microelectromechanical system (MEMS) resonator filters are actively considered for deployment in transceivers for radio frequency and intermediate frequency (IF) signal filter and oscillator applications. In this study, the authors propose dual frequency capacitive transduced MEMS resonator with two-port electrical configuration. Clamped-clamped beam resonator was selected to serve as a basic resonant tank for the filter concept validation. Five design strategies low loss structural material, array design, mixed electrical and mechanical coupling scheme, sub-micro meter transduction gap and large transduction area were explored. With these strategies, the device achieves dual band filter characteristics, narrow pass band, desired bandwidth, low insertion loss and better stop band rejection. Dual frequency response of the proposed resonator is demonstrated at centre frequencies 400 kHz and 2.57 MHz with a narrow pass band of 3 and 20 kHz, respectively. Low insertion loss of 19.8 and 25.6 dB for frequencies centred at 400 kHz and 2.57 MHz, respectively and stop band rejection >35 dB was achieved. The proposed MEMS resonator may be incorporated in the implementation of dual band pass filter for IF signal filter and dual frequency oscillator applications.

Single-Resonator Dual-Frequency BEOL-Embedded CMOS-MEMS Oscillator With Low-Power and Ultra-Compact TIA Core

This letter reports on the design and characterization of a dual-frequency oscillator that consist of a reliable seesaw-shaped tungsten resonator integrated in the back end of line of a standard 0.35-μm complementary metal-oxide-semiconductor (CMOS) technology and a high-gain, low power (<; 10 μW) and ultra-compact transimpedance amplifier (TIA) core. The 550-/900-kHz prototyped CMOS-MEMS oscillator can be operated with reduced TIA supply voltage (V DD =1.65 V) and moderated dc MEMS bias (V DC =18 V) while consuming only 8.5 μW and maintaining satisfactory performance. The measured phase noise is -103.8 dBc/Hz and -99.6 dBc/Hz at 1-kHz offset for the first and second operating frequencies, respectively, which is comparable and competitive with the state of the art.

Single-resonator dual-frequency AIN-on-Si MEMS oscillators.

This paper reports on the design, implementation, and phase-noise optimization of low-power interface IC for dual-frequency oscillators that utilize two high quality factor (Q) width-extensional bulk acoustic modes of the same AlN-on-silicon resonator. Two 0.5-μm CMOS transimpedance amplifiers (TIA) have been designed, characterized, and interfaced with two dual-mode resonators operating at 35.5/105.7 MHz (first/third order modes) and 35.5/174.9 MHz (first/ fifth order modes). One TIA uses open-loop regulated cascode (RGC) topology in the first stage to enable low power operation, whereas the second one uses an inverter with shunt-shunt feedback to deliver higher gain with lower phase noise. An on-chip switching network is incorporated into each TIA to change the oscillation frequency based on the different phase shift. The effect of TIA on the phase-noise performance of oscillators is studied and compared for both topologies. The measured phase noise of low- and high-frequency modes at 1 kHz offset from carrier are -114 and -108 dBc/Hz for the 35/105 MHz oscillator, and -108 and -105 dBc/Hz for the 35/175 MHz oscillator, respectively, whereas the far-from-carrier reaches below -140 dBc/Hz in all cases.

Class-A dual-frequency VECSEL at telecom wavelength.

We report class-A dual-frequency oscillation at 1.55 μm in a vertical external cavity surface emitting laser with more than 100 mW optical power. The two orthogonal linear polarizations of different frequencies oscillate simultaneously as their nonlinear coupling is reduced below unity by spatially separating them inside the active medium. The spectral behavior of the radio frequency beatnote obtained by optically mixing two polarizations and the phase noise of the beatnote have been explored for different coupling strengths between the lasing modes.

Chaos in a chemical system

Chaotic oscillations have been observed experimentally in dual-frequency oscillator OAP - Ce+4-BrO−3-H2SO4 in CSTR. The system shows variation of oscillating potential and frequencies when it moves from low frequency to high frequency region and vice-versa. It was observed that system bifurcate from low frequency to chaotic regime through periode-2 and period-3 on the other hand system bifurcate from chaotic regime to high frequency oscillation through period-2. It was established that the observed oscillations are chaotic in nature on the basis of next amplitude map and bifurcation sequences.

Simultaneous TE1 and TE2 mode lasing yielding dual-wavelength oscillation in a semiconductor laser with a tunnel junction

Dual-frequency oscillation is obtained and investigated in a new type of injection heterolaser, an interband two-stage cascade laser with a tunneling p-n junction separating two active regions with quantum wells located in a common waveguide. The laser design provides for simultaneous oscillation at the first-order TE mode of wavelength λ = 1.086 μm and the second-order TE mode of wavelength λ = 0.96 μm in the continuous-wave regime at room temperature.

Tunable dual-frequency oscillators of carbon nanotubes

We propose a carbon nanotube oscillator that is composed of a cantilever inner tube and a short outer tube. When the inner tube vibrates, the centrifugal force and the van der Waals force drive the outer tube to oscillate along the inner tube, which means that the oscillator can simultaneously output two frequencies. The operation frequencies of the oscillator may be tunable in a wide range (from tens of gigahertz to more than 100 GHz) by controlling the initial conditions. The combination of tunability and high-frequency operation makes the oscillators promising for a variety of scientific and technological applications. A continuum model is presented to study the frequency properties of the oscillator. The model is validated by the molecular dynamics simulations.

Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations

Tunable dual-frequency oscillation is demonstrated in a vertical external-cavity surface-emitting laser. Simultaneous and robust oscillation of the two orthogonally polarized eigenstates is achieved by reducing their overlap in the optical active medium. The class-A dynamics of this laser, free of relaxation oscillations, enables one to suppress the electrical phase noise in excess that is usually observed in the vicinity of the beat note.

Concurrent Dual-Frequency Oscillators and Phase-Locked Loops

A dual-frequency oscillator employing a fourth-order tank is shown to have the ability to generate simultaneous oscillations at two frequencies. A nonlinear analysis to determine the steady-state and transient behavior of this oscillator is presented. Further, the phase-noise expression for the dual-frequency oscillator is derived and compared with that of a single-frequency oscillator. A dual-loop phase-locked loop (PLL) is designed to lock the frequencies of the dual-frequency oscillator to two external references independently. A prototype of a dual-frequency voltage-controlled oscillator (VCO) along with the dual-loop PLL is implemented in a BiCMOS SiGe technology. The dual-frequency VCO oscillates simultaneously at 2.33 and 4.98 GHz with 12.5% and 10.3% tuning ranges, respectively. The PLL has locking ranges of 4.2% and 3.6% for 2.33 and 4.98 GHz, respectively. Potential applications of concurrent multifrequency oscillators in multifunctional communication systems and multiband beam forming are discussed.

Injection Locking in Concurrent Dual-Frequency Oscillators

In a separate paper, the authors show that a nonlinear active core with a fourth-order resonator can generate two stable independent frequencies simultaneously. In this paper, the effect of injecting two frequencies into such a concurrent dual-frequency oscillator is analyzed and experimentally verified. It is shown that, for weak injection, the effect of injection at one frequency is decoupled from the effect of injection at the other frequency. The differential equation describing the effect of injection at either of the two frequencies is similar to the Adler's injection-locking equation for single-frequency oscillators. A theoretical analysis for a linear array of coupled concurrent dual-frequency oscillators is provided. It is shown that a linear phase progression at both frequencies can be achieved independently by detuning the array's end elements. Dual-frequency quadrature signal generation using two coupled concurrent dual-frequency oscillators is also demonstrated. To verify the theoretical derivations, an integrated circuit in a 0.18-m SiGe BiCMOS process is designed and fabricated. Measurement results closely match the theoretical predictions. The application of concurrent coupled oscillator array in dual-frequency beam forming with steering capability is also demonstrated.

Mono‐ and dual‐frequency fast cerebellar oscillation in mice lacking parvalbumin and/or calbindin D‐28k

Calbindin is a fast Ca2+-binding protein expressed by Purkinje cells and involved in their firing regulation. Its deletion produced approximately 160-Hz oscillation sustained by synchronous, rhythmic Purkinje cells in the cerebellar cortex of mice. Parvalbumin is a slow-onset Ca2+-binding protein expressed in Purkinje cells and interneurons. In order to assess its function in Purkinje cell firing regulation, we studied the firing behavior of Purkinje cells in alert mice lacking parvalbumin (PV-/-), calbindin (CB-/-) or both (PV-/- CB-/-) and in wild-type controls. The absence of either protein resulted in Purkinje cell firing alterations (decreased complex spike duration and pause, increased simple spike firing rate) that were more pronounced in CB-/- than in PV-/- mice. Cumulative effects were found in complex spike alterations in PV-/- CB-/- mice. PV-/- and CB-/- mice manifested approximately 160-Hz oscillation that was sustained by Purkinje cells firing rhythmically and synchronously along the parallel fiber axis. This oscillation was dependent on GABA(A), N-methyl-D-aspartate and gap junction transmission. PV-/- CB-/- mice exhibited a dual-frequency (110 and 240 Hz) oscillation. The instantaneous spectral densities of both components were inversely correlated. Simple and complex spikes of Purkinje cells were phase-locked to one of the two oscillation frequencies. Mono- and dual-frequency oscillations presented similar pharmacological properties. These results demonstrate that the absence of the Ca2+ buffers parvalbumin and calbindin disrupts the regulation of Purkinje cell firing rate and rhythmicity in vivo and suggest that precise Ca2+ transient control is required to maintain the normal spontaneous arrhythmic and asynchronous firing pattern of the Purkinje cells.