A broad-band sub-harmonic mixer for W-band applications

In order to improve the bandwidth of the conventional sub-harmonic mixer, a broad-band, high intermediate frequency（IF） sub-harmonic mixer for W-band applications is proposed. Replacing the open and short stubs that are used in the convertional sub-harmonic mixer with a broad-band band-pass filter and a low-pass filter, respectively, a wide operating frequency band is achieved. Furthermore, without the use of the edge-coupled band-pass filter at radio frequency（RF） port, the proposed structure can be realized by common hybrid microwave integrated circuit technology at W- band. The measured results show that the proposed subharmonic mixer can operate from 80 to 107.5 GHz for RF frequency and support up to 18 GHz for the IF bandwidth. Also, the measured results show that the single-sideband conversion loss is less than 13. 7 dB over the available RF frequency band, while the minimum conversion loss is about 9 dB at an RF of 92. 5 GHz and an 1F of 3 GHz. Thus, a large operating bandwidth performance at W-band can be achieved by the orooosed mixer.

Investigation on the relationship between overpressure and sub-harmonic response from encapsulated microbubbles

Sub-harmonic component generated from microbubbles is proven to be potentially used in noninvasive blood pressure measurement. Both theoretical and experimental studies are performed in the present work to investigate the dependence of the sub-harmonic generation on the overpressure with different excitation pressure amplitudes and pulse lengths. With 4-MHz ultrasound excitation at an applied acoustic pressure amplitude of 0.24 MPa, the measured sub-harmonic amplitude exhibits a decreasing change as overpressure increases; while non-monotonic change is observed for the applied acoustic pressures of 0.36 MPa and 0.48 MPa, and the peak position in the curve of the sub-harmonic response versus the overpres- sure shifts toward higher overpressure as the excitation pressure amplitude increases. Furthermore, the exciting pulse with long duration could lead to a better sensitivity of the sub-harmonic response to overpressure. The measured results are ex- plained by the numerical simulations based on the Marmottant model. The numerical simulations qualitatively accord with the measured results. This work might provide a preliminary proof for the optimization of the noninvasive blood pressure measurement through using sub-harmonic generation from microbubbles.

A Broadband 630-720 GHz Schottky Based Sub-Harmonic Mixer Using Intrinsic Resonances of Hammer-Head Filter

An room temperature low noise anti-parallel Schottky diode based 630-720 GHz sub-harmonic mixer(SHM) is designed, built and measured. Intrinsic resonances in lowpass hammer-head filter have been adopted to prevent the LO and RF power leak from the IF channel, while greatly minimizing the transmission line size. The mixer consists of 15 um quartz terahertz circuit and 127 um Al2 O3 IF transformer circuit. An improved lumped element equivalent noise model of SBDs guarantees the accuracy of simulation. The measurement indicates that with local oscillating(LO)signal of 2-8 mW, the lowest double sideband(DSB) conversion loss is 8.2 dB at 645 GHz,and the best DSB noise temperature is 2800 K at 657 GHz. The 3 dB bandwidth of conversion loss is 75 GHz from 638 to 715 GHz. The work IF frequency band is above 20 GHz ranging from 1 to 20 GHz with-10 dB return loss.

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Sub-Harmonic Resonances of Periodic Parameter Excited Oscillators with Discontinuities

It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.

A 220 GHz Frequency-Division Multiplexing Wireless Link with High Data Rate

With the development of wireless communication,the 6G mobile communication technology has received wide attention.As one of the key technologies of 6G,terahertz(THz)communication technology has the characteristics of ultra-high bandwidth,high security and low environmental noise.In this paper,a THz duplexer with a half-wavelength coupling structure and a sub-harmonic mixer operating at 216 GHz and 204 GHz are designed and measured.Based on these key devices,a 220 GHz frequency-division multiplexing communication system is proposed,with a real-time data rate of 10.4 Gbit/s for one channel and a transmission distance of 15 m.The measured constellation diagram of two receivers is clearly visible,the signal-to-noise ratio(SNR)is higher than 22 dB,and the bit error ratio(BER)is less than 10^(−8).Furthermore,the high definition(HD)4K video can also be transmitted in real time without stutter.

Heave-Roll-Pitch Coupled Nonlinear Internal Resonance Response of a Spar Platform Considering Wave and Vortex Exciting Loads

Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.

The Nonlinear Bifurcation and Chaos of Coupled Heave and Pitch Motions of a Truss Spar Platform

This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincare maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave fre- quency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional temately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.

PSE as applied to problems of secondary instability in supérsonic boundary layers

Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.

THE EXISTENCE OF MULTIPLE SOLUTIONS OF p-LAPLACIAN ELLIPTIC EQUATION

This paper considers the quasilinear elliptic equation where , and 0 < m < p-1 < q < +∞, Ω is a bounded domain in RN(N 3).λ is a positive number. Object is to estimate exactly the magnitute of λ* such that (1)λ has at least one positive solution if λ ∈ (0, λ*) and no positive solutions if λ > λ*. Furthermore, (1)λ has at least one positive solution when λ = λ*, and at least two positive solutions when λ ∈ (0, λ*) and . Finally, the authors obtain a multiplicity result with positive energy of (1)λ when 0 < m < p - 1 < q = (Np)/(N-p) - 1.

Design of Subharmonic Mixers above 100 GHz

This paper presents the design and simulation of several fixed-tuned sub-harmonic mixers cover frequencies from 110 GH to 130 GHz, 215 GH to 235 GHz, 310 GH to 350 GHz, and 400 GH to 440 GHz. Among them, 120 GHz, 225 GHz, 330 GHz subharmonic mixers are designed with flip-chipped planar schottky diode mounted onto a suspended quartz-based substrate, the 225 GHz and 425 GHz subharmonic mixers are GaAs membrane integrated, and the 115 GHz subharmonic mixer has been fabricated and tested already.

A 16-QAM 45-Gbps 7-m Wireless Link Using InP HEMT LNA and GaAs SBD Mixers at 220-GHz-Band

This paper presents a 220-GHz-band 7-m wireless link with a 45-Gbps transmission data rate by using 16 quadrature amplitude modulation(16-QAM).Super-heterodyne transceiver modules are developed for transmission and reception of the modulated signals,which consist of a Schottky barrier diodes(SBD)based sub-harmonic mixer(SHM),an InP HEMT low noise amplifier(LNA),a waveguide band-pass filter(BPF),and a 108-GHz local oscillator(LO)multiplier chain.The transmitter features a peak transmit power of 1.41 dBm,and the IF frequency varies from 5 GHz to 20 GHz.Besides,the receiver features a conversion gain of 9.3 dB in average and a noise temperature of 3052.8 K.The measured results indicate that the transceiver modules enable data transmission of a 45-Gbps 16-QAM signal with Signal-Noise-Ratio(SNR)from 11.59 dB to 15.36 dB in a 7-m line-of-sight channel.

Analysis of 1/2 sub-harmonic resonance in a maneuvering rotor system

This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.

Sub-harmonicity,monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent

A monotonicity formula for stable solutions to a class of weighted semilinear elliptic equations with ＂negative exponent＂ is established. It is well known that such a monotonieity formula plays an essential role in the study of finite Morse index solutions of equations with ＂positive exponent＂. Unlike the positive exponent case, we will see that both the monotonicity formula and the sub-harmonicity play crucial roles in classifying positive finite Morse index solutions to the equations with negative exponent and obtaining sharp results for their asymptotic behaviors.

Experimental Investigations on the Out-of-Plane Sub-harmonic Vibration of a Circular Dielectric Elastomer Actuator

Dielectric elastomers have found interesting applications in soft loudspeakers,where vibrations subject to alternating electrical excitations are the key features.Although there are many t heore tical studies on the nonlinear vibrations of dielec trie elasto mers subject to electromechanical coupling loads,the systematic experimental research is rare.In this work,we design a simple experimental setup to observe the out-of-plane vibrations of a circular dielec trie elastomer actuator.We find that the dielec trie elastomer has different response modes including the harmonic,super-harmonic and sub-harmonic responses at different excitation frequencies.We analyze the responses by using the short-time Fourier transformation.We find that the equivalent voltage and the AC/DC ratio are the main parameters affecting the occurrence of sub-harmonic responses.The phenomenon of mode shift is also observed in our experiments.These experimental observations provide a deeper unders tanding of the dynamic responses of dielec trie elasto mer subject to electromechanical loads.

Ka-band ultra low voltage miniature sub-harmonic resistive mixer with a new broadside coupled Marchand balun in 0.18-μm CMOS technology

A Ka-band sub-harmonically pumped resistive mixer （SHPRM） was designed and fabricated using the standard 0.18-μm complementary metal-oxide-semiconductor （CMOS） technology. An area-effective asymmetric broadside coupled spiral Marchand balance-to-unbalance （balun） with magnitude and phase imbalance compensation is used in the mixer to transform local oscillation （LO） signal from single to differential mode. The results showed that the SHPRM achieves the conversion gain of -15- -12.5 dB at fixed fIF=0.5 GHz with 8 dBm LO input power for the radio frequency （RF） bandwidth of 28 35 GHz. The in-band LO-intermediate freqency （IF）, RF-IF, and LO-RF isolations are better than 31, 34, and 36 dB, respectively. Besides, the 2LO-IF and 2LO-RF isolations are better than 60 and 45 dB, respectively. The measured input referred PIdB and 3rd-order inter-modulation intercept point （IIP3） are 0.5 and 10.5 dBm, respectively. The measurement is performed under a gate bias voltage as low as 0.1 V and the whole chip only occupies an area of 0.33 mm^2 including pads.

Study of multipacting effect in sub-harmonic buncher of SSRF linac

During the design process, multipacting effect has been taken into consideration using a 2D simulation code MultiPac and all of the corners are rounded to suppress the multipacting effect in the pill-box cavity. However, unexpected multipacting effect prevents the increase of the input power when the magnetic field of focusing coils is added after adequate conditioning and a novel method is adopted to suppress it by introducing extra coils to counteract the field. This paper focuses on the simulation of multipacting effect in different magnetic field configurations. The experimental observations and simulation results of multipacting effect are presented and details of the multipacting process are also analyzed.

QUASI-PERIODIC SOLUTIONS AND SUB-HARMONIC BIFURCATION OF DUFFING'S EQUATIONS WITH QUASI-PERIODIC PERTURBATION

The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

The nonlinear transverse vibrations of ordered and disordered twodimensional(2D)two-span composite laminated plates are studied.Based on the von Karman’s large deformation theory,the equations of motion of each-span composite laminated plate are formulated using Hamilton’s principle,and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin’s method.The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales.The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out.The effects of the disorder ratio and ply angle on the two different resonances are analyzed.From the numerical results,it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon,and with the increase of the disorder ratio,the vibration localization phenomenon will become more obvious.Moreover,the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration,and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.