The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is deri...The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.展开更多
Two different frequency bandwidth subharmonic mixers（SHM） using planar Schottky mixing diodes are discussed and fabricated.Full-wave analysis is carried out to find the optimum diode embedding impedances with a lump...Two different frequency bandwidth subharmonic mixers（SHM） using planar Schottky mixing diodes are discussed and fabricated.Full-wave analysis is carried out to find the optimum diode embedding impedances with a lumped port for modeling the nonlinear junction.The SHM circuit is divided into several different parts and each part is optimized using the calculated diode impedances.The divided parts are then combined and optimized together.The exported S-parameter files of the global circuit are used for conversion loss（CL） discussion.For the 150 GHz SHM,the lowest measured CL is 10.7 dB at 153 GHz,and typical CL is 12.5 dB in the frequency range of 135-165 GHz.The lowest measured CL of the 180 GHz SHM is 5.8 dB at 240 GHz,and typical CL is 13.5 dB and 11.5 dB in the frequency range of 165-200 GHz and 210-240 GHz,respectively.展开更多
文摘The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.
文摘Two different frequency bandwidth subharmonic mixers（SHM） using planar Schottky mixing diodes are discussed and fabricated.Full-wave analysis is carried out to find the optimum diode embedding impedances with a lumped port for modeling the nonlinear junction.The SHM circuit is divided into several different parts and each part is optimized using the calculated diode impedances.The divided parts are then combined and optimized together.The exported S-parameter files of the global circuit are used for conversion loss（CL） discussion.For the 150 GHz SHM,the lowest measured CL is 10.7 dB at 153 GHz,and typical CL is 12.5 dB in the frequency range of 135-165 GHz.The lowest measured CL of the 180 GHz SHM is 5.8 dB at 240 GHz,and typical CL is 13.5 dB and 11.5 dB in the frequency range of 165-200 GHz and 210-240 GHz,respectively.
