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Journal of Signal Processing

Circuit Theory Based on New Concepts and Its Application to Quantum Theory:2. Resonance and Transient Responses Obtained from Commensurate Transmission Line Circuit

Nobuo Nagai, Takashi Yahagi

Published Jan 1, 2015• 0 citations
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In the steady-state of lossless circuits, resonance can be obtained using the Laplace transform. We focus on commensurate transmission line circuits constructed using eight unit elements as an example and determine the resonance, transient response, and nonstationary response of the circuits using a z-transform. In old quantum theory, light quanta are assumed to satisfy the heat conduction equation. When considering the response of light quanta as a physical phenomenon from the viewpoint of circuit theory, we can interpret that the heat conduction equation describes the propagation of waves on a lossy distributed RC transmission line, in which light quanta repeatedly collide with each other. We demonstrate that light quanta are different from photons, which are interpreted as satisfying the Maxwell's equations and propagating on a lossless transmission line.

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A lossless transmission line of length l is called a unit element. By showing numerical examples, we demonstrate that resonance and eigen-oscillation can be obtained using a unit element as a circuit element. Because resonance and eigen-oscillation are responses in the steady state, the transient response that occurs until the circuit reaches the steady state should be considered. Although the transient response has been conventionally considered a phenomenon of exponential attenuation that depends on a time constant, we numerically demonstrate that the transient response of a unit element is a phenomenon of discrete attenuation that can be expressed using a z-transform. In addition, resonance and eigen-oscillation involve reactive power, which is not related to energy, because the transient response of the circuit using a unit element is closely related to the phases expressed by the z-transform. We also numerically show that the reactive power is confined in the circuit.

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Physical phenomena showing both particle and wave natures at the same time exhibit resonance. In addition, resonance is a physical phenomenon occurring in the steady state. Transient and steady-state responses can be discriminated when transmission lines are used. We demonstrate that (1) extended telegrapher's equations can be obtained using the Riccati differential equation, (2) lossless transmission lines called Pasteur, Tellegen, and bi-isotropic (BI) media can be characterized using the extended telegrapher's equations, and (3) the resonance conditions can be determined for each of these media.

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In the steady-state of lossless circuits, resonance can be obtained using the Laplace transform. We focus on commensurate transmission line circuits constructed using eight unit elements as an example and determine the resonance, transient response, and nonstationary response of the circuits using a z-transform. In old quantum theory, light quanta are assumed to satisfy the heat conduction equation. When considering the response of light quanta as a physical phenomenon from the viewpoint of circuit theory, we can interpret that the heat conduction equation describes the propagation of waves on a lossy distributed RC transmission line, in which light quanta repeatedly collide with each other. We demonstrate that light quanta are different from photons, which are interpreted as satisfying the Maxwell's equations and propagating on a lossless transmission line.
A lossless transmission line of length l is called a unit element. By showing numerical examples, we demonstrate that resonance and eigen-oscillation can be obtained using a unit element as a circuit element. Because resonance and eigen-oscillation are responses in the steady state, the transient response that occurs until the circuit reaches the steady state should be considered. Although the transient response has been conventionally considered a phenomenon of exponential attenuation that depends on a time constant, we numerically demonstrate that the transient response of a unit element is a phenomenon of discrete attenuation that can be expressed using a z-transform. In addition, resonance and eigen-oscillation involve reactive power, which is not related to energy, because the transient response of the circuit using a unit element is closely related to the phases expressed by the z-transform. We also numerically show that the reactive power is confined in the circuit.
Physical phenomena showing both particle and wave natures at the same time exhibit resonance. In addition, resonance is a physical phenomenon occurring in the steady state. Transient and steady-state responses can be discriminated when transmission lines are used. We demonstrate that (1) extended telegrapher's equations can be obtained using the Riccati differential equation, (2) lossless transmission lines called Pasteur, Tellegen, and bi-isotropic (BI) media can be characterized using the extended telegrapher's equations, and (3) the resonance conditions can be determined for each of these media.