| Transmission lines are not only the important medium for information transmission and energy distribution in electronic equipment,but also the important coupling ways of electromagnetic interference.Electromagnetic interference generates interference current on the transmission line through field-line coupling and enters the terminal equipment of the transmission line through conductive coupling,which brings serious security risks to the normal operation of the system.The efficient analysis method of field-line coupling effect is of great significance to electromagnetic compatibility design.Generalized field-line coupling problems include electromagnetic radiation sensitivity of transmission lines under incident field excitation and crosstalk between transmission lines under lumped source excitation.The calculation methods include full wave method and transmission line theory approximation method,etc.Full-wave methods based on Maxwell equation,such as finite difference time domain method,moment method and finite element method,have formed commercial electromagnetic simulation software such as CST,HFSS and FEKO.The transmission line theory approximation method based on the transmission line equation adopts the assumption of transverse electromagnetic wave,which simplifies the complexity of electromagnetic equation.The early research on the transmission line theory approximation method focused on the uniform transmission line with deterministic parameters and linear load.In practice,the parameters of transmission line inevitably presented randomness and non-uniformity due to uncontrollable factors such as manufacturing process error and layout limitation of transmission line.Transmission lines connecting electronic devices often end up with non-linear loads,which brings great challenges to the solution of field-line coupling effect.To study the field-line coupling effect of stochastic non-uniform and end-connected non-linear load transmission lines is not only the need of the development of electromagnetic compatibility theory,but also the need of solving practical engineering problems.In recent years,significant progress has been made in the field-line coupling effects of stochastic inhomogeneous and terminated non-linear load transmission lines.Perturbation decomposition technique uses equivalent distributed sources to characterize the nonuniformity of transmission lines.Compared with the uniform cascade method,this method does not need to segment the transmission lines.At present,the research of perturbation decomposition technique focuses on the crosstalk between non-uniform transmission lines under lumped sources.However,the effectiveness of perturbation decomposition technique in analyzing the sensitivity of non-uniform transmission lines under plane wave irradiation has not been verified.The generation and conversion mechanism of modal interference for inhomogeneous differential transmission lines irradiated by plane waves need to be further studied.The polynomial chaotic expansion method maps the stochastic transmission line equation to the deterministic augmented transmission line equation,which ensures the accuracy of the solution and has high computational efficiency.At present,the research of polynomial chaotic expansion method focuses on random uniform transmission lines,but there is no effective fast method to calculate the field-line coupling problem of transmission lines with random and non-uniform characteristics.In order to solve the above problems,this paper starts from the transmission line theory approximation method,and verifies the effectiveness of perturbation decomposition technology in the field-line coupling problem of non-uniform differential transmission lines through theoretical derivation.A fast calculation method based on perturbation decomposition technique and polynomial chaos method for the field-line coupling problem of stochastic non-uniform transmission lines is established.The Foster-type equivalent circuit based on eigen-mode expansion has the advantages of passivity,stability,fast convergence and clear physical meaning.It can effectively analyze the time-domain response of end-connected non-linear load transmission lines.Combing with the polynomial chaotic expansion method,transmission line theory approximation method,partial element equivalent circuit and dyadic Green's function,etc.this paper extends the Foster-type equivalent circuit to the field-line coupling problem of random uniform transmission line,near-position transmission line in shielding cavity and arbitrary position transmission line in shielding cavity.It provides a new method and approach for the application of Foster equivalent circuit to the field-line coupling problem of end-connected non-linear load transmission lines in different scenarios.The main contents and innovative work of this paper are as follows:(1)A fast calculation method based on perturbation decomposition and polynomial chaotic expansion is proposed to solve the field-line coupling problem of stochastic inhomogeneous transmission lines irradiated by plane waves.For non-uniform differential transmission lines,the coupled field-line equation is decomposed into differential mode and common mode transmission line equation with equivalent mode distribution source by similarity transformation and perturbation decomposition.For stochastic inhomogeneous transmission lines,the stochastic inhomogeneous transmission line equation is transformed into a deterministic augmented transmission line equation with equivalent distribution sources by using perturbation decomposition and polynomial chaotic expansion.The simulation results show that the proposed method can effectively calculate the mean,variance and probability density function of the induced voltage at the transmission line terminal load.Under the same simulation environment,the computation time of the proposed method is only about 0.79% of that of the uniform cascade-Monte Carlo method.(2)A Foster-type equivalent circuit based on polynomial chaos expansion is proposed to solve the field-line coupling problem of a random transmission line terminated with non-linear loads under plane wave irradiation.Based on polynomial chaotic expansion and random Galerkin projection,the stochastic transmission line equation is projected to deterministic augmented transmission line equations.The equivalent admittance circuit of random transmission line is obtained by eigen decomposition and convergence acceleration.Stochastic boundary conditions for transmission lines terminated with non-linear loads are solved by Gauss orthogonal rule.The simulation results show that the proposed equivalent circuit can accurately estimate the admittance function of random transmission lines.Under the same simulation environment,the computation time of the proposed equivalent circuit is only about 1.64% of that of the finite difference time domain-Monte Carlo method.(3)A Foster-type equivalent circuit based on transmission line theory and dyadic Green's function is proposed to solve the field-line coupling problem of near-position transmission lines terminated with non-linear loads in the shielding cavity.The electric field in the cavity is represented by the eigen modes of Helmholtz equation,and the current on the transmission line is represented by the eigen modes of transmission line equation.The field-line coupling relationship is described by Agrawal formula.Convergence of the circuit is accelerated by equivalent static inductance and capacitance.The resonant effect of the shielding cavity and the influence of the loss of the filling medium on the induced current are analyzed.The simulation results show that under the same simulation environment,the computation time of the proposed equivalent circuit is only about 31.94% of that of the CST commercial software simulation.(4)A Foster-type partial element equivalent circuit is proposed to solve the field-line coupling problem of transmission Lines terminal with nonlinear load at arbitrary positions in shielded cavity.For transmission lines located in a single shielding cavity,the integral equation of electric field is transformed into partial element equivalent circuit by using method of moment and Kirchhoff voltage law.Circuit elements and controlled sources in the circuit network are realized by Foster-type equivalent circuit.For transmission lines located in a slot-coupled cascaded shielded cavity,based on the principle of surface equivalence and the method of moment with global modal basis function,the mixed potential integral equation of slots is transformed into the Foster-type equivalent circuit.Based on the method of moment with domain dividing basis function and Kirchhoff voltage law,the mixed potential integral equation of transmission line is transformed into Foster-type partial element equivalent circuit.The simulation results show that under the same simulation environment,the computation time of the proposed equivalent circuit is only about 9.12% of that of the CST commercial software simulation. |
PDF Full Text Request