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(a) Parallel transmission-line circuit describing E . (b) Series transmission-line circuit describing H . magnetic resistance associated with and with the corresponding node quantities yields
Source publication
A new transmission line matrix (TLM) formulation in terms of magnetic flux pulses is presented for the numerical modeling of time-varying electromagnetic media. After redefining the Thevenin theorem in terms of magnetic flux and electric charge, this conceptually new approach is used to develop a dynamic generalized TLM node for the modeling of ele...
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... each line, the node can be considered as six coupled circuits: three parallel nodes to define each electric field component and three series nodes to define each mag- netic field component. This circuit separation is analogous to considering the rotational Maxwell equations as six sim- pler scalar equations. For the values of , , and , in the set Fig. 3(a) shows the dynamic parallel circuit defining the -component of the electric field at the th timestep, , while Fig. 3(b) is a plot of the dy- namic series circuit defining the -component of the magnetic field, . In Fig. 3, both circuits are represented only at the incidence stage. Their quantities change to reflected values after the ...
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... and three series nodes to define each mag- netic field component. This circuit separation is analogous to considering the rotational Maxwell equations as six sim- pler scalar equations. For the values of , , and , in the set Fig. 3(a) shows the dynamic parallel circuit defining the -component of the electric field at the th timestep, , while Fig. 3(b) is a plot of the dy- namic series circuit defining the -component of the magnetic field, . In Fig. 3, both circuits are represented only at the incidence stage. Their quantities change to reflected values after the incident flux pulses reach the node center. Identifying the medium capacity, inductance, electric conductance, and ...
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... to considering the rotational Maxwell equations as six sim- pler scalar equations. For the values of , , and , in the set Fig. 3(a) shows the dynamic parallel circuit defining the -component of the electric field at the th timestep, , while Fig. 3(b) is a plot of the dy- namic series circuit defining the -component of the magnetic field, . In Fig. 3, both circuits are represented only at the incidence stage. Their quantities change to reflected values after the incident flux pulses reach the node center. Identifying the medium capacity, inductance, electric conductance, and Considering all possible values of , , and in (6) yields a set of 12 linear independent equations, which ...
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... and electric charge, , at the circuits depicted in Fig. 3(a) and (b), respectively. The circuits are represented at the incidence stage, but reflection values must also be considered. This time vari- ation can easily be accounted for by considering the modified Thevenin circuit described in Section II for each line at the connection terminals. Doing so, the circuits in Fig. 4(a) and (b) can be ...
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... are represented at the incidence stage, but reflection values must also be considered. This time vari- ation can easily be accounted for by considering the modified Thevenin circuit described in Section II for each line at the connection terminals. Doing so, the circuits in Fig. 4(a) and (b) can be substituted for the dynamic circuits sketched in Fig. 3(a) and (b), respectively. It should be noted that incident pulses for the electric and magnetic losses lines are not included because of their infinite length. Since flux and charge in these circuits meet Ohm's law in an identical manner to voltage and current, the global charge at the parallel circuit and the global magnetic flux at the ...
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... in [24] to the dynamic case. To do this, let us consider a unitary pulse, , trav- eling toward the node center through the link line with . In mathematical terms, this pulse excites the terms in the -component of Ampere's law The different terms in (9) correspond to the fields and directions of the lines appearing in the parallel circuit of Fig. 3(a), while the terms in (10) correspond to fields and directions appearing in the series circuit of Fig. 3(b). From a mathematical point of view, all the terms appearing in (9) and (10) may appear at the reflec- tion stage, due to the excitation of and terms. Alternatively and in simpler circuit terms, pulses reflected at all the lines in ...
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... center through the link line with . In mathematical terms, this pulse excites the terms in the -component of Ampere's law The different terms in (9) correspond to the fields and directions of the lines appearing in the parallel circuit of Fig. 3(a), while the terms in (10) correspond to fields and directions appearing in the series circuit of Fig. 3(b). From a mathematical point of view, all the terms appearing in (9) and (10) may appear at the reflec- tion stage, due to the excitation of and terms. Alternatively and in simpler circuit terms, pulses reflected at all the lines in the parallel and the series circuits associated to line may appear. An initial form of the reflected ...
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... circuits, but there is one drawback still not taken into account: the original equations are not independent. On the contrary, they share some field components, and in this case, which means that they are coupled differential equations. In circuit terms, this coupling is partially described by a pair of shared or common lines in the circuits of Fig. 3. The remaining lines appear only in the par- allel or only in the series circuit and correspond to field quanti- ties appearing only in (9) or only in (10), i.e., corresponding to uncoupled terms in the differential equations. We will refer to the shared lines and as the common lines, while the rest will be termed the uncommon lines. ...
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... the guidelines described above, let us first obtain the coefficients corresponding to the uncommon lines. As re- gards the parallel circuit, coefficient equals the transmis- sion line coefficient, , for the time-varying parallel circuit of Fig. 3(a) for incidence from line . The incidence and refle- cion characteristic admittances used in (3) are (12) Substituting the above parameters in the transmission coeffi- cient (3) yields (13) When we consider the series node, the unitary incident pulse through line reaches a series connection of transmission lines. The impedances required ...
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... continuity at the series node leads to (18) The following coefficients at the common lines are obtained by substituting the coefficients in (13) and (16) in (17) and (18) (19) Columns associated with the capacitive stubs are obtained by considering an incident flux pulse entering the node through each capacitive line. For the parallel circuit of Fig. 3(a), the uni- tary pulse generates the following reflected ...
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... in (9), but does not appear in Faraday's equation, (10). Therefore, the information regarding this term is uncoupled from Faraday's equation, or equivalently, all the information regarding reflected pulses in (20) may be obtained by considering only the reflection and transmission coefficients, , and , given by (3) for the parallel circuit in Fig. 3(a). Doing so (21) Finally, columns associated with the inductive stubs are solved by choosing a unitary flux pulse entering through any inductive stub. Each stub is associated with a component of Faraday's law, which means that information is fully described by the reflection and transmission coefficients, , and , at a series node. The ...
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... columns associated with the inductive stubs are solved by choosing a unitary flux pulse entering through any inductive stub. Each stub is associated with a component of Faraday's law, which means that information is fully described by the reflection and transmission coefficients, , and , at a series node. The pulses reflected at the circuit in Fig. 3(b) when an incident pulse travels through the inductive line are (22) The reflection coefficient for the series circuit associated to and the transmission coefficient combined with a flux divider leads to (23) An explicit form of the full scattering matrix may be simply obtained from the previous coefficients by taking all the possible ...
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Citations
... The unit equivalent circuit of a transmission line can be connected to the resistors, inductors, and capacitors under constraints of a physical meaning of systems to be modeled [16,17]. In this approach, electromagnetic field quantities are substituted by the analogous incident and reflected voltage and current propagating through this unit circuit [18,19]. This conceptually new approach greatly simplifies calculations by the definite physical meaning of circuit elements in the unit circuit. ...
Microwave-assisted chemical reactions have been widely used, but the inhomogeneous heating limits further applications. The aim of this paper is to investigate the power transfer behavior in the simple polar-molecule reactions whose polarization changes with the proceeding of the reactions. At the temporal boundary, based on the continuity of charge and flux and the equivalent transmission line approach of the simple polar-molecule reactions, we discover the power changes in the reactions. The numerical results are in agreement with the theory of the temporal boundary. When the time scale of the component concentration variation is smaller than the wave period, the polarization is not continuous at the temporal boundary. The impedance of the reactions across the temporal boundary changes, and the reflection occurs. Moreover, when the dielectric property of the reactions decreases, the power of the waves increases after the temporal boundary and the waves experience a net energy gain. The results may be helpful in disclosing the non-uniform electromagnetic energy distribution in chemical reactions.
... Recently, transmission line matrix method is widely used to solve electromagnetic problems [1][2][3][4][5][6][7][8][9]. This method utilizes voltage and current concepts to satisfy Maxwell's equations and distinguish field distributions over desired environment. ...
In this paper the transmission line matrix (TLM) method is exploited to evaluate the electromagnetic field distribution over a new radio frequency micro electromechanical system (RF-MEMS). A hybrid symmetrical condensed node is used to analyze S-parameters of the switch in on and off states. Furthermore, the effects of spring zigzag cuts over the bridge are analyzed. Results have authorized that TLM method offers a much faster and more reliable results compare to other numerical methods because of its time domain behavior and transmission line basis.
... This particular version of 2D nodes is explained by the fact that most of the TLM effort has been concentrated on the design of general 3D condensed nodes. It has been only in later years that general condensed and lossy condensed nodes in 2D problems have been reported in the literature [17,18], independently defining permittivity, permeability, together with electric and magnetic losses in a node with arbitrary length along each Cartesian direction. In this situation, we propose using the technique described in [18,19] to design a 2D condensed node with a minimum number of inductive and capacitive stubs appropriately connected so as to model not only usual materials but also metamaterials with negative permittivity and/or permeability values. ...
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