CN106326548B - Solution scheme for frequency domain response of impedance discontinuous transmission line - Google Patents

Solution scheme for frequency domain response of impedance discontinuous transmission line Download PDF

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CN106326548B
CN106326548B CN201610707669.3A CN201610707669A CN106326548B CN 106326548 B CN106326548 B CN 106326548B CN 201610707669 A CN201610707669 A CN 201610707669A CN 106326548 B CN106326548 B CN 106326548B
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impedance
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frequency domain
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张如彬
金杰
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Tianjin University
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Abstract

The invention discloses a solution scheme for frequency domain response of an impedance discontinuous transmission line. Firstly, dividing an impedance discontinuous line into n sections of impedance uniform sections, establishing a signal flow diagram according to a traveling wave theory, then obtaining a scattering coefficient of each node according to an electromagnetic topological theory, then establishing a wave propagation relation equation according to the wave propagation theory, establishing a wave scattering equation according to the relation between incident waves and reflected waves, and finally combining the two equations to obtain the frequency domain response of each node. The technical scheme is used, and the frequency domain response of the impedance discontinuous transmission line is effectively and reasonably solved through software simulation verification.

Description

Solution scheme for frequency domain response of impedance discontinuous transmission line
Technical Field
The invention relates to the field of transmission line performance analysis, in particular to a solution scheme for frequency domain response of an impedance discontinuous transmission line.
Background
The transmission line is an electrical device for guiding signals and energy, and is widely applied. In a power system, the research on the characteristics of a line has important application value in the aspects of relay protection element parameter determination, fault distance measurement, lightning protection and the like.
The method for analyzing the transmission line values can be generally divided into two categories, namely a time domain method and a frequency domain method. The frequency domain analysis method is to convert a transmission line equation into a partial differential equation in a frequency domain to solve, and finally obtain the voltage and current frequency domain response of the whole transmission line. The frequency domain characteristic analysis of the transmission line is an indispensable consideration for researching electromagnetic interference and compatibility analysis.
At present, frequency domain analysis techniques based on simple uniform lossy transmission lines are mature. In practical high-speed circuitry, however, non-uniform, impedance discontinuities often occur in the transmission lines connecting the various signal processes in the system. The following typical methods are mainly used for the research of such problems in the frequency domain.
The first method is to solve the analytic solution by dividing the non-uniform transmission line into the product of multiple sections of uniform transmission matrices based on the BLT equation of the frequency domain, but this method does not consider the reflection problem of the discrete sections of the non-uniform transmission line due to impedance discontinuity.
The second method is to equate the whole non-uniform section to a multi-port network and to adopt a rational approximation function of the transfer function of the vector matching port, thereby obtaining the voltage-current frequency domain response.
The third method is Fast Fourier Transform (FFT), which has a wide range of applications, but when performing time-frequency conversion, enough frequency samples must be removed within a certain frequency range to avoid spectrum aliasing and consuming computing memory and time. The fourier transform method may be a Laplace Transform (LT) method, a mode reduction method, or the like. The above method can only analyze linear time invariant circuits.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a solution for the frequency domain response of an impedance discontinuous transmission line, which is combined with the relationship between nodes and pipelines in an electromagnetic topology to improve and process discrete uniform sections of a non-uniform line so as to obtain a more accurate frequency domain solution.
The purpose of the invention is realized by the following technical scheme:
a solution scheme of frequency domain response of an impedance discontinuous transmission line is characterized in that a signal flow diagram of the impedance discontinuous transmission line, scattering parameters of transmission nodes in an electromagnetic topology and a BLT equation are combined, and the solution scheme specifically comprises the following steps:
(1) dividing the impedance discontinuous line into n sections of impedance uniform sections, and establishing a signal flow diagram according to the relation between incident waves and reflected waves of a traveling wave theory by combining the concepts of pipelines and nodes;
(2) according to an electromagnetic topological theory, obtaining scattering parameters of each node;
(3) establishing a wave propagation relation equation according to a wave propagation theory;
(4) establishing a wave scattering relation equation according to the scattering parameters obtained in the step (2) and the relation between the incident wave and the reflected wave;
(5) and (4) simultaneously establishing the propagation relation equation in the step (3) and the scattering relation equation in the step (4) to obtain the frequency domain response of each transmission node.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects: the scheme of the invention combines the relationship between nodes and pipelines in the electromagnetic topology to improve the discrete uniform sections of the non-uniform lines, thereby obtaining a more accurate frequency domain solution; more flexible application, less occupied computer resources, high computing efficiency,
Drawings
Fig. 1 is a signal flow diagram of an impedance discontinuity transmission line.
Fig. 2 is a far end frequency domain response of an impedance discontinuity transmission line solved using the inventive arrangements.
Fig. 3 shows the far-end frequency-domain response of the impedance discontinuity transmission line simulated using the spice circuit analysis program.
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
assuming that the transmission line is a two-conductor transmission line including n impedance discontinuity sections, the characteristic impedance of each section is set to be Zc1，Zc2，…，Zcn. The impedance at the power supply section and the load end is Z respectively1And Z2。
First, combining with the traveling wave theory, the voltage and current of the transmission line are decomposed into the sum of forward traveling wave and backward traveling wave, and a signal flow diagram is constructed, as shown in fig. 1.
Node 1 and node n +1 represent the power supply and load terminals, respectively, of the data transmission channel, and nodes 2 to n represent the connection points of the discrete uniform segments.
And secondly, solving the scattering parameters of each node, and solving the relation between the incident wave and the reflected wave by using a wave theory for the scattering parameters of the nodes 1 and n + 1. For the node 2, the scattering parameter solution of n can be regarded as a transmission node in the topological theory, and the scattering parameter can be obtained by using the scattering parameter solution formula of the transmission node.
Node 1 scattering parameter
Figure BDA0001088228620000031
The scattering parameter of node n +1 is
Figure BDA0001088228620000032
The scattering parameter of the node 2 is
Figure BDA0001088228620000033
By analogy, the scattering parameters of other nodes are obtained as
Figure BDA0001088228620000034
i is 2,3, … … n, wherein
Figure BDA0001088228620000035
Thirdly, according to the propagation characteristics of the wave, the propagation relation equation of the system can be obtained as
Figure BDA0001088228620000036
The above formula is expressed as a matrix form as Vref＝Vinc-Vs。
Wherein
Figure BDA0001088228620000037
Is the transfer function of the pipe i, λiFor the transmission constant of the pipe i, the general definition
Figure BDA0001088228620000038
Ri，Li，Ci，GiI parameter of the distribution pipe, liIs the length of the pipe i, Vinc(i,k)，Vref(i,k)Representing the incident and reflected waves, respectively, at node k connected to pipe i.
Figure BDA0001088228620000039
For voltage excitation on the pipe i, V0i，I0iIs the voltage and current source, x, of the pipe isiAnd in its place, when the pipe i is not excited,
Figure BDA00010882286200000310
fourthly, according to the relation between the incident wave and the reflected wave, the scattering relation equation of each node is obtained
Figure BDA00010882286200000311
Expressed in matrix form as Vref＝SVinc。
Wherein S1，S2，…，Sn+1From the second step, already, Vinc(i,k)，Vref(i,k)Representing the incident and reflected waves, respectively, at node k connected to pipe i.
Fifthly, the voltage wave of each node is obtained, and the voltage wave V of each node is equal to Vinc+VrefIn conjunction with the above formulas, the voltage at each node can be obtained as
V＝(S+I)(S-)-1Vs
Wherein S is a scattering matrix, a propagation matrix, I is a 2 n-order unit matrix, and VsIs the excitation source vector. And substituting the parameters to obtain the voltage of each node.
The impedance discontinuity transmission line was analyzed using SPICE circuit analysis program and compared with the proposed solution of the present invention:
three transmission lines with different impedances are arranged in free space and have a length of l1＝30m，l2＝45m，l360m, load impedance Zl1＝75，Zl2＝50，Zl3150, impedance matching at the power and load terminals, Z1＝75，Z2150, the technical solution of the present invention and the SPICE circuit analysis program are respectively adopted for comparison, and the results are shown in fig. 2 and fig. 3.
Fig. 2 shows the amplitude-frequency characteristic diagram of the transmission line at the load end obtained by using the scheme of the present invention, fig. 3 shows the frequency domain characteristic of the load end obtained by using the SPICE simulation analysis program, as can be seen from fig. 2 and fig. 3, the bandwidth of the embodiment is 100kHz, the amplitude is 660 mV-670 mV, and the result of the software simulation is basically consistent with the result of the scheme of the present invention.
Because the SPICE circuit analysis program only has accurate solution to the lossless line and has great limitation to the lossy line, compared with software simulation, the technical scheme of the invention is more flexible, the occupied computer resource is less, and the calculation efficiency is high.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (1)

1. A method for solving frequency domain response of an impedance discontinuous transmission line is characterized in that a signal flow diagram of the impedance discontinuous transmission line, scattering parameters of transmission nodes in electromagnetic topology and a BLT equation are combined, and the method specifically comprises the following steps:
(1) dividing the impedance discontinuous line into n sections of impedance uniform sections, and establishing a signal flow diagram according to the relation between incident waves and reflected waves of a traveling wave theory by combining the concepts of pipelines and nodes; the node 1 and the node n +1 respectively represent a power supply end and a load end of a data transmission channel, and the nodes 2 to the node n represent connection points of discrete uniform sections;
(2) according to an electromagnetic topological theory, obtaining scattering parameters of each node; solving the relation between incident waves and reflected waves by using a wave theory for the scattering parameters of the node 1 and the node n + 1; solving the scattering parameters of the nodes 2 and n to be regarded as transmission nodes in the topological theory, and solving the scattering parameters by using a scattering parameter solving formula of the transmission nodes; node 1 scattering parameter
Figure FDA0002422004590000011
The scattering parameter of node n +1 is
Figure FDA0002422004590000012
The scattering parameter of the node 2 is
Figure FDA0002422004590000013
By analogy, the scattering parameters of other nodes are obtained as
Figure FDA0002422004590000014
Wherein
Figure FDA0002422004590000015
Wherein Z isc1，Zc2，…，ZcnRespectively, characteristic impedance, Z1And Z2A power supply terminal impedance and a load terminal impedance, respectively.
(3) According to the wave propagation theory, establishing a wave propagation relation equation:
Figure FDA0002422004590000016
the above formula is expressed as a matrix form as Vref＝Vinc-Vs(ii) a Wherein
Figure FDA0002422004590000017
Is the transfer function of the pipe i, λiFor the transmission constant of the pipe i, the general definition
Figure FDA0002422004590000018
Ri，Li，Ci，GiI parameter of the distribution pipe, liIs the length of the pipe i, Vinc(i,k)，Vref(i,k)Respectively representing an incident wave and a reflected wave of a node k connected with a pipeline i;
Figure FDA0002422004590000021
for voltage excitation on the pipe i, V0i，I0iIs the voltage and current source, x, of the pipe isiAnd in its place, when the pipe i is not excited,
Figure FDA0002422004590000022
the above formula is expressed as a matrix form as Vref＝Vinc-Vs；
(4) Establishing a scattering relation equation of the waves according to the scattering parameters in the step (2) and the relation between the incident waves and the reflected waves;
Figure FDA0002422004590000023
expressed in matrix form as Vref＝SVinc(ii) a Wherein S1，S2，…，Sn+1From the second step, already, Vinc(i,k)，Vref(i,k)Respectively representing an incident wave and a reflected wave of a node k connected with a pipeline i;
(5) combining the propagation relation equation in the step (3) and the scattering relation equation in the step (4) to obtain the frequency domain response of each transmission node; specifically, the method comprises the following steps: in conjunction with the above formulas, the voltage at each node can be obtained as
V＝(S+I)(S-)-1Vs
Wherein S is a scattering matrix, a propagation matrix, I is a 2 n-order unit matrix, and VsIs an excitation source vector; and substituting the parameters to obtain the voltage of each node.
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CN102411647A (en) * 2011-08-03 2012-04-11 西安电子科技大学 Time domain analysis method for transient response of lossy nonuniform multi-conductor transmission lines
CN105677998A (en) * 2016-01-13 2016-06-15 沈阳航空航天大学 Method for analyzing transmission line transient response

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CN102411647A (en) * 2011-08-03 2012-04-11 西安电子科技大学 Time domain analysis method for transient response of lossy nonuniform multi-conductor transmission lines
CN105677998A (en) * 2016-01-13 2016-06-15 沈阳航空航天大学 Method for analyzing transmission line transient response

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