CN106656093B - Design method and circuit of dual-band non-uniform transmission line impedance converter - Google Patents
Design method and circuit of dual-band non-uniform transmission line impedance converter Download PDFInfo
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Abstract
The invention provides a design method of a dual-band non-uniform transmission line impedance converter, which optimizes the structural size of the impedance converter through a mathematical optimization model, so that the corresponding transmission line of the impedance converter is a non-uniform transmission line, the width of the transmission line in the longitudinal direction is continuously changed, and the smooth transmission of electromagnetic wave signals on the transmission line is realized. The invention also provides a circuit of the dual-band non-uniform transmission line impedance transformer, which comprises a T-type impedance transformer, a pi-type impedance transformer and an H-type impedance transformer, and the impedance transformer realized by the design method has the advantages of small reflection coefficient, large harmonic suppression, small insertion loss, large bandwidth, smaller physical size than that of the traditional uniform transmission line impedance transformer and more flexible design. Moreover, the impedance transformer can be used for matching any complex terminal impedance without any concentrated reactance element, and has the advantages of less resource application, wide application range, economy and high cost performance.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a design method and a circuit of a dual-band non-uniform transmission line impedance converter.
Background
Microwave technology is widely used in industries such as industry, agriculture, remote sensing, military and the like, and in order to meet the development requirements of civil communication, electronic detection and electronic countermeasure, a microwave communication system is developed towards the directions of high performance, miniaturization, broadband and multiband. The microwave transmission line has been the most basic and important part of all microwave components as a guided wave system for transmitting electromagnetic waves, however, most researches have been focused on uniform transmission line direction at present, mainly because characteristic parameters of the uniform transmission line can be obtained from corresponding theoretical formulas, and the parameters include S parameters (scattering parameters) and ABCD parameters (transmission matrix, A, D is dimensionless parameters, C is admittance, and B is impedance), and the researches thereof have been well developed.
In the prior art, impedance transformers are one of the most common and important key components in microwave circuits, and uniform transmission lines or step impedance transmission lines are generally used. However, the dual-band impedance transformer based on the uniform transmission line often has the defects of parasitic passband, large insertion loss, narrow bandwidth, large physical size and the like, so that the application of the dual-band impedance transformer is greatly limited.
Disclosure of Invention
The invention provides a design method and a circuit of a dual-band non-uniform transmission line impedance converter, which solve the technical problem that the structural size of the impedance converter is optimized through a mathematical optimization model, so that a corresponding transmission line of the impedance converter is a non-uniform transmission line, and the width of the transmission line in the longitudinal direction is continuously changed.
In order to solve the above technical problems, the present invention provides a method for designing a dual-band non-uniform transmission line impedance transformer, comprising the steps of:
s1, expanding the characteristic impedance of each non-uniform transmission line of the impedance converter by using truncated Fourier to obtain a normalization expression;
s2, equally dividing each non-uniform transmission line into at least two sections according to the length;
s3, solving a transmission matrix of each non-uniform transmission line;
s4, solving a transmission matrix of the whole impedance transformer;
s5, according to discrete frequency f in double frequency bandsjDetermining the reflection coefficient of the input of an impedance converterin(fj)；
S6, constructing a frequency objective function
S7, constructing an impedance constraint condition Zmin≤Z≤ZmaxZ is the characteristic impedance of any point of the non-uniform transmission line in the impedance transformer;
s8, minimizing the frequency objective function based on the impedance constraint condition, and constructing a mathematical optimization model
S9, obtaining a Fourier coefficient an,bn,cn,dn,en,gn,hn,kn,pn,qn；
S10, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting the obtained signal into the step S5, analyzing and judging whether the reflection coefficient of the output end of the input terminal impedance is smaller than a preset value, if so, executing the step S11, otherwise, returning to the step S2;
s11, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting into the normalization expression of the characteristic impedance of each non-uniform transmission line in the step S1 to obtain the characteristic impedance of each non-uniform transmission line;
s12, solving the physical size of each non-uniform transmission line according to the transmission line synthesis method and the characteristic impedance of each non-uniform transmission line obtained in the step S11;
and S13, performing three-dimensional electromagnetic simulation on the circuit in which each non-uniform transmission line in the step S12 is respectively connected with the input terminal impedance and the output terminal impedance to check the impedance matching effect of the impedance converter.
Further, in the step S5, the two dual bands are respectively represented as [ f [ ]1L,f1H]And [ f2L,f2H]And f is2L＞f1H，fjConsists of a series of discrete frequencies located in a dual band, j 1, 2.
Further, the constraint condition in step S7 is set to 20 Ω < Z <120 Ω in accordance with the accuracy of the circuit processing process in practice.
Further, in step S8, the frequency objective function is minimized by a least squares method to construct a mathematical optimization model.
The invention also provides a circuit of the dual-band non-uniform transmission line impedance converter, which comprises a T-shaped circuit, a pi-shaped circuit or an H-shaped circuit, wherein the T-shaped circuit, the pi-shaped circuit or the H-shaped circuit is formed by connecting a horizontal non-uniform transmission line, an open-circuit non-uniform transmission line and/or a short-circuit non-uniform transmission line, an input terminal impedance and an output terminal impedance; the horizontal non-uniform transmission line is connected between an input terminal impedance output end and an output terminal impedance input end, and the input terminal impedance input end and the output terminal impedance output end are respectively grounded; and taking the direction of the horizontal non-uniform transmission line as an X axis, and taking a vertical bisector of the horizontal non-uniform transmission line as a Y axis.
Furthermore, the T-shaped circuit is provided with a horizontal non-uniform transmission line, an open-circuit non-uniform transmission line and a short-circuit non-uniform transmission line; and one end of the open-circuit non-uniform transmission line and one end of the short-circuit non-uniform transmission line are both connected to the output terminal impedance input end.
Furthermore, the pi-type circuit is provided with a horizontal non-uniform transmission line and two parallel open-circuit non-uniform transmission lines or two parallel short-circuit non-uniform transmission lines; one of the two open-circuit non-uniform transmission lines is connected with the input terminal impedance output end, and the other one of the two open-circuit non-uniform transmission lines is connected with the output terminal impedance input end, or one of the short-circuit non-uniform transmission lines is connected with the input terminal impedance output end, and the other one of the short-circuit non-uniform transmission lines is connected with the output terminal impedance input end; the pi-type circuit is symmetrical along the Y axis.
Furthermore, the H-shaped circuit is provided with a horizontal non-uniform transmission line, two parallel open-circuit non-uniform transmission lines and two parallel short-circuit non-uniform transmission lines; one of the two open-circuit non-uniform transmission lines is connected to the input terminal impedance output end, and the other open-circuit non-uniform transmission line is connected to the output terminal impedance input end; one of the two short-circuit non-uniform transmission lines is connected to the input terminal impedance output end, and the other short-circuit non-uniform transmission line is connected to the output terminal impedance input end; the H-shaped circuit is symmetrical along the Y axis.
Further, the input termination impedance and the output termination impedance are arbitrary complex numbers.
Further, the circuit operates in a dual frequency band.
According to the design method of the dual-band non-uniform transmission line impedance converter, the structural size of the impedance converter is optimized through a mathematical optimization model, so that the transmission line corresponding to the impedance converter is a non-uniform transmission line, the width of the transmission line in the longitudinal direction is continuously changed, and smooth transmission of electromagnetic wave signals on the transmission line is realized. The circuit of the dual-band non-uniform transmission line impedance transformer constructed by the method has the advantages of small reflection coefficient, large harmonic suppression, small insertion loss, large bandwidth, smaller physical size than that of the traditional uniform transmission line impedance transformer and more flexible design. Moreover, the impedance transformer can be used for matching any complex terminal impedance without any concentrated reactance element, and has the advantages of less resource application, wide application range, economy and high cost performance.
Drawings
FIG. 1 is a flow chart of a method for designing a dual-band non-uniform transmission line impedance transformer according to the present invention;
fig. 2 is a circuit configuration diagram of a T-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention;
fig. 3 is a circuit configuration diagram of a first pi-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention;
fig. 4 is a circuit configuration diagram of a second pi-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention;
fig. 5 is a circuit configuration diagram of an H-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The following are only preferred embodiments and should not be construed as limiting the scope of the invention.
Referring to fig. 1, it is a flow chart of a design method of a dual-band non-uniform transmission line impedance transformer provided by the present invention. In this embodiment, the method for designing a dual-band non-uniform transmission line impedance transformer includes the following steps:
s1, expanding the characteristic impedance of each non-uniform transmission line of the impedance converter by using truncated Fourier transform to obtain a normalized expression
Wherein i is a differential subscript of different circuits, A-E are differential subscripts of each non-uniform transmission line in one circuit, and Z0Is the source impedance, ZAi、ZBi、ZCi、ZDi、ZEiCharacteristic impedances of the A-th to E-th non-uniform transmission lines respectively,
respectively correspond to ZAi、ZBi、ZCi、ZDi、ZEiX and y are the horizontal and vertical coordinate values of the non-uniform transmission line, lAi、lBi、lCi、lDi、lEiRespectively showing the length values of the A-th to E-th non-uniform transmission lines;
s2, equally dividing each non-uniform transmission line into K sections according to the length, wherein K is a natural number larger than 1;
s3, solving the transmission matrix of each non-uniform transmission line
h＝A,B,C,D,E；ZiIs the characteristic impedance of the ith segment from the 1 st segment to the kth segment.
S4, solving a transmission matrix [ ABCD ] of the whole impedance transformer, wherein A, D is a dimensionless parameter, C is an admittance, and B is an impedance;
s5, according to discrete frequency f in double frequency bandsjDetermining the reflection coefficient of the input termination impedance output
Wherein ZL(fj) Is the load impedance, Z0Is the source impedance, Z0 *Represents Z0Conjugated complex number of (a), B (f)j) At a discrete frequency fjTo the transmission matrix [ ABCD ]]The value of the middle parameter B;
s6, constructing a frequency objective function
S7, constructing an impedance constraint condition Zmin≤Z≤ZmaxZ is the characteristic impedance of any point of any non-uniform transmission line in the impedance transformer;
s8, minimizing the frequency objective function based on the impedance constraint condition, and constructing a mathematical optimization model
S9, obtaining a Fourier coefficient an,bn,cn,dn,en,gn,hn,kn,pn,qn；
S10, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting the obtained signal into the step S5, analyzing and judging whether the reflection coefficient of the output end of the input terminal impedance is smaller than a preset value, if so, executing the step S11, otherwise, returning to the step S2;
s11, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting into the normalization expression of the characteristic impedance of each non-uniform transmission line in the step S1 to obtain the characteristic impedance of each non-uniform transmission line;
s12, solving the physical size of each non-uniform transmission line according to the transmission line synthesis method and the characteristic impedance of each non-uniform transmission line obtained in the step S11;
and S13, performing three-dimensional electromagnetic simulation on the circuit in which each non-uniform transmission line in the step S12 is respectively connected with the input terminal impedance and the output terminal impedance to check the impedance matching effect of the impedance converter.
In the present embodiment, in the step S5, two dual bands are respectively represented as [ f [ ]1L,f1H]And [ f2L,f2H]And f is2L＞f1H，fjConsists of a series of discrete frequencies located in a dual band, j 1, 2.. M; the constraint condition in step S7 is set to 20 Ω in accordance with the accuracy of the actual circuit processing process<Z<120 Ω; in the step S8, the frequency objective function is minimized by a least squares method to construct a mathematical optimization model.
The invention also provides a circuit of the dual-band non-uniform transmission line impedance converter, which comprises a T-shaped circuit, a pi-shaped circuit or an H-shaped circuit, wherein the T-shaped circuit, the pi-shaped circuit or the H-shaped circuit is formed by connecting a horizontal non-uniform transmission line, an open-circuit non-uniform transmission line and/or a short-circuit non-uniform transmission line, an input terminal impedance and an output terminal impedance; the horizontal non-uniform transmission line is connected between an input terminal impedance output end and an output terminal impedance input end, and the input terminal impedance input end and the output terminal impedance output end are respectively grounded; and taking the direction of the horizontal non-uniform transmission line as an X axis, and taking a vertical bisector of the horizontal non-uniform transmission line as a Y axis.
Fig. 2 is a circuit structure diagram of a T-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention. In this embodiment, the T-shaped circuit has a horizontal non-uniform transmission line 101, an open-circuit non-uniform transmission line 102 and a short-circuited non-uniform transmission line 103; one end of the open-circuit non-uniform transmission line 102 and one end of the short-circuit non-uniform transmission line 103 are both connected to the output terminal impedance input terminal Zout1。
The horizontal non-uniform transmission line 101 has a length lA1Its characteristic impedance ZA1Expressed in truncated fourier transforms;
the open-circuit non-uniform transmission line 102 has a length lB1Its characteristic impedance ZB1Expressed in truncated fourier transforms;
the short-circuited non-uniform transmission line 103 has a length lC1Its characteristic impedance ZC1Represented by a truncated fourier expansion.
Fig. 3 is a circuit structure diagram of a first pi-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention. In this embodiment, the first pi-type circuit is provided with a horizontal non-uniform transmission line 201 and two parallel open-circuit non-uniform transmission lines 202 and 203; when the two parallel open-circuit non-uniform transmission lines 302, 303 can also be replaced by two parallel short-circuit non-uniform transmission lines 302, 303, which are connected in series with the horizontal non-uniform transmission line 301, the second pi-type circuit is obtained, as shown in fig. 4;
in FIG. 3, the open-circuited non-uniform transmission line 202 is connected to the input termination impedance output Zin2An open-circuit non-uniform transmission line 203 connected to the output termination impedance input Zout2(ii) a In FIG. 4, the short-circuited non-uniform transmission line 302 is connected to the input termination impedance output Zin3A short-circuited non-uniform transmission line 303 connected to the output termination impedance input Zout3；
The horizontal non-uniform transmission line 201 has a length lA2Its characteristic impedance ZA2Expressed in truncated fourier transforms;
the open-circuit non-uniform transmission line 202 has a length lB2Its characteristic impedance ZB2Expressed in truncated fourier transforms;
the open-circuit non-uniform transmission line 203 has a length lC2Its characteristic impedance ZC2Expressed in truncated fourier transforms;
the horizontal non-uniform transmission line 301 has a length lA3Its characteristic impedance ZA3Expressed in truncated fourier transforms;
the short-circuited non-uniform transmission line 302 has a length lB3Its characteristic impedance ZB3Expressed in truncated fourier transforms;
the short-circuit non-uniform transmission line 303 has the length lC3Its characteristic impedance ZC3Represented by a truncated fourier expansion.
The first pi-type circuit and the second pi-type circuit are symmetrical along the Y axis.
Fig. 4 is a circuit structure diagram of an H-type circuit in a circuit of a dual-band non-uniform transmission line impedance transformer according to an embodiment of the present invention. In this embodiment, the H-type circuit is provided with a horizontal non-uniform transmission line 401, two parallel open-circuit non-uniform transmission lines 402, 403 and two parallel short-circuit non-uniform transmission lines 404, 405; the open-circuit non-uniform transmission line 402 is connected to the input-termination impedance output terminal Zin4An open-circuited non-uniform transmission line 403 connected to said output termination impedance input Zout4(ii) a The short-circuited non-uniform transmission line 404 is connected to the input termination impedance output terminal Zin4A short-circuited non-uniform transmission line 405 connected to the output termination impedance input Zout4(ii) a The H-shaped circuit is symmetrical along the Y axis.
The horizontal non-uniform transmission line 401 has a length lA4Its characteristic impedance ZA4Expressed in truncated fourier transforms;
the open non-uniform transmission line 402 has a length lB4Its characteristic impedance ZB4Expressed in truncated fourier transforms;
the open-circuit non-uniform transmission line 403 has a length lC4Its characteristic impedance ZC4Expressed in truncated fourier transforms;
the short non-uniform transmission line 404 has a length lD4Its characteristic impedance ZD4Expressed in truncated fourier transforms;
the short circuit is not uniformly transmittedTransmission line 405 has a length lE4Its characteristic impedance ZE4Expressed in truncated fourier transforms;
in this embodiment, the input termination impedance Z0And an output termination impedance ZLCan be any plural number; the T-type circuit, the pi-type circuit and the H-type circuit all work in double frequency bands.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (10)
1. A design method of a dual-band non-uniform transmission line impedance transformer is characterized by comprising the following steps:
s1, expanding the characteristic impedance of each non-uniform transmission line of the impedance converter by using truncated Fourier transform to obtain a normalized expression
Wherein i is a differential subscript of different circuits, A-E are differential subscripts of each non-uniform transmission line in one circuit, and Z0Is the source impedance, ZAi、ZBi、ZCi、ZDi、ZEiCharacteristic impedances of the A-th to E-th non-uniform transmission lines respectively,
respectively correspond to ZAi、ZBi、ZCi、ZDi、ZEiX and y are the horizontal and vertical coordinate values of the non-uniform transmission line, lAi、lBi、lCi、lDi、lEiRespectively showing the length values of the A-th to E-th non-uniform transmission lines;
s2, equally dividing each non-uniform transmission line into at least two sections according to the length;
s3, solving a transmission matrix of each non-uniform transmission line;
s4, solving a transmission matrix [ ABCD ] of the whole impedance transformer, wherein A, D is a dimensionless parameter, C is an admittance, and B is an impedance;
s5, according to discrete frequency f in double frequency bandsjDetermining the reflection coefficient of the input terminal of the input termination impedance
Wherein ZL(fj) Is the load impedance, Z0Is the source impedance, Z0 *Represents Z0Conjugated complex number of (a), B (f)j) At a discrete frequency fjTo the transmission matrix [ ABCD ]]The value of the middle parameter B;
s6, constructing a frequency objective function
S7, constructing an impedance constraint condition Zmin≤Z≤ZmaxZ is the characteristic impedance of any point of the non-uniform transmission line in the impedance transformer, ZminAnd ZmaxRespectively representing the minimum characteristic impedance and the maximum characteristic impedance at any point of the non-uniform transmission line;
s8, minimizing the frequency objective function based on the impedance constraint condition, and constructing a mathematical optimization model
S9, obtaining a Fourier coefficient an,bn,cn,dn,en,gn,hn,kn,pn,qn；
S10, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting the reflection coefficient in the step S5in(fj) Analyzing and determining whether the reflection coefficient of the input terminal of the input termination impedance is less than a predetermined valueIf yes, go to step S11, otherwise, go back to step S2;
s11, Fourier coefficient a obtained in the step S9n,bn,cn,dn,en,gn,hn,kn,pn,qnSubstituting into the normalization expression of the characteristic impedance of each non-uniform transmission line in the step S1 to obtain the characteristic impedance of each non-uniform transmission line;
s12, solving the physical size of each non-uniform transmission line according to the transmission line synthesis method and the characteristic impedance of each non-uniform transmission line obtained in the step S11;
and S13, performing three-dimensional electromagnetic simulation on the circuit in which each non-uniform transmission line in the step S12 is respectively connected with the input terminal impedance and the output terminal impedance to check the impedance matching effect of the impedance converter.
2. The method of claim 1, wherein the method further comprises the steps of: in the step S5, the two dual bands are respectively represented as [ f [ ]1L,f1H]And [ f2L,f2H]And f is2L＞f1H，fjConsists of a series of discrete frequencies located in a dual band, j 1, 2.. M; f. of1L,f1HRepresenting the lower and upper frequencies, f, respectively, of a first of the two frequency bands2L,f2HRespectively representing the lower and upper frequencies of the second of the two frequency bands.
3. The method of claim 1, wherein the method further comprises the steps of: the impedance constraint condition in step S7 is set to 20 Ω < Z <120 Ω in accordance with the accuracy of the circuit processing process in practice.
4. The method of claim 1, wherein the method further comprises the steps of: in step S8, the frequency objective function is minimized by a least squares method to construct a mathematical optimization model.
5. A circuit of a dual-band non-uniform transmission line impedance transformer is characterized by comprising a T-shaped circuit, a pi-shaped circuit or an H-shaped circuit which is formed by connecting a horizontal non-uniform transmission line, an open-circuit non-uniform transmission line and/or a short-circuit non-uniform transmission line, an input terminal impedance and an output terminal impedance; the horizontal non-uniform transmission line is connected between the output end of the input terminal impedance and the input end of the output terminal impedance, and the input end of the input terminal impedance and the output end of the output terminal impedance are respectively grounded; and taking the direction of the horizontal non-uniform transmission line as an X axis, and taking a vertical bisector of the horizontal non-uniform transmission line as a Y axis.
6. The circuit of a dual-band non-uniform transmission line impedance transformer of claim 5, wherein: the T-shaped circuit is provided with a horizontal non-uniform transmission line, an open-circuit non-uniform transmission line and a short-circuit non-uniform transmission line; and one end of the open-circuit non-uniform transmission line and one end of the short-circuit non-uniform transmission line are both connected to the input end of the output terminal impedance.
7. The circuit of a dual-band non-uniform transmission line impedance transformer of claim 5, wherein: the pi-shaped circuit is provided with a horizontal non-uniform transmission line, two parallel open-circuit non-uniform transmission lines or two parallel short-circuit non-uniform transmission lines; one of the two open-circuit non-uniform transmission lines is connected with the output end of the input terminal impedance, and the other one of the two open-circuit non-uniform transmission lines is connected with the input end of the output terminal impedance, or one of the two short-circuit non-uniform transmission lines is connected with the output end of the input terminal impedance, and the other one of the two short-circuit non-uniform transmission lines is connected with the input end of the output terminal impedance; the pi-type circuit is symmetrical along the Y axis.
8. The circuit of a dual-band non-uniform transmission line impedance transformer of claim 5, wherein: the H-shaped circuit is provided with a horizontal non-uniform transmission line, two parallel open-circuit non-uniform transmission lines and two parallel short-circuit non-uniform transmission lines; one of the two open-circuit non-uniform transmission lines is connected to the output end of the input terminal impedance, and the other open-circuit non-uniform transmission line is connected to the input end of the output terminal impedance; one of the two short-circuit non-uniform transmission lines is connected to the output end of the input terminal impedance, and the other short-circuit non-uniform transmission line is connected to the input end of the output terminal impedance; the H-shaped circuit is symmetrical along the Y axis.
9. The circuit of a dual-band non-uniform transmission line impedance transformer of claim 5, wherein: the input termination impedance and the output termination impedance are arbitrary complex numbers.
10. The circuit of a dual-band non-uniform transmission line impedance transformer of claim 5, wherein: the circuit operates in dual frequency bands.
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