CN111294008A - Double-frequency point impedance converter of parallel transmission line with complex number terminal and its establishing method and application - Google Patents

Double-frequency point impedance converter of parallel transmission line with complex number terminal and its establishing method and application Download PDF

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CN111294008A
CN111294008A CN202010118040.1A CN202010118040A CN111294008A CN 111294008 A CN111294008 A CN 111294008A CN 202010118040 A CN202010118040 A CN 202010118040A CN 111294008 A CN111294008 A CN 111294008A
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electrical length
range
transmission line
frequency
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CN111294008B (en
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谢泰洋
王小龙
卢革宇
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Jilin University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/38—Impedance-matching networks

Abstract

The invention introduces a parallel transmission line impedance transformer with a plurality of terminal loads, which is used for dual-frequency (DF) design, and four different designable area mapping modes exist on an electrical length-electrical length (EL-EL) plane by analyzing different initial conditions of the plurality of terminal loads. By adding an additional vertical Frequency Ratio (FR) axis, a novel 3D cube can be created on the FR-EL coordinate system, and the range of designable frequency ratios can then be easily drawn in this 3D cube; thus, this newly proposed visible 3D mapping method is used to match complex termination loads of parallel transmission line impedance transformers at two different frequencies, and for a particular mode, a clear boundary can be drawn to distinguish between designable and non-designable ranges.

Description

Double-frequency point impedance converter of parallel transmission line with complex number terminal and its establishing method and application
Technical Field
The invention relates to a dual-frequency design problem of a load with a plurality of terminals, in particular to a dual-frequency point impedance converter of a parallel transmission line with a plurality of terminals, and an establishment method and application thereof.
Background
Transmission line impedance transformers (TLTs) are essential passive components in RF/microwave systems. It can transform the source load impedance to a different termination load impedance for a particular frequency, while providing maximum power. Depending on the application requirements, the input or output impedance of a power transistor, antenna, power divider or balun is not always a real load impedance, requiring a flexible TLT to match different kinds of complex impedances.
The impedance transformer of only one transmission line can be used not only for actual to actual impedance matching but also for complex to complex impedance matching in single band operation. By adding an additional cascade transmission line, on the premise of realizing real impedance matching, a single-frequency-band impedance converter with a harmonic suppression function and an impedance converter with a double-frequency-band or broadband performance can be designed for different purposes. As the number of transmission lines cascaded increases, multiple frequency bands can be realized. Furthermore, the multi-band cascaded transmission line impedance transformer can be designed not only for real impedance matching but also for complex impedance matching.
Coupled lines are another basic impedance transformer topology. Coupled impedance transformers can provide additional parametric variables compared to cascaded transmission line topologies, useful for broadband matching, DC modules, compact circuit size, and multi-band applications. Since the designable coupling strength of the coupled lines is very limited, it is preferable to use short-circuited stub lines in the design. Thus, single-band, dual-band and even multi-band applications can be easily implemented. Several different types of band pass filtered impedance transformers may also be proposed for different system requirements, taking into account the exact bandwidth requirements. Parallel transmission lines are also an interesting structure for single band impedance transformers, filters and duplexer applications.
Due to the limitations of the range of designable characteristic impedances (or electrical lengths), the designable values for different topologies vary widely, and therefore, differentiating circuit performance is a very important and efficient method. For example, it can be used to evaluate (1) the design range of termination duty ratio in transmission line impedance transformer applications, (2) the designable bandwidth of filter applications, (3) the design range of frequency ratio in dual band (DF) circuits, and so on. The allowed and forbidden regions may provide a very clearly visible boundary on the smith chart, separating the designable and un-designable ranges, as compared to the fuzzy constraint formula derived from the matching conditions. To our knowledge, this method is only suitable for single frequency applications. For dual-band and even multi-band applications, the flow chart is merely a way to describe the relationship between all the mathematical constraints. Typically, several numerical examples are also listed to show trends for all design parameters. However, the boundaries of the designable range for a particular topology are unpredictable.
Disclosure of Invention
The invention designs and develops a double-frequency point impedance converter of a parallel transmission line with a plurality of terminals, and aims to solve the problems of miniaturization and complex load matching of double-frequency signals on a microwave device.
The invention designs and develops an establishing method of a double-frequency point impedance converter of a parallel transmission line with a plurality of terminals, aims to establish a double-frequency matching structure of the parallel transmission line aiming at the double-frequency matching theory of a complex load impedance changing along with frequency, and discusses an establishing constraint condition of a double-frequency passive device under a complex load.
The invention designs and develops a double-frequency point impedance converter of a parallel transmission line with a plurality of terminals, aims to provide a measuring mode of a complex load and solves the problem of three-dimensional visualization of a design range of the double-frequency point complex load impedance converter.
The technical scheme provided by the invention is as follows:
the dual-frequency point impedance converter of the parallel transmission line with the complex number terminal comprises a source end impedance unit with a complex number load, a terminal impedance unit with a real number load, and a first transmission line and a second transmission line which are connected in parallel and are connected between the source end impedance unit with the complex number load and the terminal impedance unit with the real number load in series; and
the first transmission line and the second transmission line need to satisfy the following conditions: first transmission line impedance Z1>0 and a second transmission line impedance Z2>0；
Wherein the first transmission line impedance Z1And a second passLine transmission impedance Z2Are respectively as
Figure BDA0002392097220000031
Or
Figure BDA0002392097220000032
In the formula (I), the compound is shown in the specification,
Figure BDA0002392097220000033
qi＝Xi 2+Ri 2-Ri·RL，βirepresenting the propagation constant, l, of transmission lines at different frequency points1Denotes the physical length of the first transmission line,/2Denotes the physical length, X, of the second transmission lineiSource end impedance imaginary part, R, with complex load representing different frequency pointsiRepresenting source end impedance real part with complex load of different frequency points, RLRepresenting the termination impedance.
The method for establishing the double-frequency point impedance converter of the parallel transmission line with the plurality of terminals is used for establishing the double-frequency point impedance converter and comprises the following steps:
step one, determining the loads of the source end impedance unit with the complex load and the terminal impedance unit with the real load, determining the ABCD matrix of the first transmission line and the second transmission line and the ABCD matrix of the parallel structure of the first transmission line and the second transmission line, and obtaining the impedance Z of the first transmission line1And a second transmission line impedance Z2Are respectively as
Figure BDA0002392097220000034
Or
Figure BDA0002392097220000035
In the formula (I), the compound is shown in the specification,
Figure BDA0002392097220000036
qi＝Xi 2+Ri 2-Ri·RL，βirepresenting the propagation constant, l, of transmission lines at different frequency points1Denotes the physical length of the first transmission line,/2Denotes the physical length, X, of the second transmission lineiSource end impedance imaginary part, R, with complex load representing different frequency pointsiRepresenting source end impedance real part with complex load of different frequency points, RLRepresenting the termination impedance;
step two, enabling the first transmission line and the second transmission line to meet the following conditions: first transmission line impedance Z1>0 and a second transmission line impedance Z2>0, further determining the value ranges of the electrical lengths, the value ranges of the electrical length ratios and the value ranges of the frequency ratios of the first transmission line and the second transmission line;
step three, selecting a frequency ratio and an electrical length ratio according to the electrical length value range, the electrical length ratio value range and the frequency ratio value range of the first transmission line and the second transmission line to obtain the first transmission line and the second transmission line, and connecting the first transmission line and the second transmission line in parallel;
and fourthly, connecting the source end impedance unit with the complex load and the terminal impedance unit in series through a first transmission line and a second transmission line which are connected in parallel to obtain the double-frequency-point impedance converter.
The application of the establishing method of the double-frequency-point impedance converter using the parallel transmission line with the plurality of terminals in determining the frequency ratio of double frequency points comprises the following steps:
step one, taking the electrical length of the first transmission line as an abscissa and the electrical length of the second transmission line as an ordinate, and obtaining a plane which becomes an EL-EL plane;
adding an additional vertical FR axis with the frequency ratio as a vertical axis according to the value ranges of the electrical lengths, the value ranges of the electrical length ratios and the value ranges of the frequency ratios of the first transmission line and the second transmission line to obtain a 3D cube;
and step three, in the 3D cube, obtaining a value range of the frequency ratio of the double frequency points according to the value ranges of the electrical lengths and the value ranges of the electrical length ratios of the first transmission line and the second transmission line.
Compared with the prior art, the invention has the following beneficial effects:
1. under different conditions of a plurality of terminals, mapping modes of four designable areas are deduced and summarized on an EL-EL plane, and the value range of the electrical length of the parallel transmission line, the value range of the electrical length ratio and the value range of the frequency ratio are determined;
2. by adding an additional vertical FR axis, a novel 3D cube is newly introduced on the FR-EL-EL coordinate system for dual-frequency point design applications.
Drawings
Fig. 1 is a topology diagram of a dual-band point impedance transformer of a parallel transmission line having a plurality of terminals according to the present invention.
Fig. 2 is a map of the achievable ranges of electrical lengths in four regions in the case where the impedance expression is (5a) in the case of the present invention on the EL-EL plane.
Fig. 3 is a map of the achievable ranges of electrical lengths in four regions in the case where the impedance expression is (5b) in the case of the present invention on the EL-EL plane.
Fig. 4(a) is a map of the achievable range of electrical lengths in four regions in the case where the impedance expression is (5a) in the second case of the present invention on the EL-EL plane.
Fig. 4(b) is a map of the achievable range of electrical lengths in the four regions when the impedance expression is (5b) in the case of the second embodiment of the present invention on the EL-EL plane.
Fig. 5 is a map of the achievable ranges of electrical lengths in four regions on the EL-EL plane in the case of three described in the present invention.
Fig. 6 is a map of the achievable ranges of electrical lengths in four regions in the case of four described in the present invention on the EL-EL plane.
Fig. 7 is a schematic diagram of an equivalent alternative topology of fig. 1.
Fig. 8(a) is a schematic view of a 3D cube of example 1.
Fig. 8(b) is a schematic diagram of the circuit simulation result of embodiment 1.
Fig. 9(a) is a schematic view of a 3D cube of example 2.
Fig. 9(b) is a schematic diagram of the circuit simulation result of embodiment 2.
Fig. 10(a) is a schematic circuit diagram produced according to the parameters in example 1.
FIG. 10(b) is a graph comparing the results of the simulation and experiment in example 1.
Fig. 11(a) is a schematic circuit diagram produced according to the parameters in example 2.
FIG. 11(b) is a graph comparing the results of the simulation and experiment in example 2.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
As shown in fig. 1, the present invention provides a dual-frequency point impedance converter of a parallel transmission line with complex terminals, which includes a source terminal impedance unit with a complex load and a terminal impedance unit with a real load, where the source terminal impedance unit with the complex load and the terminal impedance unit with the real load are connected in series through a transmission line 1 and a transmission line 2 connected in parallel, and the transmission line 1 and the transmission line 2 need to satisfy the following conditions: transmission line 1 impedance Z1>0, and transmission line 2 impedance Z2>0; wherein the transmission line 1 has an impedance Z1And transmission line 2 impedance Z2Are respectively as
Figure BDA0002392097220000061
Or
Figure BDA0002392097220000062
In the formula (I), the compound is shown in the specification,
Figure BDA0002392097220000063
qi＝Xi 2+Ri 2-Ri·RL，βirepresenting the propagation constant, l, of transmission lines at different frequency points1Denotes the physical length of the transmission line 1,/2Denotes the physical length, X, of the transmission line 2iSource end impedance imaginary part, R, with complex load representing different frequency pointsiRepresenting source end impedance real part with complex load of different frequency points, RLRepresenting the termination impedance; z1And Z2Are respectively the characteristic impedance of two transmission lines, and the physical length is respectively l1And l2Can define l1>l2In order to design double frequency points, two frequency points are respectively defined as f1And f2Wherein is defined as1<f2And defining a ratio u ═ f2/f1,β1and beta2Are respectively at a frequency f1And f2The complex load at the last two frequencies can be respectively ZS1＝R1+jX1Representing a frequency f1Source load of, with ZS2＝R2+jX2Representing a frequency f2A source load of wherein R1，R2Is a positive number, and j is a representation of a complex number.
The invention also provides a method for establishing the double-frequency-point impedance converter of the parallel transmission line with the plurality of terminals, which comprises the following steps:
step one, determining the relation between characteristic impedance and electrical length:
the ABCD matrix of transmission lines 1 and 2 is obtained first, as shown in formula (1)
Figure BDA0002392097220000064
Figure BDA0002392097220000065
According to the parallel formula (2), the ABCD matrix of the structure after the ABCD matrixes of the two transmission lines are connected in parallel can be obtained,
APTLT＝(A1B2+A2B1)/(B1+B2) (2a)
BPTLT＝B1B2/(B1+B2) (2b)
CPTLT＝(C1+C2)+(A1-A2)(D2-D1)/(B1+B2) (2c)
DPTLT＝(B2D1+B1D2)/(B1+B2) (2d)
to communicate with a terminal load RLMatch to obtain formula (3a)
Figure BDA0002392097220000066
Equations (3b) and (3c) are obtained from the real part and the imaginary part being equal, respectively
DPTLTR＝APTLTRL+jCPTLTRLX (3b)
BPTLT＝CPTLTR·RL-jDPTLTX (3c)
Since the matrix itself has the characteristic AD-BC ═ 1, equation (4) can be derived from equation (3)
Figure BDA0002392097220000071
Figure BDA0002392097220000072
Thereby obtaining BPTLTDue to BPTLTIs two, Z can be obtained1And Z2There are two sets of expressions of (a) and (b), respectively as shown in equations (5a) and (5 b).
Figure BDA0002392097220000073
Or
Figure BDA0002392097220000074
Wherein p and q are represented by (5c) and (5d)
Figure BDA0002392097220000075
qi＝Xi 2+Ri 2-Ri·RL(5d)
Step two, determining the relation between the electrical length and the frequency ratio:
according to the impedance value being constant positive number, the frequency ratio u is divided into l range by analyzing the value range of trigonometric function in formula (5)2/l1the length of the two transmission lines can be selected at will in the realizable range, so the electrical length β at the first frequency point is defined1l1and beta1l2The value range of (a) is formula (6a), and in order to achieve the characteristic of double frequency points, the electrical length relationship under the two frequency points is defined as formula (6b), wherein a and b are non-negative integers, and m and n are positive integers.
Figure BDA0002392097220000076
Figure BDA0002392097220000081
In the present invention, | can be obtained2/l1M/n and gives the formula (7)
Figure BDA0002392097220000082
Figure BDA0002392097220000083
Step three, determining constraint conditions of complex terminal loads for double-frequency point design:
plural load (R) at two frequency points1，R2，X1，X2) Can be determined by the value of m + n, and, discussed separately, p at two frequency bins can be defined by (5c) and (5d)1，p2，q1，q2Equations (8a) and (8b) are respectively introduced into (5a) and (5b), and equation (9) is obtained, and the complex load relationship under two frequency points is solved:
Figure BDA0002392097220000084
Figure BDA0002392097220000085
Figure BDA0002392097220000086
when n + m is an even number, (R)1，R2，X1，X2) The relational expression between is (10)
Figure BDA0002392097220000087
When n + m is an odd number, (R)1，R2，X1，X2) The relational expression between (a) and (d) is (11a)1，d2Is expressed by two of d in (11b) and (11b)1And d2Respectively corresponding to impedance expressions of (5a) and (5b)
Figure BDA0002392097220000088
Figure BDA0002392097220000091
Step four, mapping analysis is carried out on the EL-EL plane, and the value ranges of the electric lengths, the value ranges of the electric length ratios and the value ranges of the frequency ratios of the transmission lines 1 and 2 are determined:
because the two frequency points have equal positions and can be interchanged, and the overall range contained in the interchange result is completely the same, the description is only carried out on the condition of the first frequency point.
by the electrical length β of the transmission line 11l1as abscissa, by the electrical length β of the transmission line 21l2As ordinate, the resulting plane becomes the EL-EL plane due to Z1>0，Z2>And 0, obtaining the mapping of the electric length value range capable of realizing the double frequency points on the EL-EL plane according to the (5a) and the (5b), and obtaining six different conditions according to the value of the complex load of different terminals:
the first condition is as follows: r1＞RL；
Case two: r1＜RLAnd is
Figure BDA0002392097220000094
Case three: r1＜RLAnd is
Figure BDA0002392097220000092
Case four: r1＜RLAnd is
Figure BDA0002392097220000093
Case five: r1＝RLAnd X1＞0；
Case six: r1＝RLAnd X1＜0；
In case one, since the impedance expressions are two groups and both can realize double frequency points, formula (5a) and formula (5b) need to be discussed separately, and in the condition that (5a) is the impedance expression, because R is1>RLAnd Z is1And Z2Are all positive numbers, p can be obtained1q1>0 and 0<|p1X1|<1, the period of the two transmission lines is 2 pi, therefore, the area in one period is divided into four areas which are named as area 1, area 2, area 3, area 4 and beta clockwise respectively1l1and beta1l2The value range is [2a pi, 2a pi + pi]&[2bπ,2bπ+π]Is marked as region 1 and has a value range of [2a pi, 2a pi + pi]&[2bπ+π,2bπ+2π]Is recorded as area 2, taking a rangeIs enclosed as [2a pi + pi, 2a pi +2 pi]&[2bπ+π,2bπ+2π]Is marked as region 3, and has a value range of [2a pi + pi, 2a pi +2 pi]&[2bπ+π,2bπ+2π]Is denoted as region 4.
First, the value of r is defined by the formula (12c), and the designable range of the electrical lengths of the two transmission lines in the region 1 is (12a) or (12b)
cos(β1l2)＞cos(rπ)＞cos(β1l1) (12a)
Or
cos(β1l1)＞cos(rπ)＞cos(β1l2) (12b)
cos(rπ)＝-p1X1(12c)
Equation (13) is derived from equation (12) and equation (7a), and the left diagonal region of region 1 in fig. 2 is drawn accordingly.
Figure BDA0002392097220000101
Or
Figure BDA0002392097220000102
The formula (13) can calculate that the ratio of the electrical lengths of the two transmission lines is in different value ranges, and the value range of the frequency ratio
2b/(2a+1)＜m/n＜(2b+r)/(2a+r) (14a)
Figure BDA0002392097220000103
Or
(2b+r)/(2a+r)＜m/n＜(2b+1)/2a (15a)
Figure BDA0002392097220000104
Similarly, the correlation results for region 2, region 3, and region 4 can be obtained, which are given in table 1(a), and a mapping of the achievable ranges of electrical lengths in the four regions on the EL-EL plane is plotted for the impedance expression (5a), as shown in fig. 2.
TABLE 1(a)
Figure BDA0002392097220000105
Figure BDA0002392097220000111
Similarly, when the impedance expression is (5b), a correlation result can be obtained and is given in table 1(b), while mapping the achievable range of electrical lengths in the four regions on the EL-EL plane is drawn as a right-oblique region in fig. 3.
TABLE 1(b)
Figure BDA0002392097220000121
Figure BDA0002392097220000131
In case two, it needs to discuss (5a) and (5b), respectively, and the final result of the extrapolation formula is given in table 2(a) and table 2(b), respectively, and the mapping result is shown in fig. 4(a) and fig. 4(b), wherein the left oblique area is the mapping range of (5a) and the right oblique area is the mapping range of (5 b).
TABLE 2(a)
Figure BDA0002392097220000132
Figure BDA0002392097220000141
TABLE 2(b)
Figure BDA0002392097220000142
Figure BDA0002392097220000151
In case three, it is necessary to discuss (5a) and (5b), respectively, and since the final derived formula results of (5a) and (5b) are completely consistent, the results of both are given in table 3, and the mapping results are shown in fig. 5, wherein the intersection region is the overlapping region of the left oblique region and the right oblique region, the left oblique region is the mapping range of (5a), and the right oblique region is the mapping range of (5 b).
TABLE 3
Figure BDA0002392097220000152
Figure BDA0002392097220000161
In case four, similar to case three, in case four, it is necessary to discuss (5a) and (5b) separately, since the final derived formula results of (5a) and (5b) are completely consistent, the results of both are given in table 4, and the mapping results are shown in fig. 6, where the intersection region is the overlapping region of the left oblique region and the right oblique region, the left oblique region is the mapping range of (5a), and the right oblique region is the mapping range of (5 b).
TABLE 4
Figure BDA0002392097220000162
Figure BDA0002392097220000171
In case five, since at R1＝RLAnd X1>At 0, the discussion results are the same as in case three, as shown in table 5.
TABLE 5
Figure BDA0002392097220000172
Figure BDA0002392097220000181
In case six, R1＝RL，X1<At 0, the discussion results are the same as in case four, as shown in table 6.
TABLE 6
Figure BDA0002392097220000182
The invention also provides the application of the establishing method of the double-frequency-point impedance converter using the parallel transmission line with the plurality of terminals in determining the frequency ratio of double frequency points, which comprises the following steps:
step 1, taking the electrical length of the transmission line 1 as an abscissa and the electrical length of the transmission line 2 as an ordinate, and obtaining a plane which becomes an EL-EL plane;
step 2, adding an additional vertical FR axis with the frequency ratio as a vertical axis according to the value ranges of the electrical lengths, the value ranges of the electrical length ratios and the value ranges of the frequency ratios of the transmission lines 1 and 2 to obtain a 3D cube;
and 3, in the 3D cube, obtaining the value range of the frequency ratio of the double frequency points according to the value ranges of the electrical lengths and the value ranges of the electrical length ratios of the transmission lines 1 and the transmission lines 2.
As shown in fig. 7, in order to realize the complex load in fig. 1, as a preferable example, a structure of fig. 7 is proposed, in which two cascaded transmission lines and one resistor are used instead of the complex load at two frequency points, and the characteristic impedances of the two transmission lines are Z respectivelySTL1And ZSTL2Electrical lengths are each thetaSTL1And thetaSTL2The resistance value of the resistor is RSTL；
Figure BDA0002392097220000191
Figure BDA0002392097220000192
All (Z) satisfying the formula (16)STL1，ZSTL2，θSTL1，θSTL2，RSTL) Can be used as an alternative parameter, so the result is not unique.
in step four, the specific results of 6 different cases have been given, including their designable range and formula in the EL-EL plane, by adding an additional vertical FR-axis named u, a novel 3D cube can be created in the FR-EL-EL coordinate system, for a given electrical length ratio β1l2/β1l1The design range of the frequency ratio u can be easily drawn in a 3D cube, and the present invention gives two design examples of case one and case three, respectively.
Examples
Plural loads ZSAt frequency f11GHz time ZS170-j50 at frequency f2Z at 3.6GHzS23.8-j2.2, when u is 3.6, since R1>RLThe mapping pattern belongs to case one, then p can be calculated from (8a) and (12c), respectively1and r from (12a) and (12b), a mapping pattern for case one can be easily drawn on the ADHE plane in FIG. 8(a), where there are two programmable areas, a light area representing (5a) and a dark area representing (5b), given β1l2/β1l1When 1/2, the line AJ will pass through region 1 and region 4, so the ABIJ plane can be easily created. If m is fixed, automatically determining n to 6, and by using (7a), drawing a solid line on the ABIJ plane, and finally, two solid lines on the ABIJ plane are the designable range of the frequency ratio u; the two black solid lines are the projections of the frequency ratio solid line on the ABFE plane and the ABCD plane, corresponding to fig. 8(a), and table 7 also lists the detailed design parameters of example 1, and the circuit simulation result thereof is shown in fig. 9(a), in which the characteristic impedance and the electrical length thereof are calculated by (5b) and (7a), respectively.
TABLE 7
Figure BDA0002392097220000201
Similarly, in example 2, the complex load ZSAt frequency f11GHz time ZS140-j200 at frequency f2Z at 2.2GHz S240+ j200, where u is 2.2, since the load condition is satisfied with case three, the mapping mode belongs to case three, the range of the 3D designable frequency ratio u is shown in fig. 8(b), the detailed design parameters are listed in table 7, and the circuit simulation result is shown in fig. 9 (b).
Two experimental circuits were manufactured, simulated and measured, respectively, corresponding to examples 1 and 2, the electromagnetic field simulation and measurement results being very well matched;
for example 1, the design parameters are shown in Table 7, using a Rogers RT/6010 plaque for experimental demonstration, with the data for the substrate being εr10.2, tan delta is 0.0023, the thickness h of the dielectric layer is 1.27mm, and the thickness t of the conductor is 0.018 mm; fig. 10(a) shows a schematic diagram of the fabricated circuit, and fig. 10(b) shows simulation and experimental results thereof.
For example 2, the design parameters are also shown in Table 7, demonstrated using the NPC-F260A baseplate; data of substrate is εr2.6, tan delta is 0.004, the thickness h of the dielectric layer is 0.996mm, and the thickness t of the conductor is 0.018 mm; fig. 11(a) shows a schematic diagram of the fabricated circuit, and fig. 11(b) shows simulation and experimental results thereof.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (10)

1. The dual-frequency point impedance converter of the parallel transmission line with the complex number terminal comprises a source end impedance unit with a complex number load and a terminal impedance unit with a real number load, and is characterized by further comprising a first transmission line and a second transmission line which are connected in parallel and are connected in series between the source end impedance unit with the complex number load and the terminal impedance unit with the real number load; and
the first transferThe transmission line and the second transmission line need to satisfy the following conditions: first transmission line impedance Z1>0 and a second transmission line impedance Z2>0；
Wherein the first transmission line impedance Z1And a second transmission line impedance Z2Are respectively as
Figure FDA0002392097210000011
Or
Figure FDA0002392097210000012
In the formula (I), the compound is shown in the specification,
Figure FDA0002392097210000013
qi＝Xi 2+Ri 2-Ri·RL，βirepresenting the propagation constant, l, of transmission lines at different frequency points1Denotes the physical length of the first transmission line,/2Denotes the physical length, X, of the second transmission lineiSource end impedance imaginary part, R, with complex load representing different frequency pointsiRepresenting source end impedance real part with complex load of different frequency points, RLRepresenting the termination impedance.
2. The dual-band point impedance transformer of claim 1, wherein the conditions to be satisfied by the first transmission line and the second transmission line according to different loads of the source impedance unit and the terminating impedance unit having the plurality of loads further comprise:
electrical length β of first transmission line at first frequency point1l1and the electrical length β of the second transmission line1l2Respectively have a value range of [2a pi, 2a pi + pi]And [2b π, 2b π + π]The time is a first threshold interval, and the value ranges are [2a pi, 2a pi + pi]And [2b π + π, 2b π +2 π]The time is a second threshold interval, and the value ranges are [2a pi + pi, 2a pi +2 pi]And [2b π + π, 2b π +2 π]The time is a third threshold interval, and the value ranges are respectively [2a pi ]+π，2aπ+2π]And [2b π + π, 2b π +2 π]The time is a fourth threshold interval; wherein a and b are any nonnegative integer, cos (r pi) ═ p1X1；
When R is1＞RLand when the value range of the electrical length is in the first threshold interval, the electrical length range is cos (β)1l2)＞cos(rπ)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(rπ)＞cos(β1l2)；
The electrical length ratio ranges from 2b/(2a +1) < m/n < (2b + r)/(2a + r) or (2b + r)/(2a + r) < m/n < (2b +1)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000021
Or
Figure FDA0002392097210000022
When R is1＞RLand when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (r pi) > cos (β)1l1)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(β1l1)＞cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2-r)/(2a + r) or (2b +2-r)/(2a + r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000023
Or
Figure FDA0002392097210000024
Or
electrical length in the cos (. beta.) range1l2)＞cos(β1l1) > -cos (r π) or-cos (r π) > cos (β)1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +1+ r)/(2a +1-r) or (2b +1+ r)/(2a +1-r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000025
Or
Figure FDA0002392097210000026
When R is1＞RLand when the value range of the electrical length is in the third threshold interval, the electrical length range is cos (β)1l1)＞-cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞-cos(rπ)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +2) < m/n < (2b +1+ r)/(2a +1+ r) or (2b +1+ r)/(2a +1+ r) < m/n < (2b +2)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000027
Or
Figure FDA0002392097210000028
When R is1＞RLand when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2) cos (r pi) or cos (r pi) > cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b + r)/(2a +2-r) or (2b + r)/(2a +2-r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000031
Or
Figure FDA0002392097210000032
Or
Range of electrical lengthis-cos (r pi) > cos (. beta.)1l2)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(β1l2)＞-cos(rπ)；
The electrical length ratio ranges from 2b/(2a +2) < m/n < (2b +1-r)/(2a +1+ r) or (2b +1-r)/(2a +1+ r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000033
Or
Figure FDA0002392097210000034
When R is1＜RL、
Figure FDA0002392097210000035
and when the value range of the electrical length is in the first threshold interval, the electrical length range is cos (β)1l1)＞-cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞-cos(rπ)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +1) < m/n < (2b +1-r)/(2a +1-r) or (2b +1-r)/(2a +1-r) < m/n < (2b +1)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000036
Or
Figure FDA0002392097210000037
When R is1＜RL、
Figure FDA0002392097210000038
and when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (r pi) > cos (β)1l2)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(β1l2)＞cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2-r)/(2a + r) or (2b +2-r)/(2a + r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000039
Or
Figure FDA00023920972100000310
Or
the electrical length range is-cos (r pi) > cos (β)1l1)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(β1l1)＞-cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +1+ r)/(2a +1-r) or (2b +1+ r)/(2a +1-r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000041
Or
Figure FDA0002392097210000042
When R is1＜RL、
Figure FDA0002392097210000043
and when the value range of the electrical length is in the third threshold interval, the electrical length range is cos (β)1l1)＞cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(rπ)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +2) < m/n < (2b +2-r)/(2a +2-r) or (2b +2-r)/(2a +2-r) < m/n < (2b +2)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000044
Or
Figure FDA0002392097210000045
When R is1＜RL、
Figure FDA0002392097210000046
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1) cos (r pi) or cos (r pi) > cos (β)1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b + r)/(2a +2-r) or (2b + r)/(2a +2-r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000047
Or
Figure FDA0002392097210000048
Or
electrical length in the cos (. beta.) range1l1)＞cos(β1l2) > -cos (r π) or-cos (r π) > cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from 2b/(2a +2) < m/n < (2b +1-r)/(2a +1+ r) or (2b +1-r)/(2a +1+ r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000049
Or
Figure FDA00023920972100000410
When R is1＜RL、
Figure FDA00023920972100000411
And the range of the electrical length is in the second threshold interval,electrical length in the cos (. beta.) range1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000051
When R is1＜RL、
Figure FDA0002392097210000052
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000053
When R is1＜RL、
Figure FDA0002392097210000054
and when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000055
When R is1＜RL、
Figure FDA0002392097210000056
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000057
When R is1＝RL、X1when the value range of the electrical length is larger than 0 and the value range of the electrical length is in the second threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000058
When R is1＝RL、X1when the value range of the electrical length is larger than 0 and the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000059
When R is1＝RL、X1when the value range of the electrical length is in the second threshold interval and is less than 0, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA00023920972100000510
When R is1＝RL、X1the electrical length is in cos (beta) range when the value range of the electrical length is less than 0 and the value range of the electrical length is in the fourth threshold interval1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000061
3. the dual-band point impedance transformer of claim 2, wherein the electrical length β of the first transmission line at the first frequency point is greater than the electrical length β of the parallel transmission line having a plurality of terminals1l1and the electrical length β of the second transmission line1l2Are respectively as
Figure FDA0002392097210000062
electrical length β of first transmission line at second frequency point2l1and the electrical length β of the second transmission line2l2Are respectively as
Figure FDA0002392097210000063
Wherein m and n are any positive integer, and m/n is l2/l1，u＝f2/f1，β1the propagation constant, beta, of the transmission line representing the first frequency point2The propagation constant, l, of the transmission line representing the second frequency point1Denotes the physical length of the first transmission line,/2Representing the physical length of the second transmission line.
4. The dual-band point impedance transformer of claim 3, wherein the source impedance element with complex load is constrained at dual-band point by the constraint of
Figure FDA0002392097210000064
When n + m is an even number,
Figure FDA0002392097210000065
when n + m is an odd number,
Figure FDA0002392097210000066
in the formula (I), the compound is shown in the specification,
Figure FDA0002392097210000071
Figure FDA0002392097210000072
X1representing the imaginary part, X, of the source end impedance with a complex load at a first frequency point2Representing the imaginary part of the source end impedance with complex load at the second frequency point, R1Representing the real part of the source end impedance with a complex load at a first frequency point, R2Representing the real part of the source end impedance with a complex load at a second frequency point, RLRepresenting the termination impedance.
5. Method for the creation of a dual-frequency point impedance transformer of a parallel transmission line with complex terminations, for the creation of a dual-frequency point impedance transformer according to any of claims 1-4, comprising the steps of:
step one, determining the loads of the source end impedance unit with the complex load and the terminal impedance unit with the real load, determining the ABCD matrix of the first transmission line and the second transmission line and the ABCD matrix of the parallel structure of the first transmission line and the second transmission line, and obtaining the impedance Z of the first transmission line1And a second transmission line impedance Z2Are respectively as
Figure FDA0002392097210000073
Or
Figure FDA0002392097210000074
In the formula (I), the compound is shown in the specification,
Figure FDA0002392097210000075
qi＝Xi 2+Ri 2-Ri·RL，βirepresenting the propagation constant, l, of transmission lines at different frequency points1Denotes the physical length of the first transmission line,/2Denotes the physical length, X, of the second transmission lineiSource end impedance imaginary part, R, with complex load representing different frequency pointsiRepresenting source end impedance real part with complex load of different frequency points, RLRepresenting the termination impedance;
step two, enabling the first transmission line and the second transmission line to meet the following conditions: first transmission line impedance Z1>0 and a second transmission line impedance Z2>0, further determining the value ranges of the electrical lengths, the value ranges of the electrical length ratios and the value ranges of the frequency ratios of the first transmission line and the second transmission line;
step three, selecting a frequency ratio and an electrical length ratio according to the electrical length value range, the electrical length ratio value range and the frequency ratio value range of the first transmission line and the second transmission line to obtain the first transmission line and the second transmission line, and connecting the first transmission line and the second transmission line in parallel;
and fourthly, connecting the source end impedance unit with the complex load and the terminal impedance unit in series through a first transmission line and a second transmission line which are connected in parallel to obtain the double-frequency-point impedance converter.
6. The method for establishing a dual-band point impedance transformer of a parallel transmission line having a plurality of terminals as set forth in claim 5, further comprising in said second step:
electrical length β of first transmission line at first frequency point1l1and the electrical length β of the second transmission line1l2Respectively have a value range of [2a pi, 2a pi + pi]And [2b π, 2b π + π]The time is a first threshold interval, and the value ranges are [2a pi, 2a pi + pi]And [2b π + π，2bπ+2π]The time is a second threshold interval, and the value ranges are [2a pi + pi, 2a pi +2 pi]And [2b π + π, 2b π +2 π]The time is a third threshold interval, and the value ranges are [2a pi + pi, 2a pi +2 pi]And [2b π + π, 2b π +2 π]The time is a fourth threshold interval; wherein a and b are any nonnegative integer, cos (r pi) ═ p1X1；
When R is1＞RLand when the value range of the electrical length is in the first threshold interval, the electrical length range is cos (β)1l2)＞cos(rπ)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(rπ)＞cos(β1l2)；
The electrical length ratio ranges from 2b/(2a +1) < m/n < (2b + r)/(2a + r) or (2b + r)/(2a + r) < m/n < (2b +1)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000081
Or
Figure FDA0002392097210000082
When R is1＞RLand when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (r pi) > cos (β)1l1)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(β1l1)＞cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2-r)/(2a + r) or (2b +2-r)/(2a + r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000083
Or
Figure FDA0002392097210000084
Or
electrical length in the cos (. beta.) range1l2)＞cos(β1l1) > -cos (r π) or-cos (r π) > cos (β)1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +1+ r)/(2a +1-r) or (2b +1+ r)/(2a +1-r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000091
Or
Figure FDA0002392097210000092
When R is1＞RLand when the value range of the electrical length is in the third threshold interval, the electrical length range is cos (β)1l1)＞-cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞-cos(rπ)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +2) < m/n < (2b +1+ r)/(2a +1+ r) or (2b +1+ r)/(2a +1+ r) < m/n < (2b +2)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000093
Or
Figure FDA0002392097210000094
When R is1＞RLand when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2) cos (r pi) or cos (r pi) > cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b + r)/(2a +2-r) or (2b + r)/(2a +2-r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000095
Or
Figure FDA0002392097210000096
Or
the electrical length range is-cos (r pi) > cos (β)1l2)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(β1l2)＞-cos(rπ)；
The electrical length ratio ranges from 2b/(2a +2) < m/n < (2b +1-r)/(2a +1+ r) or (2b +1-r)/(2a +1+ r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000097
Or
Figure FDA0002392097210000098
When R is1＜RL、
Figure FDA0002392097210000099
and when the value range of the electrical length is in the first threshold interval, the electrical length range is cos (β)1l1)＞-cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞-cos(rπ)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +1) < m/n < (2b +1-r)/(2a +1-r) or (2b +1-r)/(2a +1-r) < m/n < (2b +1)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000101
Or
Figure FDA0002392097210000102
When R is1＜RL、
Figure FDA0002392097210000103
When the value range of the electrical length is in the second threshold interval, the electrical lengthin the range cos (r pi) > cos (. beta.)1l2)＞cos(β1l1) or cos (. beta.) of1l1)＞cos(β1l2)＞cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2-r)/(2a + r) or (2b +2-r)/(2a + r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000104
Or
Figure FDA0002392097210000105
Or
the electrical length range is-cos (r pi) > cos (β)1l1)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(β1l1)＞-cos(rπ)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +1+ r)/(2a +1-r) or (2b +1+ r)/(2a +1-r) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000106
Or
Figure FDA0002392097210000107
When R is1＜RL、
Figure FDA0002392097210000108
and when the value range of the electrical length is in the third threshold interval, the electrical length range is cos (β)1l1)＞cos(rπ)＞cos(β1l2) or cos (. beta.) of1l2)＞cos(rπ)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +2) < m/n < (2b +2-r)/(2a +2-r) or (2b +2-r)/(2a +2-r) < m/n < (2b +2)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000109
Or
Figure FDA00023920972100001010
When R is1＜RL、
Figure FDA00023920972100001011
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1) cos (r pi) or cos (r pi) > cos (β)1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b + r)/(2a +2-r) or (2b + r)/(2a +2-r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000111
Or
Figure FDA0002392097210000112
Or
electrical length in the cos (. beta.) range1l1)＞cos(β1l2) > -cos (r π) or-cos (r π) > cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from 2b/(2a +2) < m/n < (2b +1-r)/(2a +1+ r) or (2b +1-r)/(2a +1+ r) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000113
Or
Figure FDA0002392097210000114
When R is1＜RL、
Figure FDA0002392097210000115
and when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000116
When R is1＜RL、
Figure FDA0002392097210000117
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000118
When R is1＜RL、
Figure FDA0002392097210000119
and when the value range of the electrical length is in the second threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA00023920972100001110
When R is1＜RL、
Figure FDA00023920972100001111
and when the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000121
When R is1＝RL、X1when the value range of the electrical length is larger than 0 and the value range of the electrical length is in the second threshold interval, the electrical length range is cos (β)1l1)＞cos(β1l2)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000122
When R is1＝RL、X1when the value range of the electrical length is larger than 0 and the value range of the electrical length is in the fourth threshold interval, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000123
When R is1＝RL、X1when the value range of the electrical length is in the second threshold interval and is less than 0, the electrical length range is cos (β)1l2)＞cos(β1l1)；
The electrical length ratio ranges from (2b +1)/(2a +1) < m/n < (2b +2)/2 a;
the range of the frequency ratio is
Figure FDA0002392097210000124
When R is1＝RL、X1the electrical length is in cos (beta) range when the value range of the electrical length is less than 0 and the value range of the electrical length is in the fourth threshold interval1l1)＞cos(β1l2)；
The electrical length ratio is in the range of 2b/(2a +2) < m/n < (2b +1)/(2a + 1);
the range of the frequency ratio is
Figure FDA0002392097210000125
7. The method for constructing a dual-band impedance transformer of a parallel transmission line having a plurality of terminals as claimed in claim 6, wherein in said step one,
the ABCD matrix of the first transmission line and the second transmission line is
Figure FDA0002392097210000126
Figure FDA0002392097210000127
The ABCD matrix of the structure after the ABCD matrixes of the first transmission line and the second transmission line are connected in parallel is
APTLT＝(A1B2+A2B1)/(B1+B2)；
BPTLT＝B1B2/(B1+B2)；
CPTLT＝(C1+C2)+(A1-A2)(D2-D1)/(B1+B2)；
DPTLT＝(B2D1+B1D2)/(B1+B2)。
8. The method for constructing a dual-band point impedance transformer of a parallel transmission line having a plurality of terminals as set forth in claim 5, wherein said step one further comprises:
determining the electrical length relationship between the first transmission line and the second transmission line under the double frequency points as
Figure FDA0002392097210000131
obtaining the electrical length β of the first transmission line under the first frequency point according to the frequency ratio of the double frequency points1l1and the electrical length β of the second transmission line1l2Are respectively as
Figure FDA0002392097210000132
electrical length β of first transmission line at second frequency point2l1and the electrical length β of the second transmission line2l2Are respectively as
Figure FDA0002392097210000133
Wherein m and n are any positive integer, and m/n is l2/l1，u＝f2/f1，β1the propagation constant, beta, of the transmission line representing the first frequency point2The propagation constant, l, of the transmission line representing the second frequency point1Denotes the physical length of the first transmission line,/2Representing the physical length of the second transmission line.
9. The method for constructing a dual-band-point impedance transformer of a parallel transmission line having a plurality of terminals as claimed in claim 5, wherein in said step one, the constraint condition of the source-side impedance unit having a plurality of loads at the dual-band point is
Figure FDA0002392097210000134
When n + m is an even number,
Figure FDA0002392097210000135
when n + m is an odd number,
Figure FDA0002392097210000141
in the formula (I), the compound is shown in the specification,
Figure FDA0002392097210000142
Figure FDA0002392097210000143
X1representing the imaginary part, X, of the source end impedance with a complex load at a first frequency point2Representing the imaginary part of the source end impedance with complex load at the second frequency point, R1Representing the real part of the source end impedance with a complex load at a first frequency point, R2Representing the real part of the source end impedance with a complex load at a second frequency point, RLRepresenting the termination impedance.
10. Use of a method of establishing a dual-band impedance transformer using a parallel transmission line with complex terminations according to any of claims 5-9 for determining the frequency ratio of dual bands, comprising the steps of:
step one, taking the electrical length of the first transmission line as an abscissa and the electrical length of the second transmission line as an ordinate, and obtaining a plane which becomes an EL-EL plane;
adding an additional vertical FR axis with the frequency ratio as a vertical axis according to the value ranges of the electrical lengths, the value ranges of the electrical length ratios and the value ranges of the frequency ratios of the first transmission line and the second transmission line to obtain a 3D cube;
and step three, in the 3D cube, obtaining a value range of the frequency ratio of the double frequency points according to the value ranges of the electrical lengths and the value ranges of the electrical length ratios of the first transmission line and the second transmission line.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102938640A (en) * 2012-10-26 2013-02-20 南京信息工程大学 Dual-frequency impedance-matching network
CN105186089A (en) * 2015-09-30 2015-12-23 南京航空航天大学 Miniaturized high-frequency ratio microwave dual-frequency power divider
CN105789849A (en) * 2014-12-18 2016-07-20 哈尔滨飞羽科技有限公司 Dual-frequency band antenna based on parallel transmission line
CN109687834A (en) * 2019-01-25 2019-04-26 吉林大学 A kind of impedance transformer and preparation method with Chebyshev's filtering characteristic of multistage transmission line and short-circuit line

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102938640A (en) * 2012-10-26 2013-02-20 南京信息工程大学 Dual-frequency impedance-matching network
CN105789849A (en) * 2014-12-18 2016-07-20 哈尔滨飞羽科技有限公司 Dual-frequency band antenna based on parallel transmission line
CN105186089A (en) * 2015-09-30 2015-12-23 南京航空航天大学 Miniaturized high-frequency ratio microwave dual-frequency power divider
CN109687834A (en) * 2019-01-25 2019-04-26 吉林大学 A kind of impedance transformer and preparation method with Chebyshev's filtering characteristic of multistage transmission line and short-circuit line

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