CN109687834B - Chebyshev filtering impedance converter and method for multi-order transmission line and short-circuit line - Google Patents

Chebyshev filtering impedance converter and method for multi-order transmission line and short-circuit line Download PDF

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CN109687834B
CN109687834B CN201910071791.XA CN201910071791A CN109687834B CN 109687834 B CN109687834 B CN 109687834B CN 201910071791 A CN201910071791 A CN 201910071791A CN 109687834 B CN109687834 B CN 109687834B
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transmission line
line
short
order
circuit
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CN109687834A (en
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王小龙
包春喜
吴斌
王庆凤
卢革宇
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Jilin University
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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
    • H03H7/01—Frequency selective two-port networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/39—Circuit design at the physical level
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/18—Manufacturability analysis or optimisation for manufacturability

Abstract

The invention discloses an impedance transformer with Chebyshev filtering characteristics of a multi-order transmission line and a short-circuit line, which comprises an input end unit and an output end unit, wherein impedance transformation units are sequentially connected in series between the input end unit and the output end unit through the multi-order transmission line; and short-circuit lines not exceeding the number of the multi-stage transmission lines; when the multi-order transmission line is an odd order, the short connection line is an even number of sections and is symmetrically distributed on two sides of the center of the multi-order transmission line; when the multi-order transmission line is in an even order and the short circuit line is in an even section, the short circuit line is symmetrically distributed on two sides of the center of the multi-order transmission line; when the multi-order transmission line is an even order and the short circuit line is an odd-order section, a section of short circuit line is arranged at the center of the multi-order transmission line, and the residual short circuit lines are symmetrically distributed on two sides of the center of the multi-order transmission line. The invention also provides a preparation method of the impedance converter with the Chebyshev filter characteristic of the multi-order transmission line and the short-circuit line.

Description

Chebyshev filtering impedance converter and method for multi-order transmission line and short-circuit line
Technical Field
The invention relates to the technical field of manufacturing of microstrip line devices of radio frequency circuits, in particular to an impedance converter with Chebyshev filter characteristics and a preparation method of the impedance converter with multistage transmission lines and short-circuit lines.
Background
With the rapid development of the times, the demand of the whole society for information elements is increasingly more. The human beings have been greatly improved in the field of communication technology from the age of transmitting information through the most original wolf smoke to the transmission of information through the use of electricity and electromagnetism at present. Wherein, the electromagnetic transmission information becomes the neutral column of the whole modern communication technology. In the case of wireless electromagnetic transmission of information, a transmitting device and a receiving device are required, the impedance transformer playing an important role. When modern communication equipment electromagnetically transmits information, noise of other frequencies except useful signals needs to be filtered out while low insertion loss and low delay effect are met, interference among other frequency bands is reduced, and transmission information quality is improved. On the other hand, as the electromagnetic communication technology is popularized, the air has many frequency band space noises, and when information is transmitted, the air noises must be filtered. The impedance transformer made of the microstrip line has good filtering effect.
The impedance converter made of the microstrip line can theoretically change the impedance of the microstrip line, has good frequency selection characteristic and is relatively sensitive. Since there is a great demand for such an impedance converter having a good filter characteristic with the spread of wireless communication technology, the impedance converter having the chebyshev filter characteristic can be manufactured at low cost and in mass production. Such as: in mobile communication, the antenna of the mobile phone is miniaturized, and the market demand is large, so that mass production is required. The impedance transformer made of the microstrip line has just these characteristics.
The general impedance converter with the ripple filter characteristics of Chebyshev and the like can achieve particularly good ripple of Chebyshev and the like only by connecting n sections of microstrip lines in series and connecting n +1 short wires (grounding wires). A circuit diagram of a typical 4-segment transmission line impedance transformer is shown in fig. 1. The circuit board is very complicated in the manufacturing process due to the need of more short wires.
Disclosure of Invention
The invention aims to design and develop an impedance converter with Chebyshev filter characteristics of a multi-order transmission line and a short-circuit line, reduce the number of short-circuit wires of the impedance converter, change the impedance of the input end of a device, have the Chebyshev filter characteristics and work at a specific frequency.
The invention also aims to design and develop a preparation method of the impedance converter with the Chebyshev filter characteristic of the multi-order transmission line and the short-circuit line, the number of the short-circuit lines of the impedance converter is reduced, the characteristic impedance of the short-circuit lines at different positions is different, a model of a device can be selected according to requirements, and the flexibility is high.
The technical scheme provided by the invention is as follows:
an impedance converter with Chebyshev filtering characteristics of a multi-order transmission line and a short-circuit line comprises an input end unit, an output end unit and an impedance transformation unit which is sequentially connected in series between the input end unit and the output end unit through the multi-order transmission line; and
short-circuit wires not exceeding the number of the multi-stage transmission lines;
when the multi-order transmission line is an odd order, the short connection line is an even number of sections and is symmetrically distributed on two sides of the center of the multi-order transmission line;
when the multi-order transmission line is in an even order and the short circuit line is in an even section, the short circuit line is symmetrically distributed on two sides of the center of the multi-order transmission line;
when the multi-order transmission line is an even order and the short circuit line is an odd-order section, a section of short circuit line is arranged at the center of the multi-order transmission line, and the residual short circuit lines are symmetrically distributed on two sides of the center of the multi-order transmission line.
Preferably, the multi-order transmission line is 4-order, the short-circuit line is 2-segment, and the short-circuit line is symmetrically distributed on two sides of the center of the 4-order transmission line.
Preferably, the multi-order transmission line has 4 orders, the short-circuit lines have 3 sections, one section of the short-circuit line is arranged in the center of the 4-order transmission line, and the remaining two sections of the short-circuit lines are symmetrically arranged on two sides of the center of the 4-order transmission line.
Preferably, the multi-order transmission line is 4-order, the short-circuit line is 4 sections, and the short-circuit line is symmetrically distributed on two sides of the center of the 4-order transmission line.
A method for preparing an impedance converter with Chebyshev filtering characteristics of a multi-order transmission line and a short-circuit line comprises the following steps:
step 1: establishing an n-order transmission line ABCD matrix and a short-circuit line ABCD matrix:
Figure GDA0002670946000000031
Figure GDA0002670946000000032
wherein the content of the first and second substances,
Figure GDA0002670946000000033
is an ABCD matrix of the ith transmission line in the n-order transmission lines,
Figure GDA0002670946000000034
is ABCD matrix of k-th section of short-circuit wire in n-stage transmission line, n is transmission line order, S is short-circuit wire number, theta is electric length of transmission line and short-circuit wire, ZiIs the characteristic impedance of the i-th transmission line of the n-order transmission line, ZskThe characteristic impedance of the kth section of short-circuit wire in the n-order transmission line;
step 2: sequentially multiplying the transmission line ABCD matrix and the short connecting line ABCD matrix along the direction from the input end to the output end of the n-order transmission line according to the position relationship of the transmission line and the short connecting line
Figure GDA0002670946000000035
And step 3: determining the transmission coefficient from the input end to the output end of the n-order transmission line as follows:
Figure GDA0002670946000000036
wherein k is ZS/ZLAnd k is not less than 1,
Figure GDA0002670946000000037
for transmission coefficient from input to output of n-order transmission line, ZSIs an n-order transmission line input terminal unitImpedance, ZLIs the unit impedance of the output end of the n-order transmission line;
and 4, step 4: according to the transmission formula of n-order Chebyshev and other ripples under ideal conditions:
Figure GDA0002670946000000038
so that
Figure GDA0002670946000000039
And determining the characteristic impedance values of the n-section transmission line and the S-section short-circuit line in the n-order transmission line.
Preferably, in step 2, the transmission line ABCD matrix and the shorting line ABCD matrix are multiplied to obtain
Figure GDA00026709460000000310
Figure GDA00026709460000000311
Figure GDA00026709460000000312
Figure GDA00026709460000000313
Figure GDA0002670946000000041
Wherein, a0,a1,...,an；b0,b1,...,bn,bn+1；c0,c1,...,cn,cn+1；d0,d1,...,dnIs a coefficient and is determined by the characteristic impedance of each section of transmission line and shorting stub.
Preferably, in step 3, the determination of the transmission coefficient from the input end to the output end of the n-th order transmission line is determined by the following formula;
Figure GDA0002670946000000042
and is
Figure GDA0002670946000000043
Wherein S is11The reflection coefficient from the input end to the output end of the n-order transmission line.
Preferably, in step 3,
Figure GDA0002670946000000044
wherein, X0,X1,...,Xn；Y0,Y1,...,Yn,Yn+1Is a characteristic impedance coefficient, and Xn＝(an-kdn)，Yn+1＝(bn+1-kcn+1)。
Preferably, in step 4:
order to
Figure GDA0002670946000000045
So that
Figure GDA0002670946000000046
Figure GDA0002670946000000047
Wherein u is0,u1,...,un,un+1Is a coefficient;
determined by the correspondence coefficient equality:
when n is an even number, the number of n,
X0＝X2＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y3＝u3,Y1＝u1；
when n is an odd number, the number of the transition metal atoms,
X1＝X3＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y2＝u2,Y0＝u0；
and determining the relation between the characteristic impedance values of the n-section transmission line and the S-section short-circuit line according to the relation between the coefficients, and solving the characteristic impedance values of the n-section transmission line and the S-section short-circuit line.
Preferably, the method further comprises the following steps:
inputting the obtained characteristic impedance values of the n-segment transmission line and the S-segment short-circuit line into ADS to obtain the line length and the line width of the n-segment transmission line and the S-segment short-circuit line,
inputting the line length and the line width into Sonnet for electromagnetic field simulation, and correcting to obtain the actual line length and line width of the n-section transmission line and the S-section short-circuit line;
and manufacturing a front panel model according to the actual line length and the line width, manufacturing the front panel model into a 1:1 picture format, printing the front panel model in a circuit board printer, and corroding the copper plate by using corrosive liquid.
The invention has the following beneficial effects:
(1) the impedance converter with the Chebyshev filter characteristic of the multi-order transmission line and the short-circuit line designed and developed by the invention reduces the number of the short-circuit wires of the impedance converter, can change the impedance of the input end of the device, has the Chebyshev filter characteristic and works at a specific frequency. And its filtering characteristics are relatively flat. On the other hand, compared with the traditional impedance converter with the Chebyshev filter characteristic, the impedance converter can realize the Chebyshev filter characteristic by a relatively flexibly changed model under a specific constraint condition.
(2) The invention designs and develops a preparation method of an impedance converter with Chebyshev filtering characteristics of a multi-order transmission line and a short-circuit line, which reduces the number of short-circuit wires of the impedance converter and the number of short-circuit wires connected with the impedance converter. The impedance transformer can be better selected according to the parameter design of the microstrip line and the like, and which model is used for making the impedance transformer. And the characteristic impedance of the short-circuit wires at different positions is different, so that the model of the device can be selected according to the engineering requirements, and the flexibility is high.
Drawings
Fig. 1 is a diagram of a design of an impedance transformer implemented by n-segment transmission lines and (n +1) -segment shorting lines of a general chebyshev filter characteristic.
Fig. 2 is a design diagram of an impedance converter according to embodiment 1 of the present invention.
Fig. 3 is a design diagram of an impedance converter according to embodiment 2 of the present invention.
Fig. 4 is a design diagram of an impedance converter according to embodiment 3 of the present invention.
Fig. 5 is a design diagram of an impedance converter according to embodiment 4 of the present invention.
Fig. 6 is a design diagram of an impedance converter according to embodiment 5 of the present invention.
Fig. 7 is a waveform diagram of a simulation of the equiripple impedance converter obtained in ADS in embodiment 1 of the present invention.
Fig. 8 is a simulated waveform diagram of the equiripple impedance converter obtained after Sonnet correction in embodiment 1 of the present invention.
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.
The invention provides an impedance transformer with Chebyshev filter characteristics for multi-order transmission lines and short-circuit lines, comprising: the input end unit and the output end unit, and also comprises impedance transformation units which are sequentially connected in series between the input end element and the output end unit through a multi-order transmission line; and the number of the short-circuit wires is not more than that of the multi-order transmission lines, when the multi-order transmission lines are of odd orders, the short-circuit wires are of even-numbered sections and are symmetrically distributed on two sides of the center of the multi-order transmission lines; when the multi-order transmission line is in an even order and the short circuit line is in an even section, the short circuit line is symmetrically distributed on two sides of the center of the multi-order transmission line; when the multi-order transmission line is an even order and the short circuit line is an odd-order section, a section of short circuit line is arranged at the center of the multi-order transmission line, and the residual short circuit lines are symmetrically distributed on two sides of the center of the multi-order transmission line.
Example 1
As shown in fig. 2, the present embodiment is a 4-order transmission line, which is sequentially connected in series between the input end unit and the output end unit, the number of shorting bars is 2, the shorting bars are symmetrically distributed at two sides of the center of the 4-order transmission line, a specific first-stage shorting bar is arranged between the first-stage transmission line and the second-stage transmission line, and a second-stage shorting bar is arranged between the third-end transmission line and the fourth-stage transmission line, so as to obtain the chebyshev-like ripple filtering characteristics.
Example 2
As shown in fig. 3, the present embodiment is a 4-step transmission line, which is sequentially and serially arranged between the input end unit and the output end unit, the number of the short-circuit wires is 2, the short-circuit wires are symmetrically distributed at two sides of the center of the 4-step transmission line, a specific first-stage short-circuit wire is arranged between the first-stage transmission line and the input end unit, and a second-stage short-circuit wire is arranged between the fourth-stage transmission line and the output end unit. In this case, the electrical length and the characteristic impedance of the shorting line were changed as compared to example 1. In this case, different options can be selected according to the engineering requirements of the user.
Example 3
As shown in fig. 4, the present embodiment is a 4-order transmission line, which is sequentially and serially arranged between an input end unit and an output end unit, the number of short-circuit lines is 3, one short-circuit line is arranged in the center of the 4-order transmission line, the remaining two short-circuit lines are symmetrically arranged on two sides of the center of the 4-order transmission line, a specific first short-circuit line is arranged between a second transmission line and a third transmission line, and a specific value is selected, the second short-circuit line is arranged between the first transmission line and the second transmission line, and the third short-circuit line is arranged between the third transmission line and a fourth transmission line.
Example 4
As shown in fig. 5, the present embodiment is a 4-order transmission line, which is sequentially and serially arranged between an input end unit and an output end unit, the number of short-circuit lines is 3, one short-circuit line is arranged in the center of the 4-order transmission line, the remaining two short-circuit lines are symmetrically arranged on two sides of the center of the 4-order transmission line, a specific first short-circuit line is arranged between a second short-circuit line and a third short-circuit line, and a specific value is selected, the second short-circuit line is arranged between the first short-circuit line and the input end unit, and the third short-circuit line is arranged between a fourth short-circuit line and the output.
Example 5
As shown in fig. 6, the present embodiment is a 4-order transmission line, which is sequentially and serially connected between an input end unit and an output end unit, the shorting lines are 4 segments, and the shorting lines are symmetrically distributed on two sides of the center of the 4-order transmission line, specifically, the first segment shorting line is arranged between the first segment transmission line and the input end unit, the 2 nd segment shorting line is arranged between the fourth segment transmission line and the output end unit, the third segment shorting line is arranged between the first segment transmission line and the second segment transmission line, and the fourth segment shorting line is arranged between the third segment transmission line and the fourth segment transmission line.
The impedance converter with the Chebyshev filter characteristic of the multi-order transmission line and the short-circuit line designed and developed by the invention reduces the number of the short-circuit wires of the impedance converter, can change the impedance of the input end of the device, has the Chebyshev filter characteristic and works at a specific frequency. And its filtering characteristics are relatively flat. On the other hand, compared with the traditional impedance converter with the Chebyshev filter characteristic, the impedance converter can realize the Chebyshev filter characteristic by a relatively flexibly changed model under a specific constraint condition.
The invention also provides a preparation method of the impedance converter with the Chebyshev filter characteristic of the multi-order transmission line and the short-circuit line, which comprises the following steps:
step 1: establishing an n-order transmission line ABCD matrix and a short-circuit line ABCD matrix:
Figure GDA0002670946000000081
Figure GDA0002670946000000082
wherein the content of the first and second substances,
Figure GDA0002670946000000083
is an ABCD matrix of the ith transmission line in the n-order transmission lines,
Figure GDA0002670946000000084
is an ABCD matrix of the kth short-circuit wire in n-stage transmission line, n is the transmission line order, S is the number of short-circuit wire segments, theta is the electrical length of the transmission line and the short-circuit wire (in the embodiment, the electrical length of the transmission line and the short-circuit wire are consistent, and are both 1/4 wave lengths), Z isiIs the characteristic impedance of the i-th transmission line of the n-order transmission line, ZskThe characteristic impedance of the kth section of short-circuit wire in the n-order transmission line;
step 2: sequentially multiplying the transmission line ABCD matrix and the short connecting line ABCD matrix along the direction from the input end to the output end of the n-order transmission line according to the position relationship of the transmission line and the short connecting line
Figure GDA0002670946000000085
Figure GDA0002670946000000086
Figure GDA0002670946000000087
Figure GDA0002670946000000088
Figure GDA0002670946000000089
Wherein, a0,a1,...,an；b0,b1,...,bn,bn+1；c0,c1,...,cn,cn+1；d0,d1,...,dnIs a coefficient and is transmitted by each segmentThe characteristic impedance of the wire and the shorting stub is determined.
And step 3: according to the following formula:
Figure GDA00026709460000000810
and is
Figure GDA00026709460000000811
Wherein S is11The reflection coefficient from the input end to the output end of the n-order transmission line.
Determining the transmission coefficient from the input end to the output end of the n-order transmission line:
Figure GDA0002670946000000091
wherein k is ZS/ZLAnd k is not less than 1,
Figure GDA0002670946000000092
for transmission coefficient from input to output of n-order transmission line, ZSIs the unit impedance of the input end of the n-order transmission line, ZLIs the unit impedance of the output end of the n-order transmission line;
that is, it can be determined that:
Figure GDA0002670946000000093
wherein, X0,X1,...,Xn；Y0,Y1,...,Yn,Yn+1Is a characteristic impedance coefficient, and Xn＝(an-kdn)，Yn+1＝(bn+1-kcn+1)。
And 4, step 4: according to the transmission formula of n-order Chebyshev and other ripples under ideal conditions:
Figure GDA0002670946000000094
Figure GDA0002670946000000095
wherein u is0,u1,...,un,un+1Is a coefficient;
so that
Figure GDA0002670946000000096
Namely, it is
Figure GDA0002670946000000097
Determined by the correspondence coefficient equality:
when n is an even number, the number of n,
X0＝X2＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y3＝u3,Y1＝u1；
when n is an odd number, the number of the transition metal atoms,
X1＝X3＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y2＝u2,Y0＝u0；
and determining a relation simultaneous equation set between the characteristic impedance values of the n-section transmission line and the S-section short connection line according to the relation between the coefficients, and solving the characteristic impedance values of the n-section transmission line and the S-section short connection line.
And 5: inputting the obtained characteristic impedance values of the n-segment transmission line and the S-segment short-circuit line into ADS to obtain the line length and the line width of the n-segment transmission line and the S-segment short-circuit line,
inputting the line length and the line width into Sonnet for electromagnetic field simulation, and correcting to obtain the actual line length and line width of the n-section transmission line and the S-section short-circuit line;
and manufacturing a front panel model according to the actual line length and the line width, manufacturing the front panel model into a 1:1 picture format, printing the front panel model in a circuit board printer, and corroding the copper plate by using corrosive liquid.
The following embodiment 1 is an example to specifically describe the method for manufacturing an impedance transformer having chebyshev filter characteristics for a multi-stage transmission line and a short-circuited line according to the present invention:
first, the concept of chebyshev-like ripples will be described. First, the n-order Chebyshev polynomial uses Tn(x) Polynomial of degree n of the representation. Wherein the first few chebyshev polynomials are:
T1(x)＝x
T2(x)＝2x2-1
T3(x)＝4x3-3x
T4(x)＝8x3-8x+1
.....
the higher order chebyshev polynomial may be represented by a recursive formula:
Tn＝2xTn-1(x)-Tn-2(x)
for the chebyshev formula, the following properties are possible:
1. for x is-1 or more and 1 or less, | Tn(x) Less than or equal to 1. For x in the interval for-1 to 1, the chebyshev polynomial oscillates between plus and minus 1.
2. For | x | > 1, do not oscillate between plus or minus 1, | Tn(x) L increases rapidly with increasing x and n.
If x is cos θ, the whole | Tn(x) And l oscillates between plus and minus 1, so that chebyshev waves and the like are obtained.
The method specifically comprises the following steps:
step 1: establishing a 4-order transmission line ABCD matrix and a short-circuit line ABCD matrix:
Figure GDA0002670946000000101
Figure GDA0002670946000000102
wherein the content of the first and second substances,
Figure GDA0002670946000000103
is an ABCD matrix of the ith transmission line in the 4-step transmission line,
Figure GDA0002670946000000104
is ABCD matrix of k-th short-circuit wire in 4-stage transmission line, 4 is transmission line order, i.e. 4-end transmission line, the number of short-circuit wire sections is 2, theta is electric length of transmission line and short-circuit wire, ZiIs the characteristic impedance of the i-th transmission line of the n-order transmission line, ZskThe characteristic impedance of the kth section of short-circuit wire in the n-order transmission line;
step 2: along the direction from the input end to the output end of the n-order transmission line, according to the position relationship of the transmission line and the short connection line (as shown in fig. 2), the transmission line ABCD matrix and the short connection line ABCD matrix are sequentially multiplied to obtain:
Figure GDA0002670946000000111
AT＝a4cos4θ+a2cos2θ+a0；
Figure GDA0002670946000000112
Figure GDA0002670946000000113
DT＝d4cos4θ+d2cos2θ+d0；
the respective coefficients are determined by the impedances of the respective transmission lines and the short-circuiting wires:
Figure GDA0002670946000000114
Figure GDA0002670946000000115
Figure GDA0002670946000000116
Figure GDA0002670946000000117
Figure GDA0002670946000000118
Figure GDA0002670946000000119
Figure GDA00026709460000001110
Figure GDA00026709460000001111
Figure GDA00026709460000001112
Figure GDA00026709460000001113
Figure GDA0002670946000000121
Figure GDA0002670946000000122
and step 3: according to the following formula:
Figure GDA0002670946000000123
and is
Figure GDA0002670946000000124
Wherein S is11The reflection coefficient from the input end to the output end of the n-order transmission line.
Determining the transmission coefficient from the input end to the output end of the n-order transmission line:
Figure GDA0002670946000000125
wherein k is Zl/ZsAnd k is not less than 1,
Figure GDA0002670946000000126
for transmission coefficient from input to output of n-order transmission line, ZsIs the unit impedance of the input end of the n-order transmission line, ZlIs the unit impedance of the output end of the n-order transmission line;
let Xn＝(an-kdn)，Yn+1＝(bn+1-kcn+1)；
That is, it can be determined that:
Figure GDA0002670946000000127
and 4, step 4: according to a 4-order Chebyshev-like ripple transmission formula under an ideal condition:
Figure GDA0002670946000000128
wherein the content of the first and second substances,
Figure GDA0002670946000000129
u1,u3,u5are coefficients and are known constants;
so that
Figure GDA00026709460000001210
Namely, it is
Figure GDA00026709460000001211
Namely, it is
Figure GDA00026709460000001212
Determined by the correspondence coefficient equality:
X0＝X2＝X4＝0；
Y5＝u5,Y3＝u3,Y1＝u1；
simultaneous can result in a system of equations containing 6 equations:
Figure GDA0002670946000000131
and a is0,a2,a4,d0,d2,d4,b1,b3,b5,c1,c3,c5The relation between the impedance of each transmission line and the impedance of the short connecting line is as the formula in the step 2, and the unique solution of the impedance of each transmission line and the impedance of the short connecting line can be solved because 6 equations correspond to 6 unknowns. The impedance values of the transmission lines and the shorting stub are shown in table 1.
TABLE 1 impedance values of transmission lines and short-circuit lines
Serial number Impedance (Ohm)
First transmission line 71.8238762
First segment shorting stub 135.3865211
Second transmission line 54.1909639
Third-segment transmission line 38.3187981
Second-stage short-circuit wire 39.0896958
A fourth transmission line 35.9119381
And 5: the ADS verifies whether the obtained value (impedance value of each transmission line and the short-circuit line) is the same as the ideal chebyshev ripple. As shown in fig. 7.
Step 6: and setting board parameters in the experiment in the ADS to obtain corresponding line length and line width, and then performing electromagnetic field simulation in the Sonnet. Since the line length and the line width calculated in the ADS are empirically calculated values, there is some error between it and the real data. Therefore, the line length of the 6 transmission lines needs to be changed during the electromagnetic field simulation to obtain the optimal data which we want.
Finally, under the correction in Sonnet, the line length and the line width of 4 transmission lines and S-short connecting lines are obtained, and the specific data are shown in table 2.
TABLE 2 corrected model data
Serial number Linear length (mm) Line width (mm)
First transmission line 18.55 1.32
First segment shorting stub 19.10 0.30
Second transmission line 18.29 2.12
Third-segment transmission line 17.95 3.52
Second-stage short-circuit wire 19.00 3.42
A fourth transmission line 17.47 3.84
From the corrected data, a waveform diagram is generated in Sonnet, and as shown in fig. 8, it can be seen that ripples such as chebyshev can be obtained, which means that the method is reasonable.
And 7: the front panel model obtained from Sonnet was prepared in a 1:1 picture format and a model drawing was prepared for printing. And printing the output picture in a microwave circuit board printer MDP-10. And etching the copper plate by using the solution to form the circuit board model.
The invention designs and develops a preparation method of an impedance converter with Chebyshev filtering characteristics of a multi-order transmission line and a short-circuit line, which reduces the number of short-circuit wires of the impedance converter and the number of short-circuit wires connected with the impedance converter. The impedance transformer can be better selected according to the parameter design of the microstrip line and the like, and which model is used for making the impedance transformer. And the characteristic impedance of the short-circuit wires at different positions is different, so that the model of the device can be selected according to the engineering requirements, and the flexibility is high.
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 (8)

1. An impedance converter with Chebyshev filter characteristics of a multi-order transmission line and a short-circuit line comprises an input end unit and an output end unit, and is characterized by also comprising impedance transformation units which are sequentially connected in series between the input end unit and the output end unit through the multi-order transmission line; and
short-circuit wires not exceeding the number of the multi-stage transmission lines;
when the multi-order transmission line is an odd order, the short connection line is an even number of sections and is symmetrically distributed on two sides of the center of the multi-order transmission line;
when the multi-order transmission line is in an even order and the short circuit line is in an even section, the short circuit line is symmetrically distributed on two sides of the center of the multi-order transmission line;
when the multi-order transmission line is an even order and the short circuit line is an odd-order section, a section of short circuit line is arranged at the center of the multi-order transmission line, and the residual short circuit lines are symmetrically distributed on two sides of the center of the multi-order transmission line.
2. The impedance transformer of claim 1, wherein the multi-order transmission line is 4-order, the shorting-line is 2-order, and the shorting-line is symmetrically distributed on both sides of the center of the 4-order transmission line.
3. The impedance transformer of claim 1, wherein the multi-order transmission line has 4 stages, and the shorting lines have 3 sections, wherein one section of the shorting line is disposed at the center of the 4-stage transmission line, and the remaining two sections of the shorting line are symmetrically disposed at two sides of the center of the 4-stage transmission line.
4. The impedance transformer of claim 1, wherein the multi-order transmission line is 4-order, the shorting bar is 4-segment, and the shorting bar is symmetrically distributed on both sides of the center of the 4-order transmission line.
5. A method for preparing an impedance converter with Chebyshev filter characteristics of a multi-order transmission line and a short-circuit line is characterized by comprising the following steps:
step 1: establishing an n-order transmission line ABCD matrix and a short-circuit line ABCD matrix:
Figure FDA0002641229720000011
Figure FDA0002641229720000012
wherein the content of the first and second substances,
Figure FDA0002641229720000021
is an ABCD matrix of the ith transmission line in the n-order transmission lines,
Figure FDA0002641229720000022
is ABCD matrix of k-th section of short-circuit wire in n-stage transmission line, n is transmission line order, S is short-circuit wire number, theta is electric length of transmission line and short-circuit wire, ZiIs the characteristic impedance of the i-th transmission line of the n-order transmission line, ZskThe characteristic impedance of the kth section of short-circuit wire in the n-order transmission line;
step 2: sequentially multiplying the transmission line ABCD matrix and the short connecting line ABCD matrix along the direction from the input end to the output end of the n-order transmission line according to the position relationship of the transmission line and the short connecting line
Figure FDA0002641229720000023
And step 3: determining the transmission coefficient from the input end to the output end of the n-order transmission line as follows:
Figure FDA0002641229720000024
wherein k is ZS/ZLAnd k is not less than 1,
Figure FDA0002641229720000025
for transmission coefficient from input to output of n-order transmission line, ZSIs the unit impedance of the input end of the n-order transmission line, ZLIs the unit impedance of the output end of the n-order transmission line;
wherein the content of the first and second substances,
Figure FDA0002641229720000026
wherein, X0,X1,...,Xn；Y0,Y1,...,Yn,Yn+1Is a characteristic impedance coefficient, and Xn＝(an-kdn)，Yn+1＝(bn+1-kcn+1)；
And 4, step 4: according to the transmission formula of n-order Chebyshev and other ripples under ideal conditions:
Figure FDA0002641229720000027
so that
Figure FDA0002641229720000028
So that
Figure FDA0002641229720000029
Figure FDA00026412297200000210
Wherein u is0,u1,...,un,un+1Is a coefficient;
determined by the correspondence coefficient equality:
when n is an even number, the number of n,
X0＝X2＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y3＝u3,Y1＝u1；
when n is an odd number, the number of the transition metal atoms,
X1＝X3＝…＝Xn＝0；Yn+1＝un+1,Yn-1＝un-1,...Y2＝u2,Y0＝u0；
and determining the relation between the characteristic impedance values of the n-section transmission line and the S-section short-circuit line according to the relation between the coefficients, and solving the characteristic impedance values of the n-section transmission line and the S-section short-circuit line.
6. The method for manufacturing an impedance transformer having Chebyshev filter characteristics for multi-order transmission lines and short-circuited lines as claimed in claim 5, wherein in step 2The transmission line ABCD matrix and the short-circuit line ABCD matrix are multiplied to obtain
Figure FDA0002641229720000031
Figure FDA0002641229720000032
Figure FDA0002641229720000033
Figure FDA0002641229720000034
Figure FDA0002641229720000035
Wherein, a0,a1,...,an；b0,b1,...,bn,bn+1；c0,c1,...,cn,cn+1；d0,d1,...,dnIs a coefficient and is determined by the characteristic impedance of each section of transmission line and shorting stub.
7. The method for manufacturing an impedance transformer having chebyshev filter characteristics for a multi-step transmission line and a short-circuited line according to claim 6, wherein in step 3, the determination of the transmission coefficient from the input terminal to the output terminal of the n-step transmission line is determined by the following formula;
Figure FDA0002641229720000036
and | S11|2+|S21|2＝1；
Wherein S is11From input to output of n-order transmission linesA reflection coefficient.
8. The method of manufacturing an impedance transformer having chebyshev filtering characteristics for a multi-order transmission line and a short-circuited line according to claim 7, further comprising:
inputting the obtained characteristic impedance values of the n-segment transmission line and the S-segment short-circuit line into ADS to obtain the line length and the line width of the n-segment transmission line and the S-segment short-circuit line,
inputting the line length and the line width into Sonnet for electromagnetic field simulation, and correcting to obtain the actual line length and line width of the n-section transmission line and the S-section short-circuit line;
and manufacturing a front panel model according to the actual line length and the line width, manufacturing the front panel model into a 1:1 picture format, printing the front panel model in a circuit board printer, and corroding the copper plate by using corrosive liquid.
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