CN109687086B - Coupling line cascaded Chebyshev filtering type Wilkinson power divider - Google Patents

Coupling line cascaded Chebyshev filtering type Wilkinson power divider Download PDF

Info

Publication number
CN109687086B
CN109687086B CN201910073598.XA CN201910073598A CN109687086B CN 109687086 B CN109687086 B CN 109687086B CN 201910073598 A CN201910073598 A CN 201910073598A CN 109687086 B CN109687086 B CN 109687086B
Authority
CN
China
Prior art keywords
parallel
lines
groups
simultaneously connected
coupling
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910073598.XA
Other languages
Chinese (zh)
Other versions
CN109687086A (en
Inventor
王小龙
张楠
吴斌
王庆凤
卢革宇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jilin University
Original Assignee
Jilin University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jilin University filed Critical Jilin University
Priority to CN201910073598.XA priority Critical patent/CN109687086B/en
Publication of CN109687086A publication Critical patent/CN109687086A/en
Application granted granted Critical
Publication of CN109687086B publication Critical patent/CN109687086B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P5/00—Coupling devices of the waveguide type
    • H01P5/12—Coupling devices having more than two ports
    • H01P5/16—Conjugate devices, i.e. devices having at least one port decoupled from one other port
    • 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
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P11/00—Apparatus or processes specially adapted for manufacturing waveguides or resonators, lines, or other devices of the waveguide type

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Manufacturing & Machinery (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)

Abstract

The invention discloses a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade, which comprises a source end impedance unit and two groups of load end impedance units, and is characterized by also comprising a power distribution unit which is connected between the source end impedance unit and the two groups of load end impedance units in parallel after being connected in series through two groups of a plurality of even-number section coupling lines; one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit through at least one transmission line with equal quantity; and two ends of the coupling line connected with the transmission line are connected through a resistor. The invention also discloses an optimized establishment method of the Wilkinson power divider with the Chebyshev filtering characteristic based on multi-section coupling line cascade.

Description

Coupling line cascaded Chebyshev filtering type Wilkinson power divider
Technical Field
The invention relates to the technical field of manufacturing of microstrip line devices of radio frequency circuits, in particular to a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade and an optimized establishment method thereof.
Background
With the development of society, people have more and more demand elements for information, and no matter in a civil communication system or a military radar system, the demand for stability in the information transmission process is higher and higher. Microwave power splitters are a vital passive component in communication systems, radar systems and electronic countermeasure systems. The function of the power divider is to divide the signal at the input end into multiple paths equally or unequally according to the requirement to transmit information, thereby achieving the purpose of power division. When high power is needed to transmit information, the output end is regarded as the input end, the input end is regarded as the output end, and the multiple paths of power are added into one path of signal to be used by the power synthesizer.
As the way radio transmits information becomes more and more popular, the requirements for its functionality also increase. The method is mainly characterized in that: 1. the power amplitude of the power allocation; 2. the insertion loss is reduced; 3. outputting the isolation between the two ports; 4. the phase consistency of the input end and the output end.
The current mainstream power divider methods include the following two methods: 1. the power divider is based on a microstrip line structure; 2. a waveguide structure based power splitter.
The microstrip structure power divider has the advantages of simple and compact circuit structure, low cost, stable performance, large frequency range and the like. Compared with the power divider made of microstrip lines, the power divider made of the waveguide structure has the advantages of low insertion loss, high power capacity, high balance degree and the like. But it is too bulky for microstrip structures. Therefore, the performance indexes of the whole power divider are the research design of the bandwidth size, the ground insertion loss, the high amplitude balance degree, the high isolation characteristic of the two ports and the high phase consistency.
Disclosure of Invention
The Wilkinson power divider with the Chebyshev filtering characteristic based on multi-section coupling line cascade is designed and developed, and one of the purposes of the invention is to replace the traditional transmission line with the coupling line, thereby solving the problem that the parallel connection ground wire realizes the same Chebyshev and other ripples.
The invention also aims to isolate the coupled line by arranging the transmission line at the source end or the load end.
The invention designs and develops an optimized establishing method of a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade, and further obtains the Wilkinson power divider with the Chebyshev filtering characteristics.
The technical scheme provided by the invention is as follows:
a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade comprises a source end impedance unit, two groups of load end impedance units, and a power distribution unit, wherein the source end impedance unit is connected with the two groups of load end impedance units in parallel after being connected in series through two groups of a plurality of even-number coupling lines;
one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit through at least one transmission line with equal quantity; and
and two ends of the coupling lines of the two groups of power distribution units, which are connected with the transmission lines, are connected through resistors.
It is preferable that the first and second liquid crystal layers are formed of,
source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel transmission lines ZTOne end of (a);
resistance R3Is simultaneously connected to the first group of transmission lines ZTAnd a first set of load side impedances RLWhile the other end is connected to a second group of transmission lines ZTAnd a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
It is preferable that the first and second liquid crystal layers are formed of,
source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And two sets of parallel coupled lines Zev2，Zod2One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel first transmission lines ZTOne end of (a);
resistance R5Are respectively and simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd two sets of second transmission lines Z connected in parallelTOne end of (a);
resistance R6Is simultaneously connected to the first group of second transmission lines ZTAnd a first set of load side impedances RLAnd the other end is simultaneously connected with a second group of second transmission lines ZTAnd a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
A Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade comprises a source end impedance unit, two groups of load end impedance units and a power distribution unit, wherein the power distribution unit is formed by connecting two groups of odd-number coupling lines in series and then connecting the odd-number coupling lines in parallel;
one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit through at least one transmission line with equal quantity, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit; and
and two ends of the coupling lines of the two groups of power distribution units, which are connected with the load end impedance unit, are connected through resistors.
It is preferable that the first and second liquid crystal layers are formed of,
source end impedance RSOne end is simultaneously connected with two groups of parallel transmission lines ZTAnd the other end is grounded; and
in the power distribution unit, two parallel Z groups are respectively and simultaneously connected with two ends of a zero ohm resistorev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel coupled lines Zev5，Zod5One end of (a);
resistance R3Is simultaneously connected with the first group of coupling lines Zev5，Zod5And a first set of load side impedances RLWhile the other end is connected with a second group of coupling lines Zev5，Zod5And a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
It is preferable that the first and second liquid crystal layers are formed of,
source end impedance RSOne end is simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd two sets of second transmission lines Z connected in parallelTOne end of (a);
resistance R2Are respectively and simultaneously connected with two groups of second transmission lines Z connected in parallelTAnd two sets of parallel coupled lines Zev1，Zod1One end of (a);
resistance (RC)R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And two sets of parallel coupled lines Zev2，Zod2One end of (a);
resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R5Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R6Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel coupled lines Zev5，Zod5One end of (a);
resistance R7Is simultaneously connected with the first group of coupling lines Zev5，Zod5And a first set of load side impedances RLWhile the other end is connected with a second group of coupling lines Zev5，Zod5And a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
A optimized establishing method of a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade comprises the following steps:
step one, determining a source end impedance value Z of a circuit in the power dividerSAnd a load terminal impedance value ZLAnd let Z beS/ZL＝2；
Step two, after determining the order of chebyshev equal ripples of the circuit in the power divider, calculating a chebyshev polynomial of the same order and a matrix of the same segment number of coupled line cascade;
calculating the transfer functions of the Chebyshev polynomial and the matrix respectively, and simultaneously enabling the transfer function of the matrix to be equal to the transfer function calculated by the Chebyshev;
fourthly, calculating the impedance value of each section of coupling line according to the constraint condition so as to obtain an original required circuit in the Wilkinson power divider;
and fifthly, keeping the impedance value of the source end in the originally required circuit unchanged, and expanding the impedance value of the load end to 2 times of the original impedance value to obtain the circuit required by the Wilkinson power divider, so as to obtain the Wilkinson power divider.
Preferably, in the second step, the chebyshev polynomials include a first type of chebyshev polynomial and a second type of chebyshev polynomial:
the first Chebyshev polynomial is Tn＝2xTn-1(x)-Tn-2(x)；
The second class of Chebyshev polynomials is Un+1(x)＝2xUn(x)-Un-1(x) (ii) a And
in the third step, the Chebyshev calculated transfer function is
Figure GDA0002525673940000051
Wherein cos (n φ + q ξ) ═ Tn(x)Tq(y)-Vn(x)Vq(y)，
Figure GDA0002525673940000052
n is the order of the chebyshev filter and q is 1.
Preferably, in the second step, the matrix of n coupled lines is
Figure GDA0002525673940000053
Wherein the matrix of the ith segment of the n segments is
Figure GDA0002525673940000054
Wherein q is cotθ，Si＝(Zevi+Zodi)/Z0，Ti＝(Zedi-Zodi)/Z0，ZeviAnd ZodiRespectively an even mode characteristic impedance and an odd mode characteristic impedance; and
in the third step, the transmission function of the n-segment coupled line circuit is
Figure GDA0002525673940000061
In the formula (I), the compound is shown in the specification,
Figure GDA0002525673940000062
preferably, the optimized establishing method of the wilkinson power divider with chebyshev filtering characteristic based on the cascade of 4-segment coupled lines comprises the following steps:
in the second step, the matrix of 4 segments of coupled lines is
Figure GDA0002525673940000063
Wherein the content of the first and second substances,
Figure GDA0002525673940000064
Figure GDA0002525673940000065
the polynomial of the first 4 th order Chebyshev equiripple is T4(x)＝8x3-8x+1；
The polynomial of the second 4-order Chebyshev equiripple is U4(x)＝16x4-12x2+1；
In the third step, the transfer function of the 4-segment coupled line matrix is
Figure GDA0002525673940000066
In the formula (I), the compound is shown in the specification,
Figure GDA0002525673940000067
wherein, Xm＝(am-k·dm)，Yn＝(bn-k·cn)；
The transfer function of the 4 th order Chebyshev-like ripple is
Figure GDA0002525673940000068
Wherein the content of the first and second substances,
Figure GDA0002525673940000069
and
at the same time, make
Figure GDA00025256739400000610
And is
Figure GDA00025256739400000611
Compared with the prior art, the invention has the following beneficial effects:
1. the traditional transmission line is replaced by a coupling line, so that the same chebyshev and other ripples can be realized without a grounding line connected in parallel;
2. in order to realize complete isolation based on multiple frequency points, for three-section coupled line cascade and five-section coupled line cascade, two 100 omega transmission lines are added at one side of a source end to increase the position of a resistor to be placed so as to realize isolation; for the two-section coupling line cascade and the four-section coupling line cascade, two transmission lines are required to be added on one side of a load to realize isolation; in most microwave systems, isolation can be realized only by adding an additional transmission line under the condition that all frequency points are not required to realize accurate isolation, and a part of resistor can be removed on the basis of a model that each frequency point is isolated.
Drawings
Fig. 1 is a block diagram of a conventional power divider having chebyshev filtering characteristics.
Fig. 2 is a structural diagram of a power divider with chebyshev filter characteristics in a four-segment coupled line cascade according to the present invention.
FIG. 3 is an even mode analysis model diagram of the four-segment coupled line cascade of the present invention.
FIG. 4 is a diagram of an odd-mode analysis model of a four-segment coupled line cascade according to the present invention.
FIG. 5 is an ADS simulation of the model of FIG. 4.
Fig. 6 is a model diagram of a simplified four-segment coupled line cascaded power divider with chebyshev filter characteristics.
FIG. 7 is an ADS simulation of the model of FIG. 6.
Fig. 8 is a structural diagram of a power divider with chebyshev filter characteristics in a five-segment coupled line cascade according to the present invention.
FIG. 9 is an ADS simulation of the model of FIG. 8.
Fig. 10 is a model diagram of a simplified five-segment coupled line cascaded power divider with chebyshev filter characteristics.
FIG. 11 is an ADS simulation of the model of FIG. 10.
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, in order to implement the conventional chebyshev-like ripple as a power divider, n transmission lines must be connected in series and n +1 ground lines must be connected in parallel. When the Wilkinson power divider is designed, in order to remove mutual interference between two transmission paths, a resistor needs to be connected between the two transmission paths and matched with an output end, so that an isolation effect is achieved, energy from a port 2 to a port 3 is consumed on the resistor in the middle, and no energy is transmitted between the two ports to obtain the isolation characteristic.
The invention provides a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade, which comprises a source end impedance unit, two groups of load end impedance units, and a power distribution unit, wherein the source end impedance unit is connected with the two groups of load end impedance units in parallel after being connected in series through two groups of a plurality of even-number coupling lines; one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit through at least one transmission line with equal quantity; and two ends of the coupling line connected with the transmission line are connected through a resistor.
In another embodiment, shown in FIG. 6, the source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And a coupling line Zev4，Zod4One end of (a); resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And the other end of the transmission line ZTOne end of (a); resistance R3Is simultaneously connected to the first group of transmission lines ZTAnd a first set of load side impedances RLWhile the other end is connected to a second group of transmission lines ZTAnd a second set of load side impedances RLOne end of (a); first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
In another embodiment, shown in FIG. 2, the source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end of the coupling line Zev2，Zod2One end of (a); resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And the other end of the coupling line Zev3，Zod3One end of (a); resistance R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3Another end of (1)And a coupling line Zev4，Zod4One end of (a); resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And the other end of the first transmission line ZTOne end of (a); resistance R5Are respectively and simultaneously connected with a first transmission line ZTAnd the other end of the second transmission line ZTOne end of (a); resistance R6Is simultaneously connected to the first group of second transmission lines ZTAnd a first set of load side impedances RLAnd the other end is simultaneously connected with a second group of second transmission lines ZTAnd a second set of load side impedances RLOne end of (a); first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
The invention also provides a Wilkinson power distributor with Chebyshev filtering characteristics based on multi-section coupling line cascade, which comprises a source end impedance unit, two groups of load end impedance units and two groups of power distribution units, wherein the two groups of power distribution units are connected in parallel after a plurality of odd-number coupling lines are connected in series; one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit through at least one transmission line with equal quantity, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit; and two ends of the coupling line connected with the load end impedance unit are connected through a resistor.
In another embodiment, shown in FIG. 10, the source end impedance RSOne end is simultaneously connected with two groups of parallel transmission lines ZTAnd the other end is grounded; in the power distribution unit, two ends of the zero ohm resistor are respectively connected with Z simultaneouslyev2，Zod2And a coupling line Zev3，Zod3One end of (a); resistance R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And the other end of the coupling line Zev4，Zod4One end of (a); resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And the other end of the coupling line Zev5，Zod5One end of (a); resistance R3Is simultaneously connected with the first group of coupling lines Zev5，Zod5And a first set of load side impedances RLWhile the other end is connected with a second group of coupling lines Zev5，Zod5And a second set of load side impedances RLOne end of (a); first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
In another embodiment, shown in FIG. 8, the source end impedance RSOne end is simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd the other end is grounded; in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd the other end of the second transmission line ZTOne end of (a); resistance R2Are respectively and simultaneously connected with two groups of second transmission lines Z connected in parallelTAnd the other end of the coupling line Zev1，Zod1One end of (a); resistance R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end of the coupling line Zev2，Zod2One end of (a); resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And the other end of the coupling line Zev3，Zod3One end of (a); resistance R5Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And the other end of the coupling line Zev4，Zod4One end of (a); resistance R6Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And the other end of the coupling line Zev5，Zod5One end of (a); resistance R7One end of the coupling line Z is connected with the coupling line Z simultaneouslyev5，Zod5Another end of (2) and a line of fusion Zev3，Zod3First set of load side impedances RLOne end of the coupling line Z and the other end of the coupling line Z are connected simultaneouslyev5，Zod5And a second set of load side impedances RLOne end of (a); first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
The invention provides an optimized establishment method of a Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade, which comprises the following steps:
step one, determining a source end impedance value Z of the circuitSAnd a load end impedance value ZLRequires ZS/ZL＝2；
Determining the order of chebyshev-like ripples of the circuit, namely the sum of the number of coupling lines and transmission lines in the circuit;
step three, calculating the expression of the Chebyshev polynomial of the same order according to the order of the Chebyshev corrugations and the like in the step two;
wherein the Chebyshev polynomial uses Tn(x) Expressing the first Chebyshev polynomial of degree n, wherein the first Chebyshev polynomials are:
Figure GDA0002525673940000101
the high-order chebyshev first-class polynomial may be represented by a recursive formula:
Tn＝2xTn-1(x)-Tn-2(x)；
chebyshev second polynomial uses Un(x) Expressing the second class Chebyshev polynomial of degree n, wherein the first Chebyshev second class polynomials are:
Figure GDA0002525673940000102
the higher-order chebyshev second-type polynomial may be represented by a recursive formula:
Un+1(x)＝2xUn(x)-Un-1(x)；
the chebyshev polynomial has the following characteristics, so that the equiripple occurs:
(1) for x is-1 or more and 1 or less, | Tn(x) Less than or equal to 1; x is in the interval of-1 to 1, and the Chebyshev polynomial oscillates within +/-1;
(2) for | x | > 1, Chebyshev does not oscillate between + -1，|Tn(x) L increases rapidly with increasing x and n. If x is cos θ, | Tn(x) Oscillating | within +/-1 so as to generate corrugations such as Chebyshev and the like;
for the chebyshev inequality:
let x be cos phi α cos theta, y be cos ξ, and have
Figure GDA0002525673940000111
α is a parameter for measuring the bandwidth of the band-pass filter, and is defined as
Figure GDA0002525673940000112
In this formula, θcAn electrical length at the lower of the two cut-off frequencies of the filter;
bandwidth of
Figure GDA0002525673940000113
Thus, the transfer function of a chebyshev is:
Figure GDA0002525673940000114
where n and q are constants, n is the order of the chebyshev filter, i.e., the number of segments of the coupled line, q is 1, and cos (n phi + q ξ) ═ Tn(x)Tq(y)-Vn(x)Vq(y)；
Wherein, TnBeing a first type of chebyshev polynomial,
Figure GDA0002525673940000115
Un(x) Is a chebyshev second-type polynomial;
step four, deducing an expression of the ABCD matrix of the same section of coupled line cascade according to the order of the chebyshev and other ripples in the step two;
wherein, the ABCD matrix of a section of coupling line is:
Figure GDA0002525673940000116
wherein q is cot θ, Si＝(Zevi+Zodi)/Z0，Ti＝(Zedi-Zodi)/Z0，ZeviAnd ZodiRespectively an even mode characteristic impedance and an odd mode characteristic impedance;
the ABCD matrix of the n sections of coupled lines is as follows:
Figure GDA0002525673940000117
in this case, the matrix has a transfer function of
Figure GDA0002525673940000118
Step five, calculating constraint conditions of the ABCD matrix and the Chebyshev polynomial calculated in the step three and the step four to enable the circuit to accord with the structure of the Chebyshev polynomial;
wherein the constraint is a transfer function S calculated by ABCD of the coupled line21And a transfer function S calculated by Chebyshev21Equal and satisfies A for the ABCD matrix of the coupled linesTOY＝kDTOY；
Step six, calculating the Z of each section of coupling line according to the constraint conditions calculated in the step fiveevAnd Zod；
Step seven, according to the calculation in the step six, a power divider with Chebyshev filtering characteristics and cascaded by a plurality of sections of coupling lines can be obtained;
step eight, designing the obtained impedance converter with the Chebyshev filter characteristic into an upper branch and a lower branch, wherein the impedance value of the left source end is ZSThe load of the two branches on the right side is expanded to 2 times without change, and at the moment ZS＝ZL；
And step nine, adding a resistor and a transmission line into the designed power divider according to the isolation method provided by the invention, so that the ports of two loads of the power divider are isolated, and the Wilkinson power divider is obtained.
Examples
Firstly, specific parameters of the corresponding model are determined
As shown in fig. 3, the model built by cascading four sections of coupled lines is subjected to even mode analysis and is built, in this embodiment, the even mode of the wilkinson power divider is equivalent to an impedance transformer with a source end of 100 Ω and a load end of 50 Ω, the even mode is analyzed by using an ABCD matrix method, and the ABCD matrix of one section of coupled line is:
Figure GDA0002525673940000121
the overall ABCD matrix is:
Figure GDA0002525673940000122
wherein the content of the first and second substances,
Figure GDA0002525673940000123
Figure GDA0002525673940000124
Figure GDA0002525673940000125
Figure GDA0002525673940000126
Figure GDA0002525673940000127
Figure GDA0002525673940000128
Figure GDA0002525673940000129
Figure GDA00025256739400001210
Figure GDA00025256739400001211
Figure GDA00025256739400001212
Figure GDA0002525673940000131
Figure GDA0002525673940000132
Figure GDA0002525673940000133
transfer function S of the model21Represented by the formula:
Figure GDA0002525673940000134
wherein k is Zl/ZsDerived from the above equation:
Figure GDA0002525673940000135
wherein, Xm＝(am-k·dm)，Yn＝(bn-k·cn)；
The transfer function of the 4 th order Chebyshev-like ripple in the ideal case can be written as:
Figure GDA0002525673940000136
wherein:
Figure GDA0002525673940000137
so as to let
Figure GDA0002525673940000138
The ripples such as chebyshev can be obtained, so the following constraint relationship can be obtained:
Figure GDA0002525673940000139
as shown in fig. 4, the odd-mode analysis is performed on the model established by the four-segment coupled line cascade, in order to achieve complete isolation based on all frequency points, for the odd-mode of the four-segment coupled line, two 50 Ω transmission lines need to be added on one side of the load, since the load of the impedance converter is 50 Ω and is conjugate-matched from the port, the addition of the two transmission lines on the port does not affect the original characteristics of the model, and in order to achieve isolation, it is required to ensure that the ports in the odd-mode analysis are all matched at five frequency points, so that the following relationships exist:
Figure GDA00025256739400001310
Figure GDA00025256739400001311
Figure GDA00025256739400001312
Figure GDA00025256739400001313
Figure GDA00025256739400001314
Figure GDA00025256739400001315
Figure GDA00025256739400001316
Figure GDA0002525673940000141
Figure GDA0002525673940000142
Figure GDA0002525673940000143
Figure GDA0002525673940000144
Figure GDA0002525673940000145
in order to realize the characteristic of isolation at each frequency point, Z is requiredTOT＝50Ω(@f1，f2，f3，f4，f5) The structure diagram and the simulation diagram of the circuit satisfying this condition are shown in fig. 2 and 5: the circuit parameters are as follows:
Zev1＝350.9924Ω，Zod1＝123.5723Ω，Zev2＝304.6944Ω，Zod2＝92Ω，Zov3＝268.1235Ω
Zod3＝92Ω，Zev4＝185.2213Ω，Zod4＝52.06098Ω，ZT＝50Ω，R1＝627.0866Ω，
R2＝6.2633Ω，R3＝64.1534Ω，R4＝81.0649Ω，R5＝185.862Ω，R6＝660.7896Ω
in engineering problems, such high isolation properties are generally not required, but only the guarantee of S in the region of the pass band23And S22Below-20 dB, so that the method can be removed on the basis of the model of the graphSome resistors and some transmission lines, and simplified circuit model diagrams and ADS simulation diagrams are shown in fig. 6 and fig. 7, parameters of specific coupling lines and transmission lines are unchanged, and the simplified resistor parameters are as follows:
R1＝63Ω，R2＝83.5Ω，R3＝234Ω；
from the figure we can see that within the Chebyshev pass-band, S23And S22All below-20 dB, the isolation effect can be achieved, and the overall size and complexity of the circuit are reduced by a part.
For cascading five-segment coupled lines, in order to achieve the optimal isolation effect, two 100 Ω transmission lines need to be added on the side of the five-segment continuous coupled lines close to the load, a circuit model diagram of which is shown in fig. 8, and the specific parameters are as follows:
ZT＝100Ω，Zev1＝278.8928Ω，Zod1＝50.34084Ω，Zev2＝258.3995Ω，Zod2＝35Ω，
Zev3＝243.3995Ω，Zod3＝41Ω，Zev4＝211.9244Ω，Zod3＝37Ω，Zev5＝148.1626Ω，
Zod5＝16.45425Ω，R1＝188.924Ω，R2＝259.831Ω，R3＝367.81Ω，R4＝364.086Ω，
R5＝489.783Ω，R6＝583.047Ω，R7＝685.26Ω
the ADS simulation result is shown in fig. 9:
similarly, we can simplify the model, and when high isolation is not needed, we can remove the transmission line near the source end and 4 resistors on the basis of the model, and connect the second segment of coupled lines, and the model diagram and the ADS simulation diagram are shown in fig. 10 and fig. 11:
the circuit model has the specific parameters as follows: r1＝105.6123Ω，R2＝220.78Ω，R3＝209.84Ω
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 (6)

1. A Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade comprises a source end impedance unit and two groups of load end impedance units, and is characterized by further comprising a power distribution unit which is connected in parallel after the source end impedance unit and the two groups of load end impedance units are connected in series through two groups of a plurality of even-number section coupling lines;
one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit through at least one transmission line with equal quantity; and
and two ends of the coupling lines of the two groups of power distribution units, which are connected with the transmission lines, are connected through resistors.
2. The Wilkinson power divider with Chebyshev filter characteristics based on multi-segment coupled line cascading of claim 1,
source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel transmission lines ZTOne end of (a);
resistance R3Is simultaneously connected to the first group of transmission lines ZTAnd a first set of load side impedances RLWhile the other end is connected to a second group of transmission lines ZTAnd a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
3. The Wilkinson power divider with Chebyshev filter characteristics based on multi-segment coupled line cascading of claim 1,
source end impedance RSOne end is simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And two sets of parallel coupled lines Zev2，Zod2One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel first transmission lines ZTOne end of (a);
resistance R5Are respectively and simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd two sets of second transmission lines Z connected in parallelTOne end of (a);
resistance R6Is simultaneously connected to the first group of second transmission lines ZTAnd a first set of load side impedances RLAnd the other end is simultaneously connected with a second group of second transmission lines ZTAnd a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
4. A Wilkinson power divider with Chebyshev filtering characteristics based on multi-section coupling line cascade comprises a source end impedance unit and two groups of load end impedance units, and is characterized by further comprising two groups of power distribution units which are formed by connecting a plurality of odd-number coupling lines in series and then connecting the odd-number coupling lines in parallel;
one end of the power distribution unit is respectively and simultaneously connected with the source end impedance unit through at least one transmission line with equal quantity, and the other end of the power distribution unit is respectively and simultaneously connected with the load end impedance unit; and
and two ends of the coupling lines of the two groups of power distribution units, which are connected with the load end impedance unit, are connected through resistors.
5. The Wilkinson power divider with Chebyshev filter characteristics based on multi-segment coupled line cascading of claim 4,
source end impedance RSOne end is simultaneously connected with two groups of parallel transmission lines ZTAnd the other end is grounded; and
in the power distribution unit, two parallel Z groups are respectively and simultaneously connected with two ends of a zero ohm resistorev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R1Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R2Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And two sets of parallel coupled lines Zev5，Zod5One end of (a);
resistance R3While one end of the first and second connecting terminals is connected toA group of coupled lines Zev5，Zod5And a first set of load side impedances RLWhile the other end is connected with a second group of coupling lines Zev5，Zod5And a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
6. The Wilkinson power divider with Chebyshev filter characteristics based on multi-segment coupled line cascading of claim 4,
source end impedance RSOne end is simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd the other end is grounded; and
in the power distribution unit, a resistor R1Are respectively and simultaneously connected with two groups of first transmission lines Z connected in parallelTAnd two sets of second transmission lines Z connected in parallelTOne end of (a);
resistance R2Are respectively and simultaneously connected with two groups of second transmission lines Z connected in parallelTAnd two sets of parallel coupled lines Zev1，Zod1One end of (a);
resistance R3Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev1，Zod1And two sets of parallel coupled lines Zev2，Zod2One end of (a);
resistance R4Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev2，Zod2And two sets of parallel coupled lines Zev3，Zod3One end of (a);
resistance R5Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev3，Zod3And two sets of parallel coupled lines Zev4，Zod4One end of (a);
resistance R6Are respectively and simultaneously connected with two groups of coupling lines Z connected in parallelev4，Zod4And the other end of the first and second groups of parallel coupled linesZev5，Zod5One end of (a);
resistance R7Is simultaneously connected with the first group of coupling lines Zev5，Zod5And a first set of load side impedances RLWhile the other end is connected with a second group of coupling lines Zev5，Zod5And a second set of load side impedances RLOne end of (a);
first set of load side impedances RLAnd a second set of load side impedances RLThe other ends of which are respectively grounded.
CN201910073598.XA 2019-01-25 2019-01-25 Coupling line cascaded Chebyshev filtering type Wilkinson power divider Active CN109687086B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910073598.XA CN109687086B (en) 2019-01-25 2019-01-25 Coupling line cascaded Chebyshev filtering type Wilkinson power divider

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910073598.XA CN109687086B (en) 2019-01-25 2019-01-25 Coupling line cascaded Chebyshev filtering type Wilkinson power divider

Publications (2)

Publication Number Publication Date
CN109687086A CN109687086A (en) 2019-04-26
CN109687086B true CN109687086B (en) 2020-08-07

Family

ID=66194719

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910073598.XA Active CN109687086B (en) 2019-01-25 2019-01-25 Coupling line cascaded Chebyshev filtering type Wilkinson power divider

Country Status (1)

Country Link
CN (1) CN109687086B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111027265B (en) * 2019-12-30 2022-03-11 吉林大学 Method for establishing ultra-wideband first-class Chebyshev multi-node Wilkinson power divider with equal-ripple isolation characteristic
CN112652871A (en) * 2020-12-16 2021-04-13 吉林大学 Three-order annular broadband band-pass equiripple filter and design method thereof

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20020012935A (en) * 2000-08-09 2002-02-20 송재인 Power divider /combiner using 3 way chebyshev matching transformer
CN103259072A (en) * 2013-04-27 2013-08-21 北京邮电大学 Ultra-wideband power divider based on exponential gradient
CN104393389A (en) * 2014-11-14 2015-03-04 电子科技大学 Broadband phase shifting power divider with amplitude and phase compensating function
CN105071000A (en) * 2015-08-13 2015-11-18 杭州电子科技大学 Broadband microwave six-port structure
CN108879057A (en) * 2018-06-14 2018-11-23 杭州维慕德科技有限公司 A kind of high degree of balance distributor of minimized wide-band

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP6017003B1 (en) * 2015-10-06 2016-10-26 株式会社フジクラ Microstrip antenna and manufacturing method thereof
CN108281744B (en) * 2018-01-30 2021-05-07 中国电子科技集团公司第三十八研究所 Broadband power divider based on Chebyshev converter and circuit parameter design method thereof
CN109066044A (en) * 2018-08-30 2018-12-21 南京理工大学 A kind of ultra wide band Wilkinson power divider

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20020012935A (en) * 2000-08-09 2002-02-20 송재인 Power divider /combiner using 3 way chebyshev matching transformer
CN103259072A (en) * 2013-04-27 2013-08-21 北京邮电大学 Ultra-wideband power divider based on exponential gradient
CN104393389A (en) * 2014-11-14 2015-03-04 电子科技大学 Broadband phase shifting power divider with amplitude and phase compensating function
CN105071000A (en) * 2015-08-13 2015-11-18 杭州电子科技大学 Broadband microwave six-port structure
CN108879057A (en) * 2018-06-14 2018-11-23 杭州维慕德科技有限公司 A kind of high degree of balance distributor of minimized wide-band

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
射频功率放大器关键技术研究;郑光明;《中国博士学位论文全文数据库》;20160603;68-83 *

Also Published As

Publication number Publication date
CN109687086A (en) 2019-04-26

Similar Documents

Publication Publication Date Title
US10277189B2 (en) Transmission line reflectionless filters
Szydlowski et al. Coupled-resonator filters with frequency-dependent couplings: Coupling matrix synthesis
Cameron Advanced filter synthesis
US10516378B2 (en) Optimal response reflectionless filter topologies
CN109818123B (en) Coupling line cascaded Chebyshev filter impedance converter and establishment method thereof
CN109687086B (en) Coupling line cascaded Chebyshev filtering type Wilkinson power divider
Guyette et al. Design of absorptive microwave filters using allpass networks in a parallel-cascade configuration
CN108023562A (en) Areflexia lattice filter
Guyette et al. Short-through-line bandstop filters using dual-coupled resonators
CN109766657B (en) Wilkinson power divider with Chebyshev filtering characteristic with isolation frequency point alignment and preparation method thereof
US9859599B2 (en) Bandstop filters with minimum through-line length
CN111740190B (en) Broadband band-stop filter based on transmission line parallel multi-section open circuit stub line and design method thereof
KR100328145B1 (en) Microwave Multiplexer with Variable Non-Bandwidth Channels
KR102593446B1 (en) Frequency filter circuit
Macchiarella et al. A design methodology for fully canonic NRN filters in coaxial technology
Osipenkov et al. Microwave filters of parallel-cascade structure
JP4434454B2 (en) Distributed constant filter
US10374577B2 (en) Optimal response reflectionless filters
Khalid et al. Design of highly selective ultra-wideband bandpass filter using multiple resonance resonator
JP4436534B2 (en) Distributed constant filter
CN105161816A (en) Method for designing unequal power divider
Yu et al. A Novel Dandelion Topology for Multiport Filtering Power Divider
CN117134738A (en) Topological structure symmetrical or approximately symmetrical acoustic wave filter and communication equipment
Sun et al. Design of a Filtering Gysel Power Divider with Quasi-Bandpass Sections and Arbitrary Power Ratio
CN115882178A (en) High-order band-pass filter with symmetrical topological structure and design method thereof

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant