CN108281744A - A kind of broadband power divider and its circuit parameter design method based on Chebyshev transformation device - Google Patents
A kind of broadband power divider and its circuit parameter design method based on Chebyshev transformation device Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
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Abstract
The invention discloses a kind of broadband power dividers based on Chebyshev transformation device, including a total port and two points of ports, it is provided with N number of isolation resistance between two points of adjacent ports, Chebyshev's impedance transformation transmission line is all made of between total port and point port, the transmission line is made of N grades of Chebyshev's impedance transformers plus 1 section of 1/4 wavelength impedance transformers, the isolation resistance is connected across corresponding every level-one Chebyshev's impedance transformer junction between two points of adjacent ports respectively, N >=1, and be natural number.The invention also discloses the circuit parameter design method of the broadband power divider, solve the problems, such as that decile power splitter such as is not difficult to design, and is equally applicable to broadband at the design for dividing power splitter in broadband.
Description
Technical field
The present invention relates to microwave engineering techniques fields, and in particular to a kind of broadband power divider based on Chebyshev transformation device
And its circuit parameter design method.
Background technology
In the microwave systems such as phased-array radar, often need microwave power being assigned to according to a certain percentage each unit or by
Each unit carries out microwave power synthesis.Power splitter full name power divider is a kind of to be divided into input power according to a certain percentage
A few road power outputs or a kind of multiport Microwave Net for synthesizing a few road input powers.Power splitter is as a kind of passive
Microwave device has a wide range of applications in microwave circuit.The important technological parameters of power splitter include：Power attenuation (including insert
Enter loss and return loss), the voltage standing wave ratio of each port, the isolation between power distribution port and frequency bandwidth etc..
With the development of military equipment and communication equipment etc., the demand to broadband power divider quickly increases.Broadband work(
It is the critical component of the microwave systems such as phased-array radar, communication equipment to divide device, is widely used in the fields such as radar and microwave measurement,
It is indispensable critical component in the systems such as various radars, particularly electronic countermeasure.
Existing broadband power divider is essentially all each point of port constant power distribution (i.e. power splitter is divided in broadband etc.), and use is led to
It is often multistage step impedance conversion technology and gradual change resistance technique." ultra wideband power divider " of Publication No. CN204167456U and
A kind of " the miniature ultra wide band microwave power distributor " of 105186083 A of Publication No. CN is all made of multistage step impedance conversion skill
Art ultra wideband power divider, this multistage step impedance conversion generally can convert table by disclosed impedance and check in；Publication No.
A kind of " Novel ultra wide band Wilkinson power divider " of 102956948 A of CN discloses a kind of Novel ultra wide band Wilkinson work(
Divide device, what is used is then gradual change resistance technique.
Traditional two-way Wilkinson power splitter principle schematics are shown in Fig. 1, if the roads a transmission line is from the O points from port 1
A points at port 2 (include ZaAnd ZA), the roads b transmission line is that the b points from the O points from port 1 at port 3 (include Zb
And ZB), when the power-division ratios between b and a two-way are K2When, if P3=K2P2, then have ZA=K2ZB, Za=K2Zb, due to this
The smaller bandwidth of single-stage power splitter, ideally relative bandwidth be typically not greater than 36%.
Currently, divide the broadband power divider (i.e. broadband not decile power splitter) that port unequal power distributes design or one
Difficult point has not been reported its succinct effective design method.
Invention content
Technical problem to be solved by the present invention lies in a kind of solution broadband is provided, decile power splitter is not difficult to design
Broadband power divider based on Chebyshev transformation device and its circuit parameter design method.
The present invention is to solve above-mentioned technical problem by the following technical programs：
A kind of broadband power divider based on Chebyshev transformation device, which is characterized in that including a total port and two points
Port is provided with N number of isolation resistance between two points of ports, is all made of between total port and each point of port
Chebyshev's impedance converts transmission line, and the transmission line is to add 1/4 wavelength of the preceding paragraph by N grades of Chebyshev's impedance transformers
Impedance transformer forms, and corresponding every level-one cuts ratio between the isolation resistance is connected across two points of adjacent ports respectively
It is natural number to avenge husband's impedance transformer junction, N >=1, and N.
Further, the N=4.
The present invention also protects the circuit parameter design method of the broadband power divider, includes the following steps：
Step 1：It is required according to the bandwidth of operation of power splitter, selects suitable converter series；
Step 2：The power-division ratios for dividing port according to power splitter, obtain impedance transformation ratio；
Step 3：It integrates to obtain converter reflectance factors at different levels using Chebyshev polynomials；
Step 4：The relational expression between adjacent impedance transformer at different levels is obtained according to reflection coefficient parameters at different levels, and according to
Relational expression calculates the impedance value of transformer sections at different levels successively；
Step 5：The impedance value for obtaining transformer sections at different levels is substituted into circuit model, isolation resistances at different levels are calculated
Value.
Further, the detailed process of the circuit parameter design method is as follows：
Step 1：Converter series is set as N, wherein N >=1, and N is natural number；
Step 2：If the position where two points of ports is a points and b points, the roads a transmission line and the roads b transmission line are respectively a points
To total port transmission line and b point to the transmission line of total port, the roads a transmission line, the roads b transmission line and the position that crosses of total port are set
For O points；The roads a transmission line before impedance transformation includes impedance ZaAnd impedance ZA, the roads the b transmission line before impedance transformation includes impedance Zb
And impedance ZB；When carrying out impedance transformation, the roads a transmission line includes N grades of Chebyshev's impedance transformer impedance Zsa1、Za2、Za3、…、ZaN
And one section of 1/4 wavelength impedance transformers impedance ZAT, the roads b transmission line includes N grades of Chebyshev's impedance transformer impedance Zsb1、Zb2、
Zb3、…、ZbNAnd one section of 1/4 wavelength impedance transformers impedance ZBTIf the power-division ratios between b and a two-way are K2, then have ZA
=K2ZBIf from O points to the roads a see into input impedance be Zain, from O points to the roads b see into input impedance be Zbin, then have Zain=
K2Zbin, then O point impedance Z0There is following relationship：
By Zain=K2ZbinFormula (1) is substituted into, is obtained：
Zain=(1+K2)Z0 (2)
When a point port is connected with external circuit, load impedance is equal to Z0, Z0Pass through one section of 1/4 wavelength rheostat Z respectivelyAT
And ZBTTransform to ZAAnd ZB, in order to keep two impedance values more reasonable, take ZA=KZ0, ZB=Z0/ K, thenIt obtainsIt can be seen that when by input impedance ZainTransform to ZA
Or by input impedance ZbinTransform to ZBWhen, impedance transformation ratio is
Step 3：When from ZainTransform to ZAWhen, there is ZaN=K2ZbN, ZaN-1=K2ZbN-1..., Za1=K2Zb1, when N is even number
When, the N grades of total reflectance factors of converter are：
When N is odd number, the N grades of total reflectance factors of converter are：
Γ (θ)=2e-jNθ[Γ0cosNθ+Γ1cos(N-2)θ+…+Γncos(N-2n)θ+…+Γ(N-1)/2cosθ]
(5)
θ in formula (4) and formula (5) represents the corresponding electrical length of impedance transformation transmission line, Γ under different frequency0,
Γ1..., ΓnIt is the reflectance factor at impedance transform node, N is the series of impedance transformer, n=0,1,2,3 ..., N-1；
Γ (θ) is set to be proportional to Chebyshev polynomials TN(secθmCos θ) carry out passband synthesis, even
Γ (θ)=Ae-jNθTN(secθmcosθ) (6)
Wherein：A is undetermined constant, θmIndicate the corresponding electrical length of passband low end frequency；
As θ=0, have in conjunction with formula (4), formula (5) and formula (6)：
Then coefficient A is：
If the maximum reflection coefficient amplitude in passband is Γm, then have：
Γm=| A | | TN(secθmcosθ)|max=| A | (9)
For passband low side θm, there is TN(secθm)>0, in conjunction with formula (8) and formula (9), can obtain：
Had according to approximation relation：
Then it obtains：
Chebyshev polynomials T as a result,i(secθmCos θ) there is following form：
T1(secθmCos θ)=sec θmcosθ (13)
T2(secθmCos θ)=sec2θm(cos2θ+1)-1 (14)
Other high-order Chebyshev polynomials can be found out with following formula：
Ti(secθmCos θ)=2sec θm cosθTi-1(secθm cosθ)-Ti-2(secθmcosθ) (15)
Wherein：I=3,4,5 ..., N；
With formula (15) to the T in formula (6)N(secθmCos θ) it is unfolded, then enable cos therein (N-2n) θ
It is equal with the respective items in formula (4) or formula (5), reflectance factor Γ at different levels can be obtainedn；
Step 4：Obtain reflectance factor Γ at different levelsnThere is following relational expression：
As n=0, Za0=ZA, for Multi-stage impedance matching, ΓnSmaller, then formula (16) is reduced to：
In addition, according to formula (4) and formula (5), there is relational expression Γ0=ΓN, Γ1=ΓN-1, Γ2=ΓN-2..., thus
Obtain the relational expression between adjacent impedance transformer at different levels：
The impedance value of transformer sections at different levels is calculated successively according to relational expression (18)；
Step 5：The impedance value for obtaining transformer sections at different levels is substituted into circuit model, isolation resistances at different levels are calculated
Value.
Further, the power-division ratios of point port continuously design according to actual needs.
Further, the impedance transformation ratio in the step 2 passes through backward impedance transformation calculations, i.e. ZATransform to input
Impedance Zain, or by ZBTransform to input impedance Zbin, at this time impedance transformation ratio be
Further, the circuit model in the step 5 is ADS circuit models.
The present invention has the following advantages compared with prior art：
The broadband power divider of the present invention adds 1 section of 1/4 wavelength impedance transformers using multistage Chebyshev's impedance transformer
The transmission line of composition carrys out spread bandwidth, and in broadband, decile does not obtain very wide relative bandwidth for decile and broadband；This
The design method that invention broadband power divider uses is succinctly effective, and the power-division ratios of port is divided to be connected according to actual use situation
Continuous design solves the problems, such as that decile power splitter such as is not difficult to design, and is equally applicable to broadband at the design for dividing power splitter in broadband.
Description of the drawings
Fig. 1 is traditional two-way Wilkinson power splitter principle schematics；
Fig. 2 is the broadband N grades of of the present invention not decile power splitter principle schematic；
Fig. 3 is 4 grades of broadbands not decile power splitter ADS circuit diagrams of the embodiment of the present invention；
Fig. 4 is that power splitter ADS circuit diagrams are divided in 4 grades of broadbands of the embodiment of the present invention etc.；
Fig. 5 is 4 grades of broadbands not each reflection coefficient of port loss S11, S22 and S33 emulation of decile power splitter of the embodiment of the present invention
Curve graph；
Fig. 6 is 4 grades of broadbands not decile power splitter point port amplitude S21 and S31 simulation curve figures of the embodiment of the present invention；
Fig. 7 is 4 grades of broadbands not isolation S23 simulation curves between decile power splitter point port of the embodiment of the present invention
Figure；
Fig. 8 is that 4 grades of broadbands of the embodiment of the present invention etc. divide each reflection coefficient of port loss S11, S22 and S33 emulation of power splitter bent
Line chart；
Fig. 9 is that power splitter point port amplitude S21 and S31 simulation curve figure is divided in 4 grades of broadbands of the embodiment of the present invention etc.；
Figure 10 is that isolation S23 simulation curve figures between power splitter point port are divided in 4 grades of broadbands of the embodiment of the present invention etc..
Specific implementation mode
It elaborates below to the embodiment of the present invention, the present embodiment is carried out lower based on the technical solution of the present invention
Implement, gives detailed embodiment and specific operating process, but protection scope of the present invention is not limited to following implementation
Example.
The present invention will be further described below in conjunction with the accompanying drawings.
Fig. 2 is the N grade broadband power divider principle schematics of the present invention, including port 1, port 2 and port 3, wherein port
1 is total port, and port 2 and port 3 are to divide port.If the roads a transmission line is a points at port 2, the roads b from the O points from port 1
Transmission line is the b points at port 3 from the O points from port 1；The roads a transmission line includes N grades of Chebyshev's impedance transformer impedances
Za1、Za2、Za3、…、ZaNAnd one section of 1/4 wavelength impedance transformers impedance ZAT, the roads b transmission line includes N grades of Chebyshev's impedances
Transformer impedance Zb1、Zb2、Zb3、…、ZbNAnd one section of 1/4 wavelength impedance transformers impedance ZBT, set between port 2 and port 3
It is equipped with N number of isolation resistance, isolation resistance R1、R2、R3、…、RNIt is connected across respectively corresponding every between two points of adjacent ports
Level-one Chebyshev's impedance transformer junction, for realizing good isolation between two branches.
The detailed process of the circuit parameter design method of the N grades of broadband power divider is as follows：
The roads a transmission line (including impedance Z before being converted for impedanceaAnd impedance ZA) and the roads b transmission line (including impedance ZbWith
Impedance ZB), if the power-division ratios between b and a two-way are K2, then have ZA=K2ZBIf from O points to the roads a see into input impedance
For Zain, from O points to the roads b see into input impedance be Zbin, then have Zain=K2Zbin, then the impedance Z of O points position0Just like ShiShimonoseki
System：
By Zain=K2ZbinFormula (1) is substituted into, is obtained：
Zain=(1+K2)Z0 (2)
When port 2 and port 3 are connected with external circuit, load impedance is equal to Z0, Z0Become respectively by one section of 1/4 wavelength
Hinder device ZATAnd ZBTTransform to ZAAnd ZB, in order to keep two impedance values more reasonable, can use ZA=KZ0, ZB=Z0/ K, thenIt can thus be concluded thatIt can be seen that by input impedance ZainIt transforms to
ZAOr by input impedance ZbinTransform to ZB, impedance transformation ratio is
When from ZainTransform to ZAWhen, there is ZaN=K2ZbN, ZaN-1=K2ZbN- 1 ..., Za1=K2Zb1, when N is even number, N grades
The total reflectance factor of converter is：
When N is odd number, the N grades of total reflectance factors of converter are：
Γ (θ)=2e-jNθ[Γ0cosNθ+Γ1cos(N-2)θ+…+Γncos(N-2n)θ+…+Γ(N-1)/2cosθ]
(5)
θ in formula (4) and formula (5) represents the corresponding electrical length of impedance transformation transmission line, Γ under different frequency0,
Γ1..., ΓnIt is the reflectance factor at impedance transform node, N is the series of impedance transformer, n=0,1,2,3 ..., N-1；
Γ (θ) is set to be proportional to Chebyshev polynomials TN(secθmCos θ) carry out passband synthesis, even
Γ (θ)=Ae-jNθTN(secθmcosθ) (6)
Wherein：A is undetermined constant, θmIndicate the corresponding electrical length of passband low end frequency；
As θ=0, have in conjunction with formula (4), formula (5) and formula (6)：
Then coefficient A is：
If the maximum reflection coefficient amplitude in passband is Γm, then have：
Γm=| A | | TN(secθmcosθ)|max=| A | (9)
For passband low side θm, there is TN(secθm)>0, in conjunction with formula (8) and formula (9), obtain：
Had according to approximation relation：
Then it obtains：
Chebyshev polynomials T as a result,i(secθmCos θ) there is following form：
T1(secθmCos θ)=sec θmcosθ (13)
T2(secθmCos θ)=sec2θm(cos2θ+1)-1 (14)
Other high-order Chebyshev polynomials can be found out with following formula：
Ti(secθmCos θ)=2sec θmcosθTi-1(secθmcosθ)-Ti-2(secθm cosθ) (15)
Wherein：I=3,4,5 ..., N；
With formula (15) to the T in formula (6)N(secθmCos θ) it is unfolded, then enable cos therein (N-2n) θ
It is equal with the respective items in formula (4) or formula (5), reflectance factor Γ at different levels can be obtainedn；
Again because of reflectance factor Γ at different levelsnThere is following relational expression：
As n=0, Za0=ZA, for Multi-stage impedance matching, ΓnSmaller, then formula (16) can be reduced to：
In addition, according to formula (4) and formula (5), there is relational expression Γ0=ΓN, Γ1=ΓN-1, Γ2=ΓN-2...,
It is hereby achieved that the relational expression between adjacent impedance transformer at different levels：
It can be obtained the impedance value of transformer sections at different levels by above formula, it is soft in ADS then according to each section of obtained impedance value
It is modeled in part, rapid Optimum obtains the resistance value of each isolation resistance.
For using 4 grades of Chebyshev transformation devices broadband power divider design, i.e. N=4 when, had according to formula (4)：
Further, available according to formula (13), formula (14) and formula (15)：
T4(secθmCos θ)=sec4θm(cos4θ+4cos2θ+3)-4sec2θm(cos2θ+1)+1 (20)
Formula (20), which is substituted into formula (6), to be had：
Γ (θ)=Ae-j4θ[sec4θm(cos4θ+4cos2θ+3)-4sec2θm(cos2θ+1)+1] (21)
Further, in conjunction with formula (19) and formula (21), cos4 θ and cos2 the θ respective items in two formulas are enabled to distinguish equal,
It is available：
Γ1=2A (sec4θm-sec2θm) (23)
Γ2=A (3sec4θm-4sec2θm+1) (24)
In addition, Γ3=Γ1, Γ4=Γ0。
Further, impedance transformation ratio isWhen, it can be obtained according to formula (12)：
In above formula, K2Divide the power-division ratios between port for power splitter two-way.
Firstly, for the broadband using 4 grades of Chebyshev transformation devices, decile power splitter, ADS circuit diagrams are not shown in Fig. 3, if
It is K to determine the power-division ratios between power splitter port 2 and port 32=1.5.Enable Γm=0.03, thus according to formula (8), formula
(9) and formula (10) has A=0.03.
Further, it can be obtained by formula (25)：
Further, Γ is had according to formula (22), formula (23) and formula (24)0=0.0470, Γ1=0.0817, Γ2
=0.0995, Γ3=Γ1=0.0817, Γ4=Γ0=0.0470.
Further, by Za0=ZA=KZ0Formula (18) is substituted into, Z then can be obtained by formula (18) successivelya1=67.27 Ω, Za2
=79.21 Ω, Za3=96.65 Ω, Za4=113.80 Ω.
Further, according to ZaN=K2ZbN, ZaN-1=K2ZbN-1..., Za1=K2Zb1, Z can be obtainedb1=44.85 Ω, Zb2=
52.81 Ω, Zb3=64.43 Ω, Zb4=75.87 Ω.
Further, according toZ can be obtainedAT=55.33 Ω, ZBT=45.18 Ω.
The ADS circuit diagrams that the impedance values at different levels being calculated above are substituted into Fig. 3, are optimized using ADS softwares, are obtained
Each values of isolation resistance R1=620 Ω, R2=330 Ω, R3=200 Ω, R4=100 Ω.
Then all impedance parameters of 4 grades of broadbands not in decile power divider circuit have obtained, when center frequency point is 10GHz
When, the power splitter S parameter emulated is shown in Fig. 5, Fig. 6 and Fig. 7.As seen from Figure 5, in 3.92~16.08GHz band limits,
The return loss S11 of port 1 is less than -20dB, and relative bandwidth is more than 121%；In 3.39~16.61GHz band limits, port
2 return loss S22 is less than -20dB, and relative bandwidth is more than 132%；In 4.35~15.65GHz band limits, port 3
Return loss S33 is less than -20dB, and relative bandwidth is more than 113%.The amplitude S parameter S21 of port 2 and the amplitude S parameter of port 3
The simulation curve figure of S31 is shown in Fig. 6, according to Fig. 6's as a result, in 4.30~15.70GHz band limits, port 3 and port 2 it
Between power-division ratios within the scope of 1.750~1.788dB, i.e., power-division ratios between port 3 and port 2 1.496~
Between 1.510, and desired power-division ratios 1.5 meet very well, and relative bandwidth is more than 114%.Simultaneously as shown in Figure 7, exist
In 3.40~16.60GHz band limits, the isolation S23 between port 3 and port 2 is less than -20dB, and relative bandwidth is more than
132%.
For dividing power splitter, ADS circuit diagrams to see Fig. 4 using the broadband etc. of 4 grades of Chebyshev transformation devices, this work(point is set
Power-division ratios K between device port 2 and port 32=1.Equally enable Γm=0.03, thus according to formula (8), formula (9) and
Formula (10) has A=0.03.
Further, it can be obtained by formula (25)：
Further, Γ is had according to formula (22), formula (23) and formula (24)0=0.0461, Γ1=0.0791, Γ2=
0.0961, Γ3=Γ1=0.0791, Γ4=Γ0=0.0461.
Further, by Za0=ZA=KZ0=Z0Formula (18) is substituted into, Z then can be obtained by formula (18) successively1=54.83
Ω, Z2=64.23 Ω, Z3=77.84 Ω, Z4=91.18 Ω.
The ADS circuit diagrams that obtained impedance values at different levels calculated above are substituted into Fig. 4, are optimized using ADS softwares, are obtained
Each values of isolation resistance R1=470 Ω, R2=300 Ω, R3=180 Ω, R4=100 Ω.
Then all impedance parameters in the power divider circuit of 4 grades of broadbands etc. point have obtained, when center frequency point is 10GHz
When, the power splitter S parameter emulated is shown in Fig. 8, Fig. 9 and Figure 10.As seen from Figure 8, in 3.7~16.3GHz band limits, end
The return loss S11 of mouth 1 is less than -20dB, and relative bandwidth is more than 126%；In 3~17GHz band limits, port 2 and port 3
Return loss S22 and S33 be respectively less than -27.9dB, relative bandwidth be more than 140%.The amplitude S parameter S21 of port 2 and port 3
The simulation curve figure of amplitude S parameter S31 see Fig. 9, according to Fig. 9's as a result, port 3 and port 2 realize good constant power
Distribution.As shown in Figure 10, in 3.34~16.66GHz band limits, isolation S23 between port 3 and port 2 is less than-
20dB, relative bandwidth are more than 133%.
As seen from the above-described embodiment, the broadband provided by the invention using 4 grades of Chebyshev transformation devices not decile power splitter
Dividing power splitter with broadband etc. realizes very wide relative bandwidth, much larger than the relative bandwidth that single-stage power splitter is no more than 36%；
And design method provided by the invention is rapidly and efficiently, and when using this method, broadband power divider divides the power-division ratios of port can
With continuous design as needed.
Those skilled in the art understand the present invention it should be clear that the embodiments described herein is to help reader
Principle, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.Obviously, this field
Technical staff can be carried out according to the technical disclosures disclosed by the invention it is various change and deformation without departing from the present invention
Spirit and scope.If these changes and deformation of the present invention belong to the claims in the present invention and its equivalent technology range it
Class, then including the present invention is also intended to comprising these changes and deforming.
Claims (7)
1. a kind of broadband power divider based on Chebyshev transformation device, which is characterized in that held including a total port and two points
Mouthful, it is provided with N number of isolation resistance between two points of ports, is all made of and cuts between total port and each point of port
Transmission line is converted than snow husband's impedance, the transmission line is to add 1/4 wavelength of the preceding paragraph to hinder by N grades of Chebyshev's impedance transformers
Resistance parallel operation forms, and the isolation resistance is connected across corresponding every level-one Qie Bixue between two points of adjacent ports respectively
Husband's impedance transformer junction, N >=1, and N are natural number.
2. a kind of broadband power divider based on Chebyshev transformation device according to claim 1, which is characterized in that described
N=4.
3. a kind of using a kind of circuit parameter of the broadband power divider based on Chebyshev transformation device as claimed in claim 1 or 2
Design method, which is characterized in that include the following steps：
Step 1：It is required according to the bandwidth of operation of power splitter, selects suitable converter series；
Step 2：The power-division ratios for dividing port according to power splitter, obtain impedance transformation ratio；
Step 3：It integrates to obtain converter reflectance factors at different levels using Chebyshev polynomials；
Step 4：The relational expression between adjacent impedance transformer at different levels is obtained according to reflection coefficient parameters at different levels, and according to relationship
Formula calculates the impedance value of transformer sections at different levels successively；
Step 5：The impedance value for obtaining transformer sections at different levels is substituted into circuit model, values of isolation resistance at different levels are calculated.
4. a kind of circuit parameter design side of broadband power divider based on Chebyshev transformation device according to claim 3
Method, which is characterized in that detailed process is as follows：
Step 1：Converter series is set as N, wherein N >=1, and N is natural number；
Step 2：If the position where two points of ports is a points and b points, the roads a transmission line and the roads b transmission line are respectively a points to always
For transmission line and the b point of port to the transmission line of total port, the roads a transmission line, the roads b transmission line and the position that crosses of total port are set as O
Point；The roads a transmission line before impedance transformation includes impedance ZaAnd impedance ZA, the roads the b transmission line before impedance transformation includes impedance ZbAnd resistance
Anti- ZB；When carrying out impedance transformation, the roads a transmission line includes N grades of Chebyshev's impedance transformer impedance Zsa1、Za2、Za3、…、ZaNAnd
One section of 1/4 wavelength impedance transformers impedance ZAT, the roads b transmission line includes N grades of Chebyshev's impedance transformer impedance Zsb1、Zb2、
Zb3、…、ZbNAnd one section of 1/4 wavelength impedance transformers impedance ZBTIf the power-division ratios between b and a two-way are K2, then have ZA
=K2ZBIf from O points to the roads a see into input impedance be Zain, from O points to the roads b see into input impedance be Zbin, then have Zain=
K2Zbin, then O point impedance Z0There is following relationship：
By Zain=K2ZbinFormula (1) is substituted into, is obtained：
Zain=(1+K2)Z0 (2)
When a point port is connected with external circuit, load impedance is equal to Z0, Z0Pass through one section of 1/4 wavelength rheostat Z respectivelyATAnd ZBT
Transform to ZAAnd ZB, in order to keep two impedance values more reasonable, take ZA=KZ0, ZB=Z0/ K, then
It obtainsAs input impedance ZainTransform to ZAOr input impedance ZbinTransform to ZBWhen, impedance becomes
It changes than being
Step 3：When from ZainTransform to ZAWhen, there is ZaN=K2ZbN, ZaN-1=K2ZbN-1..., Za1=K2Zb1, when N is even number, N
The total reflectance factor of grade converter is：
When N is odd number, the N grades of total reflectance factors of converter are：
Γ (θ)=2e-jNθ[Γ0cosNθ+Γ1cos(N-2)θ+…+Γncos(N-2n)θ+…+Γ(N-1)/2cosθ] (5)
θ in formula (4) and formula (5) represents the corresponding electrical length of impedance transformation transmission line, Γ under different frequency0, Γ1...,
ΓnIt is the reflectance factor at impedance transform node, N is the series of impedance transformer, n=0,1,2,3 ..., N-1；
Γ (θ) is set to be proportional to Chebyshev polynomials TN(secθmCos θ) carry out passband synthesis, even
Γ (θ)=Ae-jNθTN(secθmcosθ) (6)
Wherein：A is undetermined constant, θmIndicate the corresponding electrical length of passband low end frequency；
As θ=0, have in conjunction with formula (4), formula (5) and formula (6)：
Then coefficient A is：
If the maximum reflection coefficient amplitude in passband is Γm, then have：
Γm=| A | | TN(secθmcosθ)|max=| A | (9)
For passband low side θm, there is TN(secθm)>0, in conjunction with formula (8) and formula (9), obtain：
Had according to approximation relation：
Then it obtains：
Chebyshev polynomials T as a result,i(secθmCos θ) there is following form：
T1(secθmCos θ)=sec θmcosθ (13)
T2(secθmCos θ)=sec2θm(cos2θ+1)-1 (14)
Other high-order Chebyshev polynomials are found out with following formula：
Ti(secθmCos θ)=2sec θmcosθTi-1(secθmcosθ)-Ti-2(secθmcosθ) (15)
Wherein：I=3,4,5 ..., N；
With formula (15) to the T in formula (6)N(secθmCos θ) it is unfolded, then enable cos therein (N-2n) θ and public affairs
Respective items in formula (4) or formula (5) are equal, obtain reflectance factor Γ at different levelsn；
Step 4：Obtain reflectance factor Γ at different levelsnThere is following relational expression：
As n=0, Za0=ZA, for Multi-stage impedance matching, ΓnSmaller, then formula (16) is reduced to：
In addition, according to formula (4) and formula (5), there is relational expression Γ0=ΓN, Γ1=ΓN-1, Γ2=ΓN-2..., thus obtain
Relational expression between adjacent impedance transformer at different levels：
The impedance value of transformer sections at different levels is calculated successively according to relational expression (18)；
Step 5：The impedance value for obtaining transformer sections at different levels is substituted into circuit model, values of isolation resistance at different levels are calculated.
5. a kind of circuit parameter design side of broadband power divider based on Chebyshev transformation device according to claim 4
Method, which is characterized in that the power-division ratios of point port continuously design according to actual needs.
6. a kind of circuit parameter design side of broadband power divider based on Chebyshev transformation device according to claim 4
Method, which is characterized in that the impedance transformation ratio in the step 2 passes through backward impedance transformation calculations, i.e. ZATransform to input impedance
Zain, or by ZBTransform to input impedance Zbin, at this time impedance transformation ratio be
7. a kind of circuit parameter design side of broadband power divider based on Chebyshev transformation device according to claim 4
Method, which is characterized in that the circuit model in the step 5 is ADS circuit models.
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| CN115313007A (en) * | 2022-04-12 | 2022-11-08 | 河北军澍电子科技有限公司 | Ultra-wideband miniaturized microstrip power divider |
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