通信工程2010級(jí)大三下微波工程ch32broad band impedance matching

1、Foundations of Microwave TechnologyFeb-Jun/2013Broad Band Impedance MatchingDr. Kun Xu （徐坤）State Key Lab of Information Photonics and Optical Communications(University of Posts and Telecommunications)Tel:E-mail: xukunOutline1. 不匹配損耗（Mismatch Losses）2. 匹配問(wèn)題（Matching Problem）3. 窄帶匹配：波長(zhǎng)線串連匹配、單節(jié)傳輸線并聯(lián)匹配、

2、雙節(jié)傳輸線并聯(lián)匹配（Narrow Band Matching）4. 寬帶匹配：波導(dǎo)段匹配、微帶線匹配和幾種特殊要求下的匹配、二項(xiàng)式阻抗變換器、切比雪夫阻抗變換器（Broad Band Matching）Broadband Matching“寬帶”匹配A New Word: Transform波形和特性阻抗相同，但不同的Meaning:傳輸線之間的變換(1) Size Transition (過(guò)渡)(2) Impedance Matching (匹配)波形相同，但特性阻抗不同的傳輸線之間的變換過(guò)渡同軸波導(dǎo)移位補(bǔ)償結(jié)構(gòu)錐形過(guò)渡結(jié)構(gòu)Z=L0=60 ln D0Ced0r通過(guò)這種方法就可以使得原來(lái)兩個(gè)

3、不同的同軸線連接之后能在較寬的頻帶內(nèi)近似實(shí)現(xiàn)匹配。在兩特性阻抗不同的/4 阻抗變換傳輸線之間一段/4的阻抗變換器同軸線波導(dǎo)內(nèi)外導(dǎo)體尺寸都不相等=ZZ02Z1/4 阻抗變換矩形波導(dǎo)（1）相速vp:波的等相位面沿波導(dǎo)軸向速度vp = w / bb =- k 2k 2cv = 1/me2 1 21= 2p- l l c 波導(dǎo)波長(zhǎng)g: 波導(dǎo)內(nèi)沿軸向電磁波相鄰兩個(gè)同相位點(diǎn)之間的距離lg = lTEM波：/4 阻抗變換矩形波導(dǎo)（2）TE10Z b 10a2 l1- 2a Z0b a不變情況下其它情況下Problem?“窄”？ 匹配長(zhǎng)度與信號(hào)波長(zhǎng) (頻率)的密切關(guān)系Frequency Response of

4、 /4 TransformerKnown: It provides a perfect matching at f0q = b l = 2p l0l4= p f2f0長(zhǎng)度僅對(duì)f0頻率nBdwdidwthdBha is small !“匹配”是窄帶的pfq= b= l2f0cosqGum allowable Reflection Coefficientq0 f0阻抗變換器帶寬：匹配頻率f0（帶中心頻率）附近，在的最大反射系數(shù)幅度|m|條件下，反射系數(shù)|的頻率范圍Multiple Reflections at Junction - 1= Z2 - Z1G1Z+ Z21Total reflectio

5、n coefficientG = . = -G21= Z3 - Z2G3Z + Z32Partial reflection coefficientPartial transmissio n coefficient= 1+ G1T12= 1+ G2 = 1- G1T21Multiple Reflections at Junction - 2Multi-reflectionq = b l = 2p l l Round Trip反射和透射系數(shù)是對(duì)于振幅而不是功率，并且有相位關(guān)系。上述項(xiàng)為傳輸距離L的相位延遲Theory of Small ReflectionsRound TripPhase dela

6、y when the incident wave travels up and down the line= 1+ G1T12G G + G e- j2qT= 1- G1G 211213G2 = -G1Multisection Transformer（1）N equal-length sectionsZn increase or decrease monotonicallyZl is realGradual Change of step sizesMultisection Transformer（2）Only a single reflection considered at each jun

7、ctionPartial reflection coefficeints at each junctionMultisection Transformer（3）Key ofDesign: ai and nTotal Reflection CoefficientQuarter- wave transfor- merGpai =q = b i G1 l=2ally Flat Transformer Equal Ripple Transformerally Flat /4 Transformer-1Reviwe:( xn )n= i=0(1+ x)nn-i nCally Flat /4 Transf

8、ormer-2Note that:= Gi= Cn-i+1aLet：inG1Sum of expanded coefficientsx = 1(1+ x)nLet：(C xn )n= i=0n-inally Flat /4 Transformer-3Distribution of Partial Reflection Coefficientsally Flat /4 Transformer-4ally Flat Passband CharacteristicKnown：um allowable=l=2l/0Reflection Coefficientally FlatResponse(1) S

9、ections N(2) Bandwidthally Flat /4 Transformer-5Design of Impedence of Each Sectionln x 2 x -1 , x 2x +1G1GnaRatio of Transform erZiiiExample 1-1Example 1-2查系數(shù) “分布”表“最平坦匹配”又稱(chēng)為：Binomial Matching2pl0ppDff2 f0pq = b l =2Dq = DqDf =l4f2f00Equal Ripple Transformer- Chebyshev PolynomialEqual Ripple Transf

10、ormer- Chebyshev Polynomial(切比雪夫多項(xiàng)式)該阻抗變換的出發(fā)點(diǎn)：切比雪夫多項(xiàng)式Equal Ripple TransformerDesign () to a Chebyshev PolynomialKey of Design: Reflect Coefficient and n總的反射系數(shù)Chebyshev Polynomial (1)遞推公式：1 0 Chebyshev Polynomial (2)示意圖(-1x+1)n=0、n=1時(shí)的圖形？Chebyshev Polynomial (3)例題：畫(huà)出n=8時(shí)-1,+1定義域的契比雪夫函數(shù)Chebyshev Polynomial (4)令：做變換：帶寬因子Chebyshev Polynomial (5)令：阻抗匹配中應(yīng)用（1）總的反射系數(shù)令：阻抗匹配中應(yīng)用（2）q = b l 0令：阻抗匹配中應(yīng)用（3）契比雪夫多項(xiàng)式匹配的入手點(diǎn)定義域、值域變換阻抗匹配中應(yīng)用（4）n=2：阻抗匹配中應(yīng)用（5）n=3：“三步 走”策略注：GiZiExample 2-1Example 2-2SummaryIn contrast with the binomial matching transformer, the Chebyshev transformeropt