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1、,*,1,Chapter 4,陣列綜合,Dolph-Chebyshev,綜合,烏特沃特綜合法,Fourier,級數(shù)法,Schelkunov,方法,泰勒綜合法,非均勻幅度分布的直線陣,n,e,為偶數(shù)時(shí)，根據(jù)直線陣場強(qiáng)相加可以得到：,式中,2,非均勻幅度分布的直線陣,n,o,為奇數(shù)時(shí),式中,3,非均勻幅度分布的直線陣,例如一,9,單元點(diǎn)源陣列，間距,/2,，等幅同相饋電。,4,5,Dolph-Chebyshev,綜合（最優(yōu)分布）,對于指定的旁瓣電平，其第一零點(diǎn)波束寬度為最窄；反之，對于指定的波束寬度，其旁瓣電平最低。綜合得到的方向圖為,(,N,T,為陣元數(shù)量,),由于主瓣與副瓣之比,r,1,，因此

2、,其中,M,=,N,T,-1,6,將陣列多項(xiàng)式與,Chebyshev,多項(xiàng)式進(jìn)行匹配，使陣列的副瓣占據(jù) 的區(qū)域，陣列的主瓣位于,z,0,1,的區(qū)域，有,當(dāng),N,T,為偶數(shù)、陣元間距,d,x,/,0.5,時(shí)，所需激勵(lì)如下,:,7,設(shè)計(jì)步驟：,選取與陣列如下多項(xiàng)式同冪次（,m=n-1,）的切比雪夫多項(xiàng)式,對于偶數(shù)個(gè)陣元,對于奇數(shù)個(gè)陣元,8,選取主瓣與副瓣之比,r,，并從下式中,解出,x,0,.,引入新的總量,w,，使得,此時(shí) 。以,w,取代 中的變量,x,，令,故波瓣圖多項(xiàng)式 和 便可表示為,w,的多項(xiàng)式。,9,使切比雪夫多項(xiàng)式和陣列多項(xiàng)式相等，即,由此可解出陣列多項(xiàng)式的系數(shù)，然后得到陣列的口徑電

3、平分布。,詳見,J.D.Kraus,天線,Dolph-Chebyshev,分布的八源陣舉例,陣列綜合的,實(shí)質(zhì),是以,Chebyshev,多項(xiàng)式表示陣列多項(xiàng)式。,10,烏特沃特綜合法,一個(gè)均勻照射的陣列方向圖有著如下的形式：,均勻照射的陣列方向圖是一組正交波束的疊加，因此可以用來綜合所需要的方向圖。,一個(gè)長度為,L,=,Nd,x,的陣列，在,u,空間中將有,N,個(gè)波束覆蓋大小為,(,N,-1),/,L,的扇區(qū)，,11,第,i,個(gè)波束由如下的相位步進(jìn),激勵(lì)：,其中,n,取值與,i,相同，方向圖函數(shù)如下：,給定的方向圖函數(shù),E,(,u,),可以由在,u,i,上的,N,個(gè)取樣近似：,在每個(gè)陣元上的總電

4、流即是形成所有波束的電流之和。對于第,n,個(gè)單元有：,12,正交波束,平頂方向圖的綜合,13,由,烏特沃特,法綜合得到的,64,個(gè)點(diǎn)源陣列的脈沖形方向圖,sinc,基函數(shù)（,i,=-13,）,14,泰勒綜合法,對于大型陣列，,Dolph-Chebyshev,綜合方法得出的是單調(diào)的口徑分布，因此該方法會(huì)導(dǎo)致口徑,tapered efficiency,降低,.,泰勒指出，由于,Chebyshev,方向圖的所有副瓣電平均相等，因此導(dǎo)致,tapered,效率的損失。對于大型陣列，這就意味著更多的能量將集中于副瓣內(nèi)。,15,泰勒建議，可以設(shè)計(jì)這樣的方向圖函數(shù)，使得靠近主瓣的方向圖零點(diǎn)類似于,Chebys

5、hev,方向圖，但遠(yuǎn)離主瓣的零點(diǎn)位置對應(yīng)于均勻分布的情況。,由,泰勒綜合法,得到的,64,個(gè)點(diǎn)源陣列的方向圖,16,副瓣比,r,即是,F,0,在,z=0,的值：,以上的理想方向圖對應(yīng)于另,一類,Chebyshev,方向圖，其零點(diǎn)位置在：,17,為了匹配兩類零點(diǎn)，泰勒引入尺度因子,，通過調(diào)整零點(diǎn)的位置,z,n,來拉伸空間因子，以使其中一個(gè)零點(diǎn)對應(yīng)于 。新的方向圖函數(shù)變?yōu)椋?所需要的口徑分布可以展開為有限項(xiàng)的傅里葉級數(shù)，且該口徑分布函數(shù)在陣列的邊緣處導(dǎo)數(shù)為零。,18,口徑分布函數(shù)可以表示為,19,Bayliss Line Source Difference Patterns,該方法通常用于脈沖系統(tǒng)

6、,.,參數(shù),A,和,通常用于控制副瓣及其下降的情況,.,陣列的激勵(lì)由如下公式給出：,此處,20,由傅里葉級數(shù)可以算出各系數(shù)的值：,在此陣列中，方向圖的零點(diǎn)位于：,21,For,A,and,n,Elliott presented a table of the coefficients themselves for SLLs from-15dB to-40dB in increments of 5dB.,22,Fourier,級數(shù)法,以上求和的結(jié)果即是有限項(xiàng)傅里葉級數(shù)，它在,u,空間是周期性的。對于一個(gè)期望的,F,(,u,),，所需激勵(lì)條件可由正交性質(zhì)得到：,該方法常用于賦形波束的綜合,.,23,

7、由,Fourier,級數(shù)法綜合得到的,64,個(gè)點(diǎn)源陣列方向圖。脈沖形方向圖（,0.4 u 0.4,，,F(u)=1,，其他,F(u)=0,）,24,Schelkunov,方法,陣因子可以寫為關(guān)于復(fù)變量,z,的多項(xiàng)式形式，其中,以上為,(,N,-1),階多項(xiàng)式，它有,(,N,-1),個(gè)零點(diǎn)，因此,對于均勻照射的陣列有：,25,基于優(yōu)化方法的方向圖綜合,GA;(R.L.Haupt,Y.Rahmat-Samii,D.H.Werner,),SA;(F.Ares,),ANN;(F.Ares,),TACO;(N.Karaboga,).,PSO;(,Y.Rahmat-Samii,D.H.Werner,).,

8、DE.(S.Yang,A.Rydberg,),Y.Rahmat-Samii and E.Michielssen,Electromagnetic Optimization by Genetic Algorithms,.New York:Wiley,1999.,26,Pattern Synthesis Using Measured Element Patterns,Where,e,0,(,u,)is the isolated element pattern and,C,mn,is an unknown coupling coefficient.The radiated signal from th

9、e whole array is,Steyskal,and J.S.Herd,“Mutual coupling compensation in small array antennas,”,IEEE Trans.Antennas Propagat.,vol.38,no.12,pp.1971-1975,Dec.1990.,Corresponding to an incident signal,A,n,at the,n,th element,the radiation,27,Tseng-Cheng Pattern Synthesis Technique,For planar array with

10、rectangular grid,conventional synthesis approach has been to assume separable and independent current distributions in the two dimensions and to employ the method of pattern multiplication.,If a Dolph-Chebyshev excitation is used,the radiation pattern of a rectangular array is optimum only in two pr

11、incipal sections;the patterns in other cross sections have a much broader main beam and greatly reduced sidelobes.,D.K.Cheng and F.I.Tseng proposed a synthesis approach for scanning rectangular arrays,which will produce a Chebyshev pattern in any cross section with the same specified SLL.,28,F.I.Tse

12、ng,and D.K.Cheng,“Optimum scannable planar arrays with an invariant sidelobe level,”,IEEE Proc.,vol.56,no.11,pp.1771-1778,1968.,Y.U.Kim,and R.S.Elliott,“Extensions of the Tseng-Cheng pattern synthesis technique,”,J.Electromag.Waves Appl.,vol.2,pp.255-268,1988.,Rivas A,Rodriguez JA,Ares F,Moreno E.Pl

13、anar arrays with square lattices circular boundaries:sum patterns from distributions with uniform amplitude or very low dynamic-range ratio.,IEEE Antennas and Propagation Magazine,2001;43(5):90-93.,29,Consider a rectangular planar array with a rectangular boundary,and assume a quadrantal symmetry in

14、 the excitation of the array elements.With 2,N,2,N,elements,the array sum pattern is given by,The pattern was connected to a polynomial of,one variable,by using the Baklanov transformation,30,Since,With The same formula applying for .Then a general polynomial of degree 2,N,-1 can be written in the f

15、orm,31,If one desired that the pattern,S,(u,v)have the characteristics of the polynomial ,comparing these two we obtain,where,Tseng and Cheng Chose as the Chebyshev Polynomial .By Comparison,a,2s-1,is obtained.Thus,I,mn,is given by,32,In which,b,2s-1,is a substitution for .Again,Alternatively,using

16、the concept of,collapsed distribution,one can deduce the excitation of a linear array laid out along the,X,-axis that will give the same,XZ,pattern as does the planar array:,33,The synthesis procedure:,Design a linear array which has the same pattern as the desired pattern in any,-cut plane,of the planar array;,Obtain the coefficients,b,2s-1,from the excitation distribution,I,m,of the linear array;,Obtain the planar distribution,I,mn,from,b,2s-1,.,Example:,A 20,20 square grid planar array with/2