切比雪夫綜合法的Matlab程序

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%% --------------------------------------------------------------------------

% 切比雪夫低副瓣陣列綜合

% 設(shè)計(jì)一個(gè)間距為d,單元數(shù)為N，主副瓣電平比為RdB，掃描角度為theta0的切比雪夫陣列。

% 2019.11.10

%--------------------------------------------------------------------------

%% 初始數(shù)據(jù)賦值

clear

clc

N = 13;%單元數(shù)N（3

ifrem(N,2)==0%求和項(xiàng)數(shù)M(奇偶不同)

M = N/2;

else

M = (N-1)/2+1;

end

RdB = 26;% 主副瓣比(dB值)

lamuda = 10;% 波長

d = 0.6*lamuda;% 單元間距

theta0 = 80/180*pi;% 掃描角度，相對于陣列排布方向的夾角

A = [1,0,0,0,0,0,0,0,0,0,0,0,0,0;% chebyshev多項(xiàng)式Tn(x) = cos(nu)= f(x)系數(shù)矩陣A

0,1,0,0,0,0,0,0,0,0,0,0,0,0;% 系數(shù)矩陣A每一行表示n，從n = 0開始

-1,0,2,0,0,0,0,0,0,0,0,0,0,0;% 列表示x的冪次方，從0次方開始

0,-3,0,4,0,0,0,0,0,0,0,0,0,0;

1,0,-8,0,8,0,0,0,0,0,0,0,0,0;

0,5,0,-20,0,16,0,0,0,0,0,0,0,0;

-1,0,18,0,-48,0,32,0,0,0,0,0,0,0;

0,-7,0,56,0,-112,0,64,0,0,0,0,0,0;

1,0,-32,0,160,0,-256,0,128,0,0,0,0,0;

0,9,0,-120,0,432,0,-576,0,256,0,0,0,0;

-1,0,50,0,-400,0,1120,0,-1280,0,512,0,0,0;

0,-11,0,220,0,-1232,0,2816,0,-2816,0,1024,0,0;

1,0,-72,0,840,0,-3584,0,6912,0,-6144,0,2048,0;

0,13,0,-364,0,2912,0,-9984,0,16640,0,-13312,0,4096];

% 初始矩陣賦值

I =zeros(1,M);% 電流幅度矩陣

S =zeros(M,M);% 陣因子系數(shù)矩陣

S_compare =zeros(1,M);% 系數(shù)比對矩陣

R = 10^(RdB/20);% 非dB 值的主副瓣比

x0 = 1/2*( (R+sqrt(R^2-1))^(1/(N-1))+...% 變量代換值x0

(R-sqrt(R^2-1))^(1/(N-1)) );

%% 求S、S_compare和I

% 從系數(shù)矩陣中擇選出M個(gè)求和項(xiàng)對應(yīng)的系數(shù)S(奇偶分開討論)

fori= 1:M

ifrem(N,2)==0% 偶數(shù)情況

forj= 1:M% 第i行表示x的i次方，

S(i,j) = A(2*j,2*i);% 第j列表示第j個(gè)求和項(xiàng)系數(shù)（未除x0)

end

S_compare(i) = A(N,2*i);% 比對矩陣，即下標(biāo)為N-1的chebyshev多項(xiàng)式的系數(shù)

else% 奇數(shù)情況

forj= 1:M

S(i,j) = A(2*j-1,2*i-1);

end

S_compare(i) = A(N,2*i-1);

end

end

% 通過S和S_compare系數(shù)比對求出電流幅度

fork = 1:M

i= M-k+1;

ifrem(N,2)==0% 偶數(shù)

I(i) = (S_compare(i)*x0^(2*i-1) -...

I*S(i,:)')/S(i,i);

else% 奇數(shù)

I(i) = (S_compare(i)*x0^(2*(i-1)) -...

I*S(i,:)')/S(i,i);

end

end

I = I/max(I);% 對I歸一化

ifrem(N,2)==0

I_final = [fliplr(I),I];% 最終的單元排列（左右對稱）

else

I_final = [fliplr(I),I(2:end)];

end

sprintf('天線單元?dú)w一化電流幅度：')

sprintf('%.3f ',I_final)

%% 獲得最終陣列方向圖S_P

theta_rad = 0pi;

theta = theta_rad*180/pi;

u =pi*d/lamuda*(cos(theta_rad)-cos(theta0));

S_P =zeros(1,length(theta_rad));% 最終方向圖

fork = 1:M

ifrem(N,2)==0

S_P = S_P + I(k)*cos((2*k-1)*u);% 偶數(shù)

else

S_P = S_P + I(k)*cos(2*(k-1)*u);% 奇數(shù)

end

end

S_P_abs =abs(S_P);% 對S_P取絕對值

S_PdB = 20*log10(S_P_abs/max(S_P_abs));% 對S_P取dB值

%% 繪圖

H = -ones(1,length(S_P_abs))*26; % 根據(jù)預(yù)先設(shè)置的主副瓣比得到的參考曲線

% 直角坐標(biāo)系

figure('NumberTitle','off','Name','S Parameter (abs)-Plot');

plot(theta,S_P_abs,'b','LineWidth',1.5)

xlabel('theta(°)')

ylabel('|S| ')

title('chebyshev低副瓣陣列直角坐標(biāo)圖')

figure('NumberTitle','off','Name','S Parameter (dB)-Plot');

plot(theta,H,'r--','LineWidth',1.5)

holdon

plot(theta,S_PdB,'b','LineWidth',1.5)

xlabel('theta(°)')

ylabel('|S| dB')

title('chebyshev低副瓣陣列直角坐標(biāo)圖')

legend('預(yù)設(shè)副瓣參考曲線','方向圖')

% 極坐標(biāo)系

figure('NumberTitle','off','Name','S Parameter (dB)-Polar');

polarplot(theta_rad,H,'r--','LineWidth',1.5)

holdon

polarplot(theta_rad,S_PdB,'b','LineWidth',1.5)

thetalim([0 180]);

rmin = S_PdB(1,1);

rmax =max(S_PdB);

rlim([-50 rmax]);

title('chebyshev低副瓣陣列極坐標(biāo)圖')

legend('預(yù)設(shè)副瓣參考曲線RdB','方向圖(dB)')