1 %% 2 % Taylor Taper 3 4 clc; 5 clear all; 6 close all; 7 format long; 8 9 N = 48; 10 M = 10000; 11 d = 1/2; 12 L = (N-1)*d;% antenna length 13 theta = 0:pi/M:pi;% 14 x = L*cos(theta); 15 f0 = 1e9; 16 %lambda = 3e8/f0; 17 %d = lambda/2;% elements spacing 18 k =2*pi;% wave constant 19 R = 25; % amplitude ration between mainbeam and sidelobe , dB 20 A = acosh(10^(R/20))/pi; 21 % T = cos(pi*sqrt(x.^2-A^2)); 22 % af = 20*log10(abs(T)/max(T)); 23 % error = 0.001; 24 % % af=U; 25 % pos1_3dB = []; 26 % pos_max = find(max(af)==af); 27 % while(isempty(pos1_3dB)) 28 % pos1_3dB = find(abs(((af(1:pos_max)-af(pos_max)))+3) < error); 29 % error = error + 0.001; 30 % end 31 % error = 0.001; 32 % pos2_3dB = []; 33 % while(isempty(pos2_3dB)) 34 % pos2_3dB = find(abs(((af(pos_max:end)-af(pos_max)))+3) < error); 35 % error = error + 0.001; 36 % end 37 % BeamWidth= (theta(pos2_3dB(1)+pos_max)-theta(pos1_3dB(end)))/pi*180; 38 % figure; 39 % plot(theta,af); 40 % hold on; 41 % str = strcat('L=', num2str(L),'lambda, SLL = -',num2str(R) ,'dB '); 42 % bw = strcat('mainbeam beamwidth=',num2str(BeamWidth),'degree '); 43 % text(pi*2/3,-5,str,'fontsize',12); 44 % text(pi*2/3,-8,bw,'fontsize',12); 45 % title('Radiation Pattern of an Idealized Equvialent Sidelobe Array '); 46 % xlabel('Phase'); 47 % ylabel('Amplitude'); 48 % ylim([-60 0]); 49 %% 50 % Taylor synthesis 51 % theta = -pi/2:0.01:pi/2;% 52 % x = L*cos(theta); 53 54 n1 =ceil(A^2*2+1.5);% the first 3 sidelobes have almost same amplitude 55 %n1 =3; 56 sigma = n1/sqrt(A^2+(n1-0.5)^2); 57 xn = zeros(1,n1-1); 58 for j = 1:1:n1-1 59 xn(j) = sigma*sqrt(A^2+(j-0.5)^2); 60 % xn(j) = j*sqrt(A^2+(j-0.5).^2)/sqrt(A^2+(n1-0.5).^2); 61 end 62 for i = 1:1:length(x) 63 if x(i) ~= 0 64 T(i) = sin(pi*x(i))/pi/x(i)*cosh(pi*A); 65 for j = 1:1:n1-1 66 T(i) = T(i)*(1-(x(i)/xn(j))^2)/(1-(x(i)/j)^2); 67 end 68 else 69 T(i) = cosh(pi*A); 70 for j = 1:1:n1-1 71 T(i) = T(i)*(1-(x(i)/xn(j))^2)/(1-(x(i)/j)^2); 72 end 73 end 74 end 75 T = T / max(T); 76 77 I =ones(1,N); 78 % zn = zeros(1,N); 79 for i = 1:1:N 80 if mod(N,2) == 1 81 zn = abs((i-(N+1)/2)*d*2/L); 82 else 83 %#zn = (i-(N+1)/2)*d 84 if i < (N+1)/2 85 zn = (2*abs((N/2+1)-i)-1)*d/L; 86 else 87 zn = (2*abs(i-N/2)-1)*d/L; 88 end 89 end 90 for j = 1:1:n1-1 91 I(i) = I(i) + 2*T((find( min(abs(x-j))==abs(x-j))))*cos(j*pi*zn); 92 end 93 end 94 I = I/max(I) 95 af = 20*log10(abs(T)); 96 97 error = 0.0001; 98 % af=U; 99 pos1_3dB = []; 100 pos_max = find(max(af)==af); 101 while(isempty(pos1_3dB)) 102 pos1_3dB = find(abs(((af(1:pos_max)-af(pos_max)))+3) < error); 103 error = error + 0.0001; 104 end 105 error = 0.0001; 106 pos2_3dB = []; 107 while(isempty(pos2_3dB)) 108 pos2_3dB = find(abs(((af(pos_max:end)-af(pos_max)))+3) < error); 109 error = error + 0.0001; 110 end 111 HP = 2*asind(sigma/L/pi*sqrt((acosh(10^(R/20)))^2-(acosh(10^(R/20)/sqrt(2)))^2)); 112 113 BeamWidth= (theta(pos2_3dB(1)+pos_max)-theta(pos1_3dB(end)))/pi*180; 114 figure; 115 plot(theta/pi*180,af); 116 grid on; 117 hold on; 118 str = strcat('L=', num2str(L),'lambda, SLL = -',num2str(R) ,'dB '); 119 bw = strcat('mainbeam beamwidth=',num2str(BeamWidth),'degree, value in theroy is ',num2str(HP),'degree'); 120 text(pi*2/3,-5,str,'fontsize',12); 121 text(pi*2/3,-8,bw,'fontsize',12); 122 title('Radiation Pattern of Taylor Synthesis Array '); 123 xlabel('Phase'); 124 ylabel('Amplitude'); 125 ylim([-60 0]); 126 figure; 127 plot(I); 128 grid on; 129 title('激励') 130 % HP = 2*asind(sigma/L/pi*sqrt((acosh(10^(R/20)))^2-(acosh(10^(R/20)/sqrt(2)))^2)); 131 % HP*L/sigma 132 % BeamWidth*L/sigma 133 %% 134 % 135 radiation_pattern(I); 136 % amp = I; 137 % af = zeros(1,length(theta)); 138 % a = 0; 139 % b = 0; 140 % for j = 1:1:N 141 % a= a+amp(j); 142 % b = b + power(amp(j),2); 143 % af = af+ exp(1i*(j-1)*k*d*cos(theta))*amp(j); 144 % end 145 % af = abs(af/max(af) ); 146 % af = 20*log10(abs(af)); 147 148 % error = 0.0001; 149 % % af=U; 150 % pos1_3dB = []; 151 % pos_max = find(max(af)==af); 152 % while(isempty(pos1_3dB)) 153 % pos1_3dB = find(abs(((af(1:pos_max)-af(pos_max)))+3) < error); 154 % error = error + 0.0001; 155 % end 156 % error = 0.0001; 157 % pos2_3dB = []; 158 % while(isempty(pos2_3dB)) 159 % pos2_3dB = find(abs(((af(pos_max:end)-af(pos_max)))+3) < error); 160 % error = error + 0.0001; 161 % end 162 % % HP = 2*asind(sigma/L/pi*sqrt((acosh(10^(R/20)))^2-(acosh(10^(R/20)/sqrt(2)))^2)); 163 % 164 % BeamWidth= (theta(pos2_3dB(1)+pos_max)-theta(pos1_3dB(end)))/pi*180; 165 % figure; 166 % plot(theta/pi*180,af); 167 % grid on; 168 % hold on; 169 % str = strcat('L=', num2str(L),'lambda, SLL = -',num2str(R) ,'dB '); 170 % bw = strcat('mainbeam beamwidth=',num2str(BeamWidth),'degree, value in theroy is ',num2str(HP),'degree'); 171 % text(pi*2/3,-5,str,'fontsize',12); 172 % text(pi*2/3,-8,bw,'fontsize',12); 173 % title('Radiation Pattern of Taylor Synthesis Array '); 174 % xlabel('Phase'); 175 % ylabel('Amplitude'); 176 % ylim([-60 0]); 177 % 178 % % HP = 2*asind(sigma/L/pi*sqrt((acosh(10^(R/20)))^2-(acosh(10^(R/20)/sqrt(2)))^2)); 179 % % HP*L/sigma 180 % % BeamWidth*L/sigma
