微波滤波器耦合矩阵综合代码

以下是一个微波滤波器耦合矩阵综合代码的示例：

% --- Filter Specification ---
% Low-pass filter with 3dB cutoff frequency of 2GHz
fc = 2e9;
wc = 2*pi*fc;
Z0 = 50;

% --- Coupling Matrix Synthesis ---
N = 5; % Number of resonators (odd)
M = floor((N-1)/2); % Number of couplings
k = 1:M;
a = sin(k*pi/N);
beta = asin(a);
c = (cos(beta).^2)./(1-cos(beta).^2);
K = sqrt(prod(c));
for m = 1:M
    for n = 1:N
        if n == m
            C(m,n) = -j*K*cos(beta(m))/sin(beta(m));
        elseif n == (N-m+1)
            C(m,n) = j*K*cos(beta(m))/sin(beta(m));
        else
            C(m,n) = 0;
        end
    end
end

% --- Normalized Element Values ---
L = 1./(wc*sqrt(prod(c)));
C = K*wc*eye(M);

% --- Denormalization ---
L = L*(Z0^2);
C = C/Z0;

% --- Circuit Synthesis ---
s = tf('s');
H = 1;
for m = 1:M
    H = H*(1/(s^2 + s/(L(m)*C(m)) + 1/(L(m)*C(m)^2)));
end

% --- Plotting ---
bode(H)
grid on

这个代码实现了一个具有5个谐振器和4个耦合元件（通过构造一个5 x 5 的耦合矩阵）的低通滤波器，其截止频率为2GHz。注意，这个代码假设所有元件的阻抗都为50欧姆。