波形松弛迭代法求解互连线的时域响应，matlab程序实现

以下是MATLAB中使用波形松弛迭代法求解互连线时域响应的程序实现：

function [t, V] = wave_relaxation(L, C, R, G, Z0, Vin, t0, tf, dt, tol, maxit)
% Waveform relaxation method for calculating the time-domain response of a transmission line
% Input: L is the inductance per unit length
%        C is the capacitance per unit length
%        R is the resistance per unit length
%        G is the conductance per unit length
%        Z0 is the characteristic impedance of the line
%        Vin is the input voltage waveform function handle
%        t0 is the initial time
%        tf is the final time
%        dt is the time step
%        tol is the tolerance for stopping criteria
%        maxit is the maximum number of iterations
% Output: t is the vector of time samples
%         V is the vector of output voltage samples

% Calculate the propagation constant
gamma = sqrt((R + sqrt(R^2 + 4*L/C))*(G + sqrt(G^2 + 4*C/L)))/(2*sqrt(L*C));

% Calculate the line parameters in the frequency domain
ZL = R + 1i*gamma*L;
YL = G + 1i*gamma*C;

% Calculate the time constant of the line
tau = L/R;

% Calculate the number of time steps
N = ceil((tf - t0)/dt) + 1;

% Initialize the output voltage vector
V = zeros(N, 1);

% Initialize the state variables
v = Vin(t0);
i = 0;

% Initialize the iteration counter
k = 0;

% Initialize the time vector
t = linspace(t0, tf, N);

while k < maxit
    k = k + 1;
    for n = 1:N
        % Update the state variables
        if n == 1
            v_prev = 0;
        else
            v_prev = V(n-1);
        end
        v_new = (Vin(t(n)) + (v_prev - ZL*i)/Z0)/(1 + tau*YL);
        i_new = i + gamma*(v_new - v_prev)/Z0;
        v = v_new;
        i = i_new;
        
        % Update the output voltage
        V(n) = v_new;
    end
    
    % Check the termination condition
    if norm(V - Vin(t)) < tol
        return
    end
end

其中，L、C、R、G和Z0分别是互连线的线性参数和特性阻抗，Vin是输入电压波形的函数句柄，t0、tf和dt分别是计算的起始时间、终止时间和时间步长，tol是停止条件的阈值，maxit是最大迭代次数。函数返回时间向量t和输出电压向量V。

使用方法：在MATLAB命令行窗口中输入以下命令：

[t, V] = wave_relaxation(L, C, R, G, Z0, Vin, t0, tf, dt, tol, maxit);

其中，L、C、R、G和Z0是互连线的线性参数和特性阻抗，Vin是输入电压波形的函数句柄，t0、tf和dt分别是计算的起始时间、终止时间和时间步长，tol是停止条件的阈值，maxit是最大迭代次数。函数将返回时间向量t和输出电压向量V。