【传输损耗】双/三面板的传输损耗（Matlab实现）-优快云博客

本文链接：https://blog.youkuaiyun.com/Matlab88888/article/details/143098023

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📋📋📋本文目录如下：🎁🎁🎁

💥1 概述

双/三面板在电子领域中具有重要作用，其中传输损耗是一个关键特性。对于双面板，其传输损耗主要受到板材的材质、导体的特性以及线路布局等因素的影响。例如，板材的介电常数和损耗角正切会直接影响信号在其中传输时的衰减程度。导体的电阻也会导致能量损失，尤其是在高频信号传输时。线路的长度、宽度以及弯曲程度等布局因素也会对传输损耗产生影响，较长和较窄的线路以及过多的弯曲可能会增加损耗。三面板在结构上比双面板更为复杂，其传输损耗除了受到与双面板类似的因素影响外，还可能由于中间层的存在而有不同的表现。中间层的材料选择和厚度会改变电场和磁场的分布，进而影响传输损耗。此外，三面板的层间连接方式以及接地策略也会对传输损耗产生重要影响。为了降低双/三面板的传输损耗，可以采取一些措施，如选择低损耗的板材材料、优化导体设计以降低电阻、合理规划线路布局以减少不必要的长度和弯曲等。同时，通过精确的仿真和测试，可以更好地理解和控制双/三面板的传输损耗，以满足不同电子设备对信号传输质量的要求。

📚2 运行结果

主函数部分代码：

clc
clear all
close all

j = sqrt(-1);
rho = 1.21; %kg/m3
c = 343; %m/s
Z_air = rho * c; %kg/(m2*s)

area=10;
L=sqrt(area);

%properties of PLATE 1
thickness_1=0.003; %m
density_1=2500; %kg/m3
youngMod_1=70e9; %Pa
posRatio_1=0.22;
lossFct_1=0.1;

%distance beetween layers
air_gap_1 =0.050 %m

%properties of PLATE 2
thickness_2=0.008; %m
density_2=2500; %kg/m3
youngMod_2=70e9; %Pa
posRatio_2=0.22;
lossFct_2=0.1;

%distance beetween layers
air_gap_2=0.010 %m

%properties of PLATE 3
thickness_3=0.008; %m
density_3=2500; %kg/m3
youngMod_3=70e9; %Pa
posRatio_3=0.22;
lossFct_3=0.1;

F_centre = [50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300 8000 10000];
F_upper=F_centre/2^(-1/4);
F_lower=F_centre*2^(-1/4);

%curves for the Calculation of Rw according to EN ISO 717-1:2013
curve_rw=[-1000 -1000 -1000 33 36 39 42 45 48 51 52 53 54 55 56 56 56 56 56 -1000 -1000 -1000 -1000 -1000];
curve_c=[-40 -36 -33 -29 -26 -23 -21 -19 -17 -15 -13 -12 -11 -10 -9 -9 -9 -9 -9 -9 -9 -100 -1000 -1000];
curve_ctr=[-1000 -1000 -1000 -20 -20 -18 -16 -15 -14 -13 -12 -11 -9 -8 -9 -10 -11 -13 -15 -1000 -1000 -1000 -1000 -1000];
curve_ctr_exp=[-25 -23 -21 -20 -20 -18 -16 -15 -14 -13 -12 -11 -9 -8 -9 -10 -11 -13 -15 -16 -18 -1000 -1000 -1000];

%array for the narrowband frequencies
Freq = logspace(log10(40),log10(12000),400);

%angle of incidence
dTheta=1;
Theta = 0:dTheta:88;
dTheta=dTheta*pi/180;
Theta = Theta.*pi/180;

%parameter for gaussian distribution of sound according to [3]
gauss_int=1;
beta=2;

%caluclation of dubble wall frequency
f0_1=c/(2*pi)*sqrt(rho*(density_1*thickness_1+density_2*thickness_2)/(density_1*thickness_1*density_2*thickness_2*air_gap_1))
f0_2=c/(2*pi)*sqrt(rho*(density_2*thickness_2+density_3*thickness_3)/(density_2*thickness_2*density_3*thickness_3*air_gap_2))

%Make room in memory for transmission matrixes
TN=zeros(2,2,5,length(Freq),length(Theta));
Tau1=zeros(length(Freq),length(Theta));
Tau2=zeros(length(Freq),length(Theta));
Tau3=zeros(length(Freq),length(Theta));

%Radiation efficiency of plates
sigma1=zeros(1,length(Freq));
sigma2=zeros(1,length(Freq));
sigma3=zeros(1,length(Freq));

%wave number segments for sigma calc according [2]
segN=50;

%layer counter
n_layer = 1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PLATE 1 Transmission matrix according to [1]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%bending stiffness
Dp_1 = youngMod_1*thickness_1^3/(12*(1-posRatio_1^2));

%critical frequency
fcrit_1 = c^2/(2*pi)*sqrt(density_1*thickness_1/Dp_1)
omegacrit_1 = 2*pi*fcrit_1;

for iterF=1:length(Freq)
    f=Freq(iterF);
    omega = 2*pi*f;
    
    %wave numbers in air and plate
    k0 = omega/c;
    kp=abs((omega^2*density_1*thickness_1/Dp_1)^(1/4));
    
    for iterT=1:length(Theta)
        theta=Theta(iterT);
        Z1 = j*omega*density_1*thickness_1*(1-(f/fcrit_1)^2*(1+j*lossFct_1)*(sin(theta)^4));
        T11 = 1;
        T12 = Z1;
        T21 = 0;
        T22 = 1;
        TN(1,1,n_layer,iterF,iterT) = T11;
        TN(1,2,n_layer,iterF,iterT) = T12;
        TN(2,1,n_layer,iterF,iterT) = T21;
        TN(2,2,n_layer,iterF,iterT) = T22;
        Tau1(iterF,iterT) = (4*abs(T11+T12*cos(theta)/Z_air+T21*Z_air/cos(theta)+T22)^-2);
    end
    
    %Calculation of radiation efficency according to [2]
    dkr=k0/segN;
    kr=0;
    %k0=k0*cos(pi/4);
    %kp=kp*sin(pi/4);
    for iterK=0:dkr:k0-2*dkr
        kr=kr+dkr;
        sigma1(iterF)=sigma1(iterF) + sin((kr-kp)*L/2)^2/(((kr-kp)*L/2)^2*sqrt(k0^2-kr^2))*dkr;
    end
    sigma1(iterF)=abs(sigma1(iterF)*L*k0/(2*pi));
end
n_layer=n_layer +1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% AIR GAP 1 Transmission matrix according to [1]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for iterF=1:length(Freq)
    f=Freq(iterF);
    k0 = omega/c;
    omega = 2*pi*f;
    
    Z = Z_air;
    for iterT=1:length(Theta)
        theta=Theta(iterT);
        
        T11=cos(k0*air_gap_1*cos(theta));
        T12=j*Z*sin(k0*air_gap_1*cos(theta))/cos(theta);
        T21=j*(sin(k0*air_gap_1*cos(theta))/Z)*cos(theta);
        T22=cos(k0*air_gap_1*cos(theta));
        
        TN(1,1,n_layer,iterF,iterT) = T11;
        TN(1,2,n_layer,iterF,iterT) = T12;
        TN(2,1,n_layer,iterF,iterT) = T21;
        TN(2,2,n_layer,iterF,iterT) = T22;
    end
end
n_layer=n_layer +1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PLATE 2 Transmission matrix according to [1]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%bending stiffness
Dp_2 = youngMod_2*thickness_2^3/(12*(1-posRatio_2^2));