How to plot 𝛽−𝑤 diagram in MATLAB?

Question

I am trying to plot the 𝛽−𝑤 diagrams for the given phase constants using MATLAB, but although I have look at many web pages, there is not a similar example plotting 𝛽−𝑤 diagram in MATLAB. Could you please clarify me how to proceed by giving some examples regarding to this problem? Any help would really be appreciated.

Plot range: 𝑓=10𝑀ℎ𝑧−10𝐺𝐻𝑧

w : Angular frequency

wc : A constant Angular frequency

Parameters for 1st: 𝑤𝑐1=0.2∗𝑤, 𝑤𝑐2=0.4∗𝑤, 𝑤𝑐3=0.6∗𝑤, 𝑤𝑐4=0.8∗𝑤 , ɛ1=1* ɛ0, μ= μ0

Parameters for 1st: a1=0.08636cm, a2=0.8636cm, a3=2.286cm, a4=29.21cm, ɛ1=1* ɛ0, μ= μ0

Answer 1

As the OP asked, this is a sort of Matlab code. I assume to map the plot of B with w in range [1,100] (but values can be changed) First case has wc has 3 different cases, 4 different plot of B (B1,B2, B3 and B4) will be mapped in four different colors

    %constant inizialization
    mu = 1.2566E-6;
    e = 1;
    start_f = 10000; %10 MHz start frequency range
    end_f = 10000000; %10 GHz end frequency range 
    step = 10 %plot the function every "step" Hz (ONLY INTEGER NUMBERS ALLOWED)
    k = 1;
    % function of B example: B = w*sqrt(mu*e)*sqrt(1-((wc^2)/w));

    %vectors initialization to avoid the "consider preallocation" Matlab not-critical warning
    range_f = ceil((end_f - start_f)/step) + 1;
    w = zeros(range_f);
    B1 = zeros(range_f);
    B2 = zeros(range_f);
    B3 = zeros(range_f);
    B4 = zeros(range_f);

    for i=start_f:step:end_f %from 10 MHz to 10 GHz with steps of 1 Hz
    %store i in the i-cell of vector w
      w(k) = i;
%values that need to be updated every time
      w1 = 0.2*w(i);
      w2 = 0.4*w(i); 
      w3 = 0.6*w(i);
      w4 = 0.8*w(i); 
%four different results of B
      B1(i) = w(i)*sqrt(mu*e)*sqrt(1-((w1^2)/w(i)));
      B2(i) = w(i)*sqrt(mu*e)*sqrt(1-((w2^2)/w(i)));
      B3(i) = w(i)*sqrt(mu*e)*sqrt(1-((w3^2)/w(i)));
      B4(i) = w(i)*sqrt(mu*e)*sqrt(1-((w4^2)/w(i)));

      k = k+1;
    end
%plot the 4 lines    
    plot(w,B1,'r') %red line of B1 = f(w) 
    hold on
    plot(w,B2,'g') %green line of B2 = f(w) 
    hold on
    plot(w,B3,'b') %blue line of B3 = f(w) 
    hold on
    plot(w,B4,'k') %black line of B4 = f(w) 

4 different cases have to be represented with 4 plot (in this example they have been overlayed).

The last notation can be done in the same way (you have 4 constant parameters a1, a2 etc.) that does not depends from w this time. So

  B1a(i) = sqrt((w(i)^2)*mu*e - ((pi^2)/a1)));
  B2a(i) = sqrt((w(i)^2)*mu*e - ((pi^2)/a1)));
  B3a(i) = sqrt((w(i)^2)*mu*e - ((pi^2)/a1)));
  B4a(i) = sqrt((w(i)^2)*mu*e - ((pi^2)/a1)));

If some errors (due to "fast" writing) occurs to you, report them in comments and I will correct and update the code