% An investigation of the Zo of a microstrip line, parameterized for w/h
% and e_r 
% 
% Hammersted and Jensen, published in Gardiol, 1994.
% 
% Modernised away from gset etc.....
%
% AlanRobertClark@gmail.com 20250823
%
1; % Not a function file :-)

% fsolve only has one var it can pass :-)
global Er; 
global ZoVal=150;


function retval = Zo (WoverH, Er)
  if (nargin != 2)
    usage ("Zo needs 2 args: w/h (vector) and Er (float)")
  endif
    
  a = 1 + 1./49.*log((WoverH.^4 + (WoverH/52).^2) / (WoverH.^4+0.432)) +...
      1./18.7.*log(1+(1./18.1.*WoverH).^3);
  b = 0.564.*((Er-0.9)./(Er+3)).^0.053;    
  EeffGardiol1994 = 0.5.*(Er+1) + 0.5.*(Er-1)./(1+10./WoverH).^(a.*b);
  F1 = 6 + (2.*pi-6).*exp(-(30.666./WoverH).^0.7528);
  ZoGardiol1994 = 60./sqrt(EeffGardiol1994).*log(F1./WoverH + ...
                  sqrt(1+(2./WoverH).^2));
  retval = ZoGardiol1994;
endfunction; 


function y = f (x)
  global Er;
  global ZoVal;
  y = Zo (x, Er) - ZoVal;
endfunction

ErVector = logspace (0,1.3,100);
ZoValVector = [200,175,150,120,100,75,60,50,35,20,10];

% Preallocate sizes :-)
Storage = zeros(length(ErVector), length(ZoValVector));
i=0; 
j=0; 

for ZoVal = ZoValVector
  i++;
  j=0;
  for Er = ErVector
    j++;
    x = fsolve("f", 1);
    if x < 0
      x = NaN;
    endif
    if x > 20
      x = NaN;
    endif  
    Storage(j,i)=x; 
  endfor
endfor  

loglog(Storage(:,1),ErVector',...
       Storage(:,2),ErVector',...
       Storage(:,3),ErVector',...
       Storage(:,4),ErVector',...
       Storage(:,5),ErVector',...
       Storage(:,6),ErVector',...
       Storage(:,7),ErVector',...
       Storage(:,8),ErVector',...
       Storage(:,9),ErVector',...
       Storage(:,10),ErVector',...
       Storage(:,11),ErVector');

title 'w/h as a function of $\epsilon_r$, parameterised by $Z_0$'; 
axis([0.1 20 1 5]);
% There is a tension between having minor ticks, and being able to label
% them. If we have minor on, grid looks fine, but only three labels (0.1,
% 1, 10), if off, then I can manually add the rest, but then thousands of
% minor lines. So kill minor, but then Must kill the minor bloody ticks
% too. Previous syntax was infinitely better.
grid on;
grid minor off;
ax=gca();
set(ax, "xtick", [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,...
                  1,2,3,4,5,6,7,8,9,10,20]);
set(ax, "xticklabel", {"0.1","0.2","","","0.5","","","","",...
                  "1","2","","","5","","","","","10","20"});
set(ax, "xminortick", "off"); % Sheesh.....

set(ax, "ytick", [1,2,2.18,3,4,4.4,5]);
set(ax, "yticklabel", {"1","2","PP","3","4","FR4","5"});
set(ax, "yminortick", "off");
xlabel "w/h";
% Note single quotes for LaTeX:
ylabel '$\epsilon_r$';
%gset label "200" at 0.17,1.5 right;
text(0.17,1.5,"200", "horizontalalignment", "right");
text(0.22,1.75,"175", "horizontalalignment", "right");
text(0.31,2,"150", "horizontalalignment", "right");
text(0.55,2.19,"120", "horizontalalignment", "right");
text(0.8,2.33,"100", "horizontalalignment", "right");
text(1.3,2.5,"75", "horizontalalignment", "right");
text(1.85,2.6,"60", "horizontalalignment", "right");
text(2.5,2.7,"50", "horizontalalignment", "right");
text(4.1,2.8,"35", "horizontalalignment", "right");
text(8.2,2.9,"20", "horizontalalignment", "right");
text(18,3,"10", "horizontalalignment", "right");
printFig("MicroZoParmsZoom");