How to solve for Z in the following equation?

Hi everyone

Could someone help me solve the following equation for Z? Here y is a voltage measurement and x is a current measurement. I want to calculate Z for a range of (x,y) values.

y = Z/((1+Z*x)*(pi+atan(Z-0.1)))

Really appreciate your help.

Thanks

Answer 1

[Andrew Newell]

The key is to define a function that is zero for the desired value of Z:

f = @(Z) Z./((1+Z.*x).*(pi+atan(Z-0.1)))-y;

Solving is a bit tricky because the function has a horizontal asymptote, so you'll have to have a reasonable initial guess. Here is a crude first cut:

zguess = y/(1-x*y);
[zsol,fval,exitflag] = fzero(f,zguess);
if exitflag < 0
  zguess = -zguess;
  [zsol,fval,exitflag] = fzero(f,zguess);
end