Electronic Circuits with MATLAB, PSpice, and Smith Chart

Appendix DNonlinear/Differential Equations with MATLAB

D.1 Nonlinear Equation Solver <fsolve>

MATLAB has the built‐in function ‘fsolve(f,x0)’, which can give us a solution for a system of (nonlinear) equations. Suppose we have the following system of nonlinear equations to solve.

(D.1)

To solve this system of equations, we should rewrite as

(D.2)

and convert it into a MATLAB function defined in an M‐file, say, ‘f_d02.m’ as follows.

function y=f_d02(x)
y(1)= x(1)*x(1)+4*x(2)*x(2) -5;
y(2)=2*x(1)*x(1)-2*x(1)-3*x(2) -2.5;

Then we type the following statements into the MATLAB Command Window.

>>x0=[0.8 0.2]; % Initial guess [0.8 0.2]
>>x=fsolve('f_d02',x0,optimset('fsolve')) % with default parameters
  x = 2.0000  0.5000

If you see some warning message with the MATLAB solution obtained by using ‘fsolve()’ like this, you can change the value(s) of the optional parameters such as

• MaxFunEvals: Maximum number of function evaluations allowed
• MaxIter: Maximum number of iterations allowed
• TolFun: Termination tolerance on the function value
• TolX: Termination tolerance on x

by using the MATLAB command ‘optimset( )’ as follows.

 options = optimset('param1',value1,'param2',value2,...)

For example, if you feel it contributive to better solution to set MaxFunEvals and TolX to 1000 ...