Electronic Circuits with MATLAB, PSpice, and Smith Chart

Appendix ESymbolic Computations with MATLAB

E.1 How to Declare Symbolic Variables and Handle Symbolic Expressions

To declare any variable(s) as a symbolic variable, you should use the sym or syms command as follows:

>>a=sym('a'); x=sym('x'); y=sym('y'); t=sym('t'); n=sym('n');
>>syms a x y t n %or, equivalently and more efficiently

Once the variables have been declared as symbolic, they can be used in expressions and as arguments to many functions without being evaluated as numeric.

>>f=x^2/(1+tan(x)^2);
>>ezplot(f,-pi,pi) % easy plot of f for [-π,+π]
>>simplify(cos(x)^2+sin(x)^2) % simplify an expression
   ans= 1
>>simplify(cos(x)^2-sin(x)^2) % simplify an expression
   ans= 2*cos(x)^2-1
>>simplify(cos(x)^2-sin(x)^2) % simple expression
   ans= cos(2*x)
>>simplify(cos(x)+i*sin(x)) % simple expression
   ans= exp(i*x)
>>eq1=expand((x+y)^3-(x+y)^2) % expand
   eq1= x^3+3*x^2*y+3*x*y^2+y^3-x^2-2*x*y-y^2
>>collect(eq1,y) % collect similar terms in descending order w.r.t. y
   ans= y^3+(3*x-1)*y^2+(3*x^2-2*x)*y+x^3-x^2
>>factor(eq1) % factorize
   ans= (x+y-1)*(x+y)^2
>>horner(eq1) % nested multiplication form
   ans= (-1+y)*y^2+((-2+3*y)*y+(-1+3*y+x)*x)*x
>>pretty(ans) % pretty form
         2
   (-1 + y) y + ((-2 + 3 y) y + (-1 + 3 y + x) x) x

If you need to substitute numeric values or other expressions for some symbolic variables in an expression or take the limit of an expression, you can use subs( ) and limit( ) as follows:

>>subs(eq1,x,0) % substitute numeric value x=0 into eq1=(x+y-1)*(x+y)^2 ...