solving equations

I am having difficulty solving an equation with a symbolic variable. If anyone has any suggestions please help!

EDU>> r1=330;

EDU>> r2=1000;

EDU>> c=.47*10^-6;

EDU>> syms f;

EDU>> w=2*pi*f;

EDU>> xc=1/(i*w*c);

EDU>> Vin=1;

EDU>> Vout=(Vin*r2*xc^2)/(1000*r1*(r2+xc)+r2*xc*(xc+1000));

EDU>> solve('abs(Vout)=.707')

ans =

0.707*exp(0.0)

EDU>> solve(abs(Vout)-.707)

Warning: Explicit solution could not be found.

> In solve at 81

ans =

[ empty sym ]

Answer 1

[Walter Roberson]

I do not have the Symbolic toolbox to test with.

The first form, with the quoted string, is not going to produce the answer you want because at that point the value of Vout has not been transfered from Matlab to the symbolic engine. Try

solve(subs('abs(Vout)=0.707'))

According to a different symbolic package I tried, there are four solutions, all complex:

-((25000/1551)*I)*(-133+(4489+13200*2^(1/2))^(1/2))/Pi

((25000/1551)*I)*(133+(4489+13200*2^(1/2))^(1/2))/Pi

(25000/1551)*(133*I-(-4489+13200*2^(1/2))^(1/2))/Pi

(25000/1551)*(133*I+(-4489+13200*2^(1/2))^(1/2))/Pi

To get these, I substituted 47*10^(-8) for your 0.47*10^(-6) so that the symbolic package would not convert everything to floating point.