Manipulation of complex expressions

Hello,

I have a problem with the manipulation of a complex expression. My code looks loke this:

syms('R', 'positive')
syms('C', 'positive')
syms('omega', 'positive')
Z_s = R + 1 / j / omega / C

Z_s = 

syms('U_2')
syms('U_C')
U_2 = 1 / j / omega / C  / Z_s * U_C

U_2 = 

U_2 = simplifyFraction(U_2)

U_2 = 

Z_p = 1 / (j * omega * C + 1 / Z_s)

Z_p = 

syms('U_1')
U_C = Z_p / (R + Z_p) * U_1

U_C = 

U_C = simplifyFraction(U_C)

U_C = 

Until here everything is fine. Now I substitute U_C in U_2 with the above result.

U_2 = subs(U_C, U_C)

U_2 = 

U_2 = simplifyFraction(U_2)

U_2 = 

That is avery complicated expression. How can I simplify this fraction? There are common divisors in this fraction and it is possible to reduce it into

.

How can I achieve this with the Symbolic Toolbox?

Kind regards

Michael

Answer 1

[Paul]

The final substitution into U_2 needs to be changed as shown below.

syms('R', 'positive')
syms('C', 'positive')
syms('omega', 'positive')
Z_s = R + 1 / 1j / omega / C;  % chnage j to 1j throughout
syms('U_2')
syms('U_C')
U_2 = 1 / 1j / omega / C  / Z_s * U_C;
U_2 = simplifyFraction(U_2);
Z_p = 1 / (1j * omega * C + 1 / Z_s);
syms('U_1')
U_C = Z_p / (R + Z_p) * U_1;
U_C = simplifyFraction(U_C);
U_2 = subs(U_2);  % this line changed, update U_2 with current value of U_C
U_2 = simplifyFraction(U_2)

U_2 = 

[Michael]

Great, that's it.

Thank you!

Michael