Manipulation of complex expressions
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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
syms('U_2')
syms('U_C')
U_2 = 1 / j / omega / C / Z_s * U_C
U_2 = simplifyFraction(U_2)
Z_p = 1 / (j * omega * C + 1 / Z_s)
syms('U_1')
U_C = Z_p / (R + Z_p) * U_1
U_C = simplifyFraction(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 = simplifyFraction(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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/781093/image.png)
How can I achieve this with the Symbolic Toolbox?
Kind regards
Michael
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Accepted Answer
Paul
on 27 Oct 2021
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)
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