Finding cross over frequency of transfer function in terms of symbols

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Anubhav 2016-7-26

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https://ww2.mathworks.cn/matlabcentral/answers/297145-finding-cross-over-frequency-of-transfer-function-in-terms-of-symbols

编辑： Anubhav 2016-7-26

Consider a typical second order transfer function H(s)= A*N(s)/D(s) where N(s)= (1+s*R*C) and D(s)= 1+s*(L/R)+s^2*(LC) and ofcourse, s=j*w. Suppose I want to keep the L, R, C and A as symbols. I want to find the cross over frequency wc (ie... when H(jwc)=1) without substituting numeric values (of L,R,C,A) in H(s). Is it possible to make MATLAB solve the equation and get an expression of wc in terms of symbolic variables (L,C,R,A)?

PS- Actually, the inspiration to my question is the fact that my actual transfer function is a 3rd or 4th order system and solving for value of wc by hand-calculation is not most feasible.