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Equation with logarithms, why it can't be solved?

Mathematica Asked by Granger Obliviate on April 2, 2021

I’m trying to find the -3 dB frequency of a filter in Mathematica. Yet, my code doesn’t seem to work as it produces imaginary values for the frequency.

Tfilter=(9.36*^6 + 44226.*s + 9.477*s^2)/(2.35521*^9 + 495801.*s + 9.477*s^2)
Eqn1 = 20*Log[10, Abs[Tfilter /. s -> I*2*Pi*f]] == -3
Solve[Eqn1, f]

What am I doing wrong? Is there any additional command I shall give to Mathematica?

One Answer

Clear["Global`*"]

Tfilter = (9.36*^6 + 44226.*s + 9.477*s^2)/(2.35521*^9 + 495801.*s + 
       9.477*s^2) // Rationalize // Simplify;

Since f is real, use ComplexExpand to eliminate Abs

Eqn1 = 20*Log[10, Abs[Tfilter /. s -> I*2*Pi*f]] == -3 // ComplexExpand // 
   Simplify;

sol = Solve[Eqn1, f, Reals] // N

(* {{f -> -7530.29}, {f -> 7530.29}} *)

Answered by Bob Hanlon on April 2, 2021

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