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What is the smallest value of C that will ensure that the 3dB frequency is not greater than 100Hz?
That is the question from the book but my question is not that exactly.
I am trying to find the cutoff frequency which is of course a step toward the solution and I have the transfer function:
$$\frac{sC_1R_2}{sC_1(R_1+R_2)+1}$$
now somehow the book goes straight from the transfer function to
$$\omega_0 = \frac{1}{C_1(R_1+R_2)}$$
I am having trouble understanding how we found \$\omega_0\$.
Best Answer
The rolloff frequency of a R-C filter is:
F = 1 / (2πRC)
When R is in Ohms, C in Farads, then F is in Hz.
Therefore to get the capacitance:
C = 1 / (2πFC) = 1 / [2π(100 Hz)(10 kΩ)] = 160 nF
Yes, it's really that easy.
R-C rolloff filter calculations come up a lot in electronics. I keep 1/2π permanently in a register in my calculator. I can then divide that by two of the frequency, capacitance, or resistance to get the third.