The answer to the exercise may be incorrect, since I get the wrong results every time I do the calculations. It's a simple circuit, and I need the capacitor value, so the output is -3dB at 100Hz.
I get the answer 583 nF, but the answer should be 160 nF
Can someone explain where the calculations goes wrong?
You have to use phasors (complex arithmetic) to account for both the phase and magnitude to solve the problem. I was lazy, and didn't do the complex arithmetic. However, I showed you that the answer given with the exercise is correct.
Do you know how to do complex calculations? You convert the rectangular function on the bottom to polar form, do the division, and then convert the result back to rectangular.
Yes, it was just the English term "complex arithmetic" (not my language), that confused be shortly. The result to the equation should have been 0.636 + angle. That's why the result was false.
I just remembered a short cut. The 3db down frequency of this high pass filter occurs when the magnitude of the capacitive reactance equals the loop resistance, i.e. |1/(2ΠfC)| = 1k + 9K
C = 1/(2Πf*(1k+9k) = 1/6.28318E6 = 159.1549E-9 = 159.1nF