Why we use noise filter in a electrical circuit?

Think of the inductor is a frequency dependant resistor, that will be calculted based upon the inductance and the frequency. Then think of the series inductor with the load as a voltage divider, where the inductor becomes larger with frequency, therefore the load gets less voltage. -3dB is the square root of 2 divided by 2 or 0.7071 or 70.7% point of the voltage drop on the load.

It is also the 29.3% of the voltage drop on the inductor. So for 0.7071 of the voltage is the frequency where the resistance and reactance in the voltage divider is 0.7071 and would be 50 / (50+XL) and the inductive reactance is found to be 0.7071 = 50 / (50+XL) 35.3553 + 0.7071XL = 50 0.7071XL = 14.6447 XL = 20.7107 ohms So if that frequency is supposed to be at 100 MHz, then the inductance is XL = 2 * pi * freq * L 20.7107 = 2 * 3.1415 * 100E6 Hz * L L = 32.9621E-9 Henries or 32.9621 nanoHenries or 32,962.1 microHenries. Remember that when the voltage is -3dB down that the power is 50% down because P = V^2 * R.

This is because 0.7071 squared is 0.5000 Butterworth and Chebychev filters describe the *rate* of the roll-off or attenuation.

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