Question

We want to synthesize a filter to extract tones that go to a sub-woofer. The filer should not attenuate tones at or below 100Hz by more than 3dB. Tones above 1kHz should be attenuated by at least 20 dB.

1)What kind of filter would we need to generate this signal?

2)Design an RC circuit that implements this filter (i.e., use resistors and capacitors to achieve this). Resistors can have values from 1k-10k and capacitors can range from 100nF-1(micro)F. On this circuit, please included the resistance and capacitance values for the components .

Answer 1

1) We need a low pass filter with to generate this signal.

2) For a 2nd order LPF with Resistances R₁, R₂ and capacitances C₁, C₂, cut off frequency:

For frequencies > f_c, slope is -40dB/decade for 2nd order LPF. Therefore, at 1000Hz = 10² Hz, i.e. after 1 decade of 100 Hz = 10² Hz, the attenuation will be 40 dB which is > 20 dB

If C₁ = C₂ = 1 F,

If R₁ = R₂,

If R₁ = R₂ = 1500 Hz,

This satisfies the requirements.