A 4th Order Butterworth LPF having cutoff frequency 1 KHz. What is the approximate level of attenuation at 2 Khz frequency?25 dB3 dB60 dB40 dB
Question
A 4th Order Butterworth LPF having cutoff frequency 1 KHz.
What is the approximate level of attenuation at 2 Khz frequency?
- 25 dB
- 3 dB
- 60 dB
- 40 dB
Solution
The level of attenuation for a 4th order Butterworth Low Pass Filter (LPF) can be calculated using the formula:
A = 20n log10(f/fc)
where:
- A is the attenuation in dB,
- n is the order of the filter,
- f is the frequency for which we want to calculate the attenuation,
- fc is the cutoff frequency of the filter.
Given that n = 4 (4th order), f = 2 KHz and fc = 1 KHz, we can substitute these values into the formula:
A = 20*4 log10(2/1) = 80 log10(2) ≈ 80 * 0.3 = 24 dB
So, the closest answer to the calculated value is 25 dB.
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