A filter is needed to remove induced 60 Hz hum from a transducer signal. The rejection bandwidth is 2 Hz. The correct combination of R damping and C values for this filter are:

 

98. A filter is needed to remove induced 60 Hz hum from a transducer signal. The rejection bandwidth is 2 Hz. The correct combination of R damping and C values for this filter are:

1. 30 Ω, 32.5 milli Farads [Option ID = 3221] 

2. 68 Ω, 30.5 milli Farads [Option ID = 3222] 

3. 82 Ω, 3.25 milli Farads [Option ID = 3223] 

4. 89 Ω, 2.65 milli Farads [Option ID = 3224] 

Correct Answer : 4

Solution

To remove the 60 Hz frequency, we use a notch filter with a center frequency (f₀) of 60 Hz and a rejection bandwidth (BW) of 2 Hz.

Step 1: Calculate the Quality Factor (Q)
The Q factor determines the sharpness of the notch:

Q = f₀ / BW = 60 / 2 = 30

Step 2: Calculate the Damping Resistance (R_damping)
Using the damping relationship for this specific filter topology:

R_damping = 3Q - 1 = 3(30) - 1 = 89 Ω

Step 3: Calculate the Angular Frequency (ω₀)

ω₀ = 2πf₀ = 2 × π × 60 ≈ 377 rad/sec

Step 4: Calculate the Capacitance (C)
Using the frequency component relationship:

C = 1 / ω₀ = 1 / 377 ≈ 0.00265 F = 2.65 mF

Conclusion:
The correct combination is 89 Ω and 2.65 milli Farads.

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