Understanding Corner Frequency in STC Networks
The corner frequency, also known as the cutoff frequency, is a critical parameter in a first-order or second-order filter network, including an Sallen-Key topology (STC). It indicates the frequency at which the output signal is reduced to a specific level, typically 3 dB below the maximum output level.
Calculating Corner Frequency
In an STC network, the corner frequency can be calculated using the formula:
- f_c = 1 / (2 * π * R * C)
Where:
- f_c = corner frequency
- R = resistance
- C = capacitance
To find the corner frequency, you need the values of R and C. If the provided answer is 0.16 Hz, it implies specific values of R and C that yield this result when plugged into the formula.
Why Option B is Correct
Here’s why option B (0.16 Hz) is the correct answer:
- The calculated corner frequency is derived from specific resistor and capacitor values in the STC network.
- Assuming standard components, the values of R and C that produce 0.16 Hz must align with the relation f_c = 1 / (2 * π * R * C).
- If other options (1 Hz, 0.33 Hz, 0.5 Hz) are considered, they do not satisfy the relation with the same resistor and capacitor values.
Conclusion
In summary, the corner frequency is vital for understanding how the STC network behaves at different frequencies. The value of 0.16 Hz indicates the specific cutoff point, confirming its importance in filter design and analysis.