Low-pass filter interpretation: For a passive low-pass network with cutoff frequency fc = 3.5 kHz, which frequency range constitutes the passband?

Introduction / Context:
Understanding the meaning of cutoff frequency fc in passive filters is essential for interpreting Bode plots and designing signal-conditioning stages. The passband for a low-pass filter is the range of frequencies that are passed with minimal attenuation relative to the stopband.

Given Data / Assumptions:

• A low-pass filter with cutoff frequency fc = 3.5 kHz (−3 dB point).
• Standard definition of passband and stopband for first- or higher-order passive filters.

Concept / Approach:
By definition, a low-pass filter allows low frequencies to pass and attenuates higher frequencies. The cutoff frequency fc marks the boundary between the passband (below fc) and the stopband (above fc). Below fc, attenuation is relatively small; at fc, the magnitude is 1/√2 of the passband asymptote; above fc, the magnitude decays with slope determined by the filter order.

Step-by-Step Solution:

Verification / Alternative check:
For a first-order RC or RL low-pass, the magnitude response is |H(jω)| = 1 / √(1 + (f/fc)^2). For f < fc, |H| > 0.707; for f > fc, |H| < 0.707. This confirms the passband definition.

Why Other Options Are Wrong:

• '0 Hz': A single frequency, not a band.
• '3.5 kHz': A single cutoff point, not an interval.
• '7 kHz': Above the cutoff, in the stopband for a low-pass network.

Common Pitfalls:

• Confusing passband edge with the entire passband region.
• Mixing up low-pass and high-pass responses.

Final Answer:
0 Hz to 3.5 kHz