Filter intuition check: Does a high-pass RC filter strongly attenuate the higher frequencies (rather than the lower ones) in its passband/stopband behavior?

Difficulty: Easy

Correct Answer: Incorrect

Explanation:


Introduction / Context:
Filters shape spectra by passing some frequency ranges while attenuating others. A high-pass filter is designed to pass high frequencies and reject low frequencies. This question probes whether that definition is being applied correctly in the context of basic RC networks.


Given Data / Assumptions:

  • First-order RC high-pass implementation (series C, shunt R, output across R).
  • Ideal components; small-signal linear operation.
  • Standard −3 dB cutoff at f_c = 1/(2πRC).


Concept / Approach:
In a high-pass filter, attenuation decreases (gain increases) with frequency above the cutoff; low frequencies are blocked because the capacitor's reactance is high (Xc is large). Thus the claim that a high-pass “heavily attenuates the higher frequencies” contradicts the definition and expected Bode magnitude plot.


Step-by-Step Solution:

Recall: high-pass ⇒ pass highs, reject lows. At low f: Xc is large ⇒ small output across R (attenuated). At high f: Xc is small ⇒ output approaches input (passed). Therefore, the statement is false.


Verification / Alternative check:
Plot |H(jω)| for the canonical high-pass transfer H(jω) = jωRC / (1 + jωRC). The magnitude tends to 1 as ω → ∞ and to 0 as ω → 0.


Why Other Options Are Wrong:
True only at cutoff / active filters only: the trend of passing highs and attenuating lows holds generally; implementation details do not reverse it.


Common Pitfalls:
Mixing up low-pass and high-pass; confusing amplitude with phase behavior around cutoff.


Final Answer:
Incorrect

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