RC high-pass topology and phase behavior For a standard RC high-pass filter (series capacitor, shunt resistor), is the output taken across the resistor and does the output lead the input in phase for much of the spectrum?

Introduction / Context:Knowing where to measure the output in first-order filters is the key to predicting both magnitude and phase behavior. The RC high-pass places the capacitor in series and the resistor to ground, with the output across the resistor.

Given Data / Assumptions:

• Series capacitor C, shunt resistor R to ground.
• Output node is the junction between C and R (across R).
• Transfer function: H(jω) = jωRC / (1 + jωRC).

Concept / Approach:

The magnitude of H rises from near 0 at very low frequency to ~1 at high frequency (20 dB/decade slope). The phase is positive (lead) at low frequency, approaching +90°, and tends to 0° at high frequency, meaning the output generally leads the input except in the asymptotic high-frequency limit.

Step-by-Step Solution:

Verification / Alternative check:

At ω = 1 / RC, |H| = 1 / sqrt(2) ≈ 0.707 and phase = +45°, a clear lead. At ω → ∞, phase → 0°, consistent with diminishing lead as the passband flattens.

Why Other Options Are Wrong:

• “False” contradicts the textbook topology and phase result.
• “True only above cutoff” misses the fact that the phase lead is strongest below cutoff.
• Component ideality and value ratios do not alter the qualitative behavior.

Common Pitfalls:

Swapping output node to the capacitor (which would create a low-pass) or assuming phase lag because many filters lag; here, the high-pass leads.

Final Answer:

True