RC lag network behavior: Which statement correctly describes how phase shift and output magnitude of a lag (low-pass RC) network change with frequency?

Introduction:
Lag networks—typically simple RC low-pass filters—are ubiquitous in analog signal conditioning, control systems, and power electronics. Understanding how their phase shift and amplitude response vary with frequency is essential for stability analysis, timing, and noise attenuation.

Given Data / Assumptions:

• Single-pole RC low-pass network with output taken across the capacitor or resistor depending on definition; here, “lag network” denotes the classic configuration producing negative phase (output lags input).
• Linear, time-invariant behavior; small-signal sinusoidal steady state.
• Cutoff frequency fc = 1 / (2 * pi * R * C) defines the transition band.

Concept / Approach:
The transfer function magnitude of a first-order low-pass is |H(jω)| = 1 / sqrt(1 + (ω/ωc)^2). The phase shift is φ(ω) = −arctan(ω/ωc). As frequency increases, the magnitude decreases and the phase becomes more negative, approaching −90 degrees as ω → ∞. Conversely, as frequency decreases toward zero, |H| approaches 1 and φ approaches 0 degrees (negligible lag). Therefore, the correct qualitative statement is that increasing frequency increases phase lag in magnitude (more negative angle).

Step-by-Step Solution:

Verification / Alternative check:
Bode plots show a −20 dB/decade magnitude slope above fc and a monotonic phase transition from 0° toward −90°. Experimental step-response also indicates longer apparent delay at higher frequency components (more lag in the frequency domain corresponds to time-domain smoothing).

Why Other Options Are Wrong:

• An increase in frequency causes an increase in the magnitude of the output voltage: Opposite of low-pass behavior; magnitude falls with frequency beyond fc.
• A decrease in frequency causes an increase in phase lag: At low frequency, phase tends toward 0°, not more lag.
• A decrease in frequency causes a decrease in the magnitude of the output voltage: At low frequency, magnitude approaches unity, so this is false.

Common Pitfalls:
Confusing lead and lag networks; assuming phase is constant; forgetting that the −3 dB point occurs at fc with φ = −45°. Also, some texts define “lag network” by where the output is taken; regardless, the low-pass case clearly shows increasing phase lag with increasing frequency.

Final Answer:
An increase in frequency causes an increase in phase lag.