RC low-pass topology and phase behavior In a standard RC low-pass filter, is the output voltage taken across the resistor with the output lagging the input, or is the output across the capacitor with a lagging phase?

Introduction / Context:
First-order RC filters are ubiquitous. Getting the node selection right (where the output is measured) is crucial for identifying whether a circuit is low-pass or high-pass, and for predicting the phase shift between input and output.

Given Data / Assumptions:

• Standard RC low-pass uses a series resistor followed by a shunt capacitor to ground.
• Output is taken across the capacitor, not across the series resistor.
• Transfer function magnitude decays at 20 dB/decade above the cutoff.

Concept / Approach:

For the low-pass configuration, the transfer function is H(jω) = 1 / (1 + jωRC). Its phase is ∠H = −arctan(ωRC), a lagging phase (negative) that approaches −90° at high frequency. Taking output across the resistor instead produces a high-pass filter, not a low-pass.

Step-by-Step Solution:

Verification / Alternative check:

Swap the output node to be across R: H_hp(jω) = jωRC / (1 + jωRC), which is a high-pass response with phase lead at low frequencies. This confirms that the statement associating low-pass with output across R is incorrect.

Why Other Options Are Wrong:

• “True” variants are incorrect because output across R defines a high-pass, not a low-pass.
• DC special cases do not change the topology-dependent classification.

Common Pitfalls:

Confusing where to probe the output and misinterpreting phase lead versus lag. Remember: RC low-pass → output across C (lag); RC high-pass → output across R (lead).

Final Answer:

False