RL low-pass topology and phase behavior For a first-order RL low-pass filter, is the output correctly taken across the inductor with a lagging phase, or should it be taken across the resistor for low-pass behavior?

Introduction / Context:
RL filters complement RC filters. The placement of the output node determines whether the network is low-pass or high-pass. Misplacing the output node flips the filter type and changes the expected phase behavior.

Given Data / Assumptions:

• Series RL network with a sinusoidal source.
• Low-pass configuration takes output across the resistor, not the inductor.
• High-pass RL takes output across the inductor.

Concept / Approach:

For RL low-pass (output across R), the transfer function is H(jω) = R / (R + jωL). Magnitude decreases as frequency increases due to the growing inductor reactance. The phase is ∠H = −arctan(ωL / R), a lagging phase that approaches −90° at very high frequency. Output across L instead yields H_HP(jω) = jωL / (R + jωL), a high-pass response.

Step-by-Step Solution:

Verification / Alternative check:

At ω → 0, H(jω) → 1 for output across R (low-pass). For output across L, H_HP(jω) → 0 at ω → 0, as expected for a high-pass shape, confirming the statement is incorrect.

Why Other Options Are Wrong:

• Conditional “True” statements are incorrect; the topology defines the filter type irrespective of frequency extremes.
• “Ideal vs real” does not change the fundamental classification.

Common Pitfalls:

Assuming the inductor’s voltage “lags” makes it low-pass. Voltage across L actually dominates at high frequency, which is characteristic of a high-pass output when measured at L.

Final Answer:

False