Operational amplifier fundamentals: evaluate the statement—“An ideal inverting amplifier provides an output that is phase-shifted by 180° relative to its input (i.e., it inverts the signal polarity).”

Introduction / Context:
The inverting amplifier is a canonical op-amp configuration used for scaling, summing, and filtering. A defining characteristic is the phase inversion between input and output. Recognizing this behavior is foundational for signal-chain design and phase-sensitive applications such as feedback and mixing.

Given Data / Assumptions:

• Ideal operational amplifier (infinite gain, bandwidth sufficiently high for the signal of interest).
• Standard inverting configuration with input resistor R_in and feedback resistor R_f.
• Linear, small-signal operation (no clipping or slew-rate limiting).

Concept / Approach:
For an ideal inverting amplifier, the gain is V_out / V_in = −R_f / R_in. The negative sign indicates a phase inversion of 180 degrees with respect to the input. The magnitude R_f / R_in sets the amplitude scaling, independent of the inversion property. In sinusoidal steady state below the op-amp's bandwidth limits, the output is an inverted, scaled version of the input.

Step-by-Step Solution:

Verification / Alternative check:
Square-wave tests show output transitions mirrored about zero; Bode plots show a constant −180° phase offset at low frequencies where the op-amp behaves ideally (before additional phase lag from finite bandwidth appears).

Why Other Options Are Wrong:

• Incorrect: contradicts the standard inverting amplifier formula.
• True only for unity gain: inversion occurs for any gain magnitude R_f / R_in.
• True only at DC, not AC: holds across the passband where the op-amp remains linear and within bandwidth.
• True only for sine: inversion applies to any waveform under linear operation.

Common Pitfalls:
Confusing “phase inversion” with “phase shift that varies with frequency”; overlooking bandwidth and stability limits that can add extra phase lag beyond the ideal −180° at higher frequencies.

Final Answer:
Correct