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).”
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ACorrect
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BIncorrect
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CTrue only for unity gain
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DTrue only at DC, not AC
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ETrue only when input is sine wave
Answer
Correct Answer: Correct
Explanation
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:
1) Write the inverting gain relation: V_out = −(R_f / R_in) * V_in. 2) Interpret the negative sign as a 180° phase shift (polarity inversion). 3) Note that the inversion holds for any linear waveform (not only sinusoids) as a sign reversal in time domain. 4) Conclude the statement is correct for the ideal model within the usable frequency range.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