Common-mode signals at the inputs of a differential amplifier: A signal is said to be common-mode if the two input nodes see signals with which shared properties?
Correct Answer: All of the above
Introduction / Context:Differential amplifiers and op-amps respond primarily to differences between the two inputs. Signals that appear identically on both inputs are called common-mode signals, and good amplifiers reject them to minimize interference and noise transmission.
Given Data / Assumptions:
- Both inputs are driven by the same time-varying waveform.
- Definitions are in the voltage domain.
- Amplifier is linear around its operating point.
Concept / Approach:A common-mode signal is identical at the two inputs in amplitude, phase, and frequency (and ideally in waveform shape). Because the amplifier ideally amplifies only the difference v(+) − v(−), such a shared signal should produce no output in the ideal case. Real devices have finite CMRR, so a small residual output can occur.
Step-by-Step Solution:
Define v_cm(t) applied to both inputs equally.Note that identical amplitude, phase, and frequency characterize “same signal”.Conclude: all three properties are shared for common-mode signals.Select “All of the above”.Verification / Alternative check:CMRR tests inject the same sinusoid (same amplitude, phase, frequency) on both inputs and measure the small output; this matches the definition used by manufacturers.
Why Other Options Are Wrong:Picking only one property is incomplete; all listed properties must match to be truly common-mode.
Common Pitfalls:Confusing common-mode with differential-mode; assuming frequency alone defines common-mode without checking amplitude and phase equality.
Final Answer:All of the above