What characteristic of an amplifier determines its ability to amplify a signal without distortion?

The ability of an amplifier to amplify a signal without distortion is primarily determined by its linearity. Linearity in amplification refers to the amplifier's capacity to produce an output signal that is directly proportional to its input signal over a specified range. When an amplifier operates linearly, it maintains the waveform shape of the input signal, meaning that the peaks and troughs are preserved without adding unwanted harmonics or altering the signal in any way.

When an amplifier is not linear, it can introduce distortion, altering the original signal and creating unwanted frequencies that were not present in the input. This is especially critical in applications where signal fidelity is vital, such as in audio equipment, where any distortion can significantly degrade sound quality.

Other characteristics like gain, bandwidth, and input impedance do play roles in an amplifier's overall performance but do not directly connect to the preservation of the original signal shape in the same way that linearity does. Gain refers to how much the amplifier increases the signal strength; bandwidth indicates the range of frequencies the amplifier can handle effectively; and input impedance relates to how much load an amplifier presents to the signal source. However, none of these attributes, while important for different reasons, specifically ensure the absence of distortion like linearity does.