Which oscilloscope stage primarily determines the maximum frequency response of the instrument?

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The vertical amplifier sets the maximum frequency response. Its bandwidth determines how faithfully the signal’s high-frequency components are reproduced in the vertical direction; if the edge or waveform contains rapid changes, a wider vertical bandwidth is needed to avoid attenuation and phase distortion. The horizontal sweep controls how the trace is drawn over time and the time scale, not the channel’s ability to pass high frequencies. The power supply powers the instrument but doesn’t set the intrinsic speed of the signal path. So the stage that primary determines how fast the oscilloscope can accurately respond is the vertical amplifier.