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How could a DC oscillator produce AC after a capacitor?
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The oscillator is creating both DC and AC. The DC component is the average value of the signal. In the case of your 0-10v square wave, that is 5v. The AC compnent is the part of the signal that changes. The effect of the capacitor is to block the DC component, leaving only the AC component. The waveform is shifted vertically to be centered around 0v.