i don't know exactly why we're adding the zener diode. My guess would be that it functions as a voltage regulator but that's as far as i can go.
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It clips positive peaks to Vd + Vz. It passes negative peaks with no change but via 2.2k resistor. As the tiotle says, it is a positive clipper (only) – Russell McMahon Apr 20 '17 at 08:35
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When Vo is positive, it clips at around 4.6v (3.9v zener + 0.7v diode). Above 4.6v, the zener and diode combined act like a clamp, conducting, to bring the voltage down. R drops the remaining voltage.
When Vo is negative, the diode blocks clipping. No current flows through the diodes. If no current is drawn to/from Vo then voltage across R is zero therefore Vo equals Vi
It's not much of a voltage regulator at all if AC is passed in. It is not possible to say what this circuit could be used for; it could be anything. But in short, it simply limits Vo to about +4.6v.

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Because a battery would be a very weird way of doing it - not that it would work well. Zener diodes are for clamping voltages. Batteries aren't. Batteries need replacing, zeners don't. +1 for the really weird idea though! – Jodes Apr 20 '17 at 00:32
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@dandavis the diode here actually prevents the bottom half being clipped. It would be clipped down to -0.7 without the diode – Jodes Apr 20 '17 at 00:59
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@Jodes - Interest only. A forward biased zener probably clips at a bit more than 0.7V in the forward direction. From some time ago now memory, 0.9V to over a volt. – Russell McMahon Apr 20 '17 at 13:01