Why is waveform of the voltage across the DC-link capacitor alternating?

Published: 25/09/2018
Why is waveform of the voltage across the DC-link capacitor alternating?
Source: ELECTRONICS.STACKEXCHANGE.COM

So I am connecting a full-wave rectifier to a half-bridge inverter as shown in the circuit below. I added a smoothing capacitor of 0.47 Farad to get a smooth DC output voltage (see the first graph), so why is the output voltage across the DC-link capacitors (C1 and C2) alternating (see the second and third graph)? As you can see in the fourth graph this also affects the waveform of the output volt

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