Why is the voltage regulator waveform identical to the diode bridge waveform?

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SUMMARY

The voltage regulator waveform (purple curve) in the discussed Power Electronics homework problem is identical to the diode bridge waveform (green curve) because it represents the voltage drop across the BJT. The output voltage of 12V is derived from the input voltage to the BJT minus this voltage drop. The confusion arises from the expectation that the waveforms should be inversely related, but they are actually additive in nature, leading to the conclusion that the purple waveform equals the green waveform minus the constant output voltage (red curve).

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I am doing a homework problem for my Power Electronics class. I have attached the relevant image. My question is, (referring to the TOP plot) why is the voltage regulator waveform (purple curve) identical to the voltage waveform coming from the diode bridge (green curve)? Shouldn't it be the inverse? My understanding was that when you add the voltage regulator waveform and the waveform that isn't constant (which would be the green curve in this case) you will get a constant voltage (red curve). However, the way it is shown, it would seem like you have to subtract them. Why is this??
 

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Purple = Green - Red.

The purple waveform is the voltage drop across the BJT. The output voltage (12V) is the input voltage to the BJT minus the voltage drop across the BJT.
 

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