Reduction of NADP in cyclic photophosphorylation

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PWiz
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I understand that an electron jumps to an excited state after absorbing a photon with the right energy (frequency) in photosystem 1 and exits the structure of the primary pigment, moves through different electron acceptors and returns to photosystem 1 (now at a lower energy state). What I don't understand is why NADP gets reduced using the energy the electron lost while moving between electron acceptors. Gain of electrons corresponds to reduction, but surely the electron returns back to the photosystem, and is not incorporated into NADP? How can reduced NADPH be formed if there is no hydrogen gain either (since photolysis does not occur in cyclic photophosphorylation)? If NADPH is not formed, then how do photoautotrophs that only use cyclic photophosphorylation perform the Calvin cycle (and produce a carbohydrate)?
 
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true NADPH +H+ is not formed in cyclic photophosphorylation but..
i'm a bit unaware as to which plant performs ONLY cyclic photophosphorylation ...could you please tell me that...because the whole reason for evolution to bring in cyclic phosphorylation was to support non-cyclic with setting up the proton gradient (PMF)