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Most of the front-end position readout circuits in positron emission tomography (PET) detectors originate from the Anger logic design. In PET detectors with position-sensitive photomultiplier tubes (PS-PMTs) and multi-channel photomultiplier tubes (MC-PMTs), anode position readout circuits are more complex due to multi-anode outputs from a single PMT. To simplify the circuits, many researches have investigated different schemes by combining multiple PMTs with simplified X-, X+, Y-, Y+ outputs. In this paper, we aim at optimizing the performance of the position readout electronic circuits. First, we compared the signal-to-noise ratios (SNRs) in different position readout schemes. Then we examined the truncation and roundoff errors in the irradiation-image processes by applying the root-sum-square (RSS) analysis and the uniform distribution simulation methods. Furthermore, we investigated the gain adjustment and balance issues in the X-, X+, Y-, Y+ analog signal channels. We demonstrated that an eight-bit analog to digital converter (ADC) is probably insufficient in the position recording if a gamma-ray event position is calculated from digitized X-, X+, Y-, Y+ signals. We also revealed that an energy nonuniformity error could be occurred if the signal gains in the front-end analog circuits are improperly adjusted. As a result, the quantitative gain adjustment criteria are given to optimize the PET position readout circuits.