Organic electrochemical transistors are hydrogen ions sensitive when the gate electrodes are modified with poly (3,4-ethylenedioxythiophene)/bromothymol blue. Previously, we have fabricated pH sensors based on pH-sensitive poly (3,4-ethylenedioxythiophene)/bromothymol blue film and the semiconducting layer of poly (3,4-ethylenedioxythiophene)/polystyrene sulfonate and proposed a theoretical model describing the current-voltage (I-V) relationship of Organic electrochemical transistors based pH-sensors. However, the model is not accurate enough to describe the transconductance curve. This paper shows that when the sigmoid function is used to modify the I-V relationship of pH-sensitive Organic electrochemical transistors, the goodness of fit of theoretical analysis for the transfer curve and transconductance curve can be as high as 0.999 and 0.984, respectively. After analyzing the Taylor expansion characteristics of the Sigmoid function, higher-order terms of the gate bias and the pH are introduced into the polynomial to modify the theoretical model. The modified model's goodness of fit to the transconductance curve's experimental results increased by 9.2%. Finally, the validity and accuracy of the modified model are verified by using the peak transconductance and the gate bias corresponding to the peak transconductance as the sensing parameters. The research provides a universal I-V characteristic relationship for pH-sensitive Organic electrochemical transistors and will provide theoretical support for designing and manufacturing flexible wearable pH sensors.