This paper presents an enhancement of a previous Conventional Carbon Nanotube Field Effect Transistor (C-CNTFET) compact model proposed by Raychowdhury et al. This improvement consists in three new extensions to the previous work: first, by adding adequate electronic noise sources to the C-CNTFET modelling the electronic noise at the source and drain access regions; i.e., thermal noise and the electronic noise in the device channel; i.e., flicker and shot noise, second by adopting a simple and a fast analytical calculating approach that models the Schottky barrier (SB) at the source and drain metal access and the semiconducting carbon nanotube (CNT) interface by including adequate noise sources, and finally by proposing a generic compact model that is suitable for circuit simulation purpose. In order to validate the proposed SB-CNTFET compact model, electrical simulation results are compared with literature reported experimental results. Good agreement is observed over a large range of the device biases. For the SB assessment, an operational amplifier (Op Amp) circuit has been designed and simulated using the SB-CNTFET compact model. A significant degradation on the Op Amp's performances is observed for large SB. As SB proprieties is associated with the CNT geometry; i.e., diameter, and to prevent circuit's performances degradation, an optimization work has been carried out to provide the circuit design community with the suitable CNT diameters that should be made.