It is desirable for an atomic frequency standard that clock transition signal is of both high S/N rate and narrow linewidth. While for a passive coherent population trapping (CPT) frequency standard, increasing S/N rate is at the expense of enwidened lidnewidth, therefore it is crucial to choose a proper combination of S/N rate and linewidth. The present paper presents the experimental results of our systematically study on the relations between clock transition signal and parameters such as temperature and laser intensity with an optical table top CPT frequency standard. The obtained results provide us the criterion of choosing the combination of S/N rate and lidnewidth. The paper also presents experimental study results of de-coherent effect caused by unperfect circular polarization laser. Those experimental results were the good reference in the realization of CPT frequency standard, and they are also the general reference to CPT phenomenon and CPT frequency standard studies.