PPP time transfer analysis requires the estimation of position and troposphere delay parameters. The aim of this study is to investigate the influence of troposphere modeling or of external troposphere corrections in PPP time transfer using a least-square analysis, like in the Atomium software. It is investigated using both simulated and real data. We also test the use of two external troposphere products as troposphere corrections, rather than estimate the troposphere parameter in the least-square. Results for two GPS stations are presented here. They show a significant improvement of the clock solution when using external troposphere products. Since external troposphere products are not always available for all stations, we also test a new approach for the troposphere estimation: using constraints on the troposphere parameter, reducing the sampling rate of this parameter to 15 minutes along with an evolution constraint of 1 mm between successive estimation epochs of the wet tropospheric delay. With this method, the clock solution gets the same level of precision as when the troposphere is corrected with external products rather than estimated.