Questions about Samsung S Pen

Is this compatible to note 20 ultra? Coz I lost my s-pen. Kind regards

I am basically satisfied with the S Pen of the S22 Ultra. For home use, however, it would be great if there was a larger pen (which works just as well as the normal S Pen). As big as a pencil, for example. For a better feel. Logically, such a pen could not be stored in the mobile phone, but at home that would not be a problem. Does anyone have any ideas? I've already thought about buying an additional original S Pen and then converting it somehow, extending it.