I don't think I would use a use case diagram at all in this case. The special device is a part of the system, and use cases are best at showing interactions with the system from outside, typically from human users.
To expand a little, consider a desktop application that uses a timer (analagous to your " special device) to fire some event, as many do. I would never use a use case to show the timer firing. Instead, I would probably use an activity or asequence diagram to explain the timer event handling.
UML does not require you to produce any specific set of diagrams. If youy are finding a particular type of diagram hard to draw or use, it probably isn't necessary for your design.
Having said all that, if you are wedded to the idea of use case diagrams, you can make your special device an actor in a use case and show it using the other parts of the system.