Wait, if you just want something that is always "high" just make it "high"?
Do you want it to be low when there is no square wave?
Use a capacitor to smooth the squarewave just like filter capacitors in power supplies. If you need a cleaner signal just use an NPN transistor, however, you may need to reduce the voltage off of the capacitor so you dont burn out the base of the transistor.
The data sheet gives saturated characteristics with β = 10. This appears to be a common figure in the industry, for a wide range of devices. The charts also show β figures for Vc=5V and 10V, a long way from saturation. β is not given, for example, for Vc=1V which would pull in the relay just fine with a supply voltage of 5V.Why do you need to assume a beta? Doesnt the DS tell you what it is equal to?
The datasheet for all transistors shows a wide range of beta when the collector to emitter voltage is fairly high so the transistor is not saturated.Why do you need to assume a beta? Doesnt the DS tell you what it is equal to?