Not sure what license you have, the rules are slightly different.
FAR rules are described in Part 61.57b.
- 3 takeoffs and landings full stop on same type/class/category
JAR rules are described in FCL 2.026a and c
- 3 circuits including takeoff and landing on same type at night
- if you have an IR(H), then 3 circuits at daylight are sufficient
None of these rules say you have to do the circuits on a licensed airfield.
Note that you have to do the 3 landings on type (if there are type ratings). To illustrate:
FAA:
- 3 circuits on R22 -> you can take passengers on R22,R44,B206,..
- 3 circuits on AW139 -> you can take passengers on an AW139
JAA:
- 3 circuits on R22 -> you can take a passenger on an R22
- 3 circuits on B206 -> you can take passengers on a B206