I sort of get what you are saying, perhaps lets say it in the following way?
This is an area that confuses many and it seems to be confusing you too!
“The difference between EIRP and ERP is that ERP compares the actual antenna to a half-wave dipole antenna, while EIRP compares it to a theoretical isotropic antenna”.
so if the max power for 868Mhz is 25mW erp, then this is expressed in dBm as 14 dBm erp (10 x log (25/1) ).
Right…
- There is no such thing as a passive 10dBm gain antenna - its a bit like saying you have 15 apples when there are really 15 oranges - Whilst the qty is correct. the UOM is wrong) . If it really was a 10dBm antenna, then an ampifier would have to be involved because you really are talking about POWER
- if you use a 10dBd gain antenna, then the equation is corrrect = 14 + 10 = 24 dBm
- If you use a 10dBi gain antenna then the equation is 14 + 10 - 2.15 = 21.85 dBm
If you use the term “dBm antenna”, you confuse those who know what dBm should mean, Using the term “dBm” means it would be reasonable to think that you must be talking about an active antenna system (which uses an powered amplifier to amplify the signal) rather than a passive one that merely shapes the total power accordingly (and doesn’t really alter the total value of the power being radiated out of the antenna)
This video nicely explains the concept of antenna gain. Note, even though he seems to say so, there is NO overall power gain as such - i.e. there is no energy being magic’d out of thin air, its just focussing - this is why it is so important to make sure that when discussing this, the correct terms are used for antenna gain (the dB figure is NOT based on power) otherwise it gives the impression that extra energy is appearing from somewhere (and it is not!)