[HFSS] Power vs Gain (Incident Power / Accepted Power / Radiated Power, Gain / Directivity / Realized Gain)

1. Incident Power, 입사전력

- HFSS의 Wave Port와 Lumped Port로 입사되는 전력

Incident power for an antenna structure is defined as the time-averaged power incident on the port(s) of the antenna: 
$ P_{inc} = Re \int _{A} \vec{E}_{inc} \times \vec{H}_{inc}^* \cdot dS $
A is the union of all port boundaries in the model, including Wave and Lumped Ports, but excluding Floquet ports.
dS is the local port-boundary unit normal directed into the 3D HFSS model.

2. Accepted Power

- Port로 입사된 전력중 안테나로 들어가는 전력으로, port 매칭이 완벽하면 Accepted Power는 Incident Power와 동일하고 미스매칭될 수록 Accepted power는 감소함 

The accepted power is the time-averaged power (in watts) entering a radiating antenna structure through one or more ports.
$ P_{acc} = Re \int _{A} \vec{E} \times \vec{H}^* \cdot dS $
A is the union of all port boundaries in the model, including Wave and Lumped Ports, but excluding Floquet ports.
dS is the local port-boundary unit normal directed into the 3D HFSS model.

3. Radiated Power, 방사전력

- 안테나로부터 방사된 전력으로 Radiation Boundary 바깥 방향으로 나가는 Poynting vector를 면적분한 값
- $ P_{rad} = P_{acc} \times e $ : accepted power에서 방사효율을 곱하면 방사전력이 됨

Radiated power is the amount of time-averaged power (in watts) exiting a radiating antenna structure through a radiation boundary.
$ P_{rad} = Re \int _{S} \vec{E} \times \vec{H}^* \cdot dS $
S represents the radiation boundary surfaces.
dS is the local radiation-boundary unit normal directed into the 3D HFSS model.

4. Gain, 이득

- 방사체로 들어간 전력 (Accepted Power) 대비 방향에 따른 방사강도를 나타낸 값으로, 안테나 포트의 미스매칭에 의한 영향이 고려되지 않고 방사효율만 고려됨

Gain is four pi times the ratio of an antenna's radiation intensity in a given direction to the total power accepted by the antenna.
$ Gain = 4\pi U / P_{acc} $

5. Realized Gain

- 안테나 포트로 입력된 전력 (Incident Power) 대비 방향에 따른 방사강도를 나타낸 값으로, 안테나 포트의 미스매칭과 방사효율 모두가 고려된 값

Realized gain is four pi times the ratio of an antenna's radiation intensity in a given direction to the total power incident upon the antenna port(s).
$ Realized Gain = 4\pi U / P_{inc} $

6. Directivity

- 모든 방향으로 평균화한 방사강도 (방사전력, Radiated Power) 대비 방향에 따른 방사강도를 나타낸 값으로, 안테나 포트 미스매칭과 방사효율 모두가 고려되지 않은 값

Directivity is defined as the ratio of an antenna's radiation intensity in a given direction to the radiation intensity averaged over all directions.
$ Directivity = 4\pi U / P_{rad} $

- $ Gain = Directivity \times e $