Powering Up (Fallout 4)

Powering Up is a quest and achievement/trophy in Fallout 4.

Quick walkthrough
Talk to Father who will ask you to find a way of boosting the transmission range of Diamond City Radio. Place the gear in Travis's shack, return to Father and place the Beryllium agitator. Then talk with the Directorate. They have already decided that it is necessary to destroy The Brotherhood of Steel.

Detailed walkthrough
When you teleport to the Institute, you must talk to Father. He will give you the task of going to Diamond City to boost the range of Diamond City Radio. Once you get to Diamond City, head over to Travis's shack where he broadcasts from. When you enter his shack, look on the ground for a box of radio things to his transmitter gear.

Place the gear in the right spot:
 * 'Radio thing with the buttons' goes to the left.
 * 'Radio thing with dials goes' in the center.
 * 'Radio thing with the tubes' goes on the right.

After that is done, return to the Institute and go to Father, who is waiting in the reactor room where he will prompt you to put in the Beryllium Agitator that you acquired from the previous mission into the reactor. When you place that in the reactor, you must activate it using the terminal near it. The door to the reactor will close and you will have to talk to Father, after which he will ask you to attend a board meeting as the director. There you will discuss the future plans of the Institute. You will discover that the Director already have made the decision to destroy the Brotherhood of Steel. If you argue for a solution that avoids conflict, it will be rejected because The Brotherhood of Steel already started it by invading the Commonwealth with their troops and airships. You have to decide whether the Institue shall focus on further development of synths or weapons (need to be clarified how that decision affects gameplay). When the meeting concludes this quest completes and the quest End of the Line starts automatically.

Bugs
When talking to father, sometimes he will tend to walk away, cutting out the dialogue and resetting it.

It seems that if the Brotherhood of Steel is attacked before this mission it will be impossible to start the meeting with the Directorate essentially breaking the main quest.