Louis Berkhof on the Eternal Generation of the Son:

“The eternal generation of the Son. The personal property of the Son is that He is eternally begotten of the Father (briefly called “filiation”), and shares with the father in the spiration of the Spirit. The doctrine of the generation of the Son is suggested by the Biblical representation of the first and second persons of the Trinity as standing in the relation of Father and Son to each other. Not only do the names “Father” and “Son” suggest the generation of the latter by the former, but the Son is also repeatedly called “the only-begotten,” John 1:14, 18; 3:16, 18; Heb. 11:17; 1 John 4:9. …

“It is an eternal act of the Father. This naturally follows from the preceding. If the generation of the Son is a necessary act of the Father, so that it is impossible to conceive of Him as not generating, it naturally shares in the eternity of the Father. This does not mean, however, that it is an act that was completed in the far distant past, but rather that it is a timeless act, the act of an eternal present, an act always continuing and yet ever completed. Its eternity follows not only from the eternity of God, but also from the divine immutability and from the true deity of the Son. …

“It is a generation of the personal subsistence rather than of the divine essence of the Son. Some have spoken as if the Father generated the essence of the Son, but this is equivalent to saying that He generated His own essence, for the essence of both the Father and the Son is exactly the same. It is better to say that the Father generates the personal subsistence of the Son, but thereby also communicates to Him the divine essence in its entirety. But in doing this we should guard against the idea that the Father first generated a second person, and then communicated the divine essence to this person, for that would lead to the conclusion that the Son was not generated out of the divine essence, but created out of nothing. In the work of generation there was a communication of essence; it was one indivisible act. And in virtue of this communication the Son also has life in Himself. This is in agreement with the statement of Jesus, “For as the Father hath life in Himself, even so gave He to the Son also to have life in Himself,” John 5:26. (4) It is a generation that must be conceived of as spiritual and divine. In opposition to the Arians, who insisted that the generation of the Son necessarily implied separation or division in the divine Being, the Church Fathers stressed the fact that this generation must not be conceived in a physical and creaturely way, but should be regarded as spiritual and divine, excluding all idea of division or change. It brings distinctio and distributio, but no diversitas and divisio in the divine Being. (Bavinck) The most striking analogy of it is found in man’s thinking and speaking, and the Bible itself seems to point to this, when it speaks of the Son as the Logos. (5) The following definition may be given of the generation of the Son: It is that eternal and necessary act of the first person in the Trinity, whereby He, within the divine Being, is the ground of a second personal subsistence like HIs own, and puts this second person in possession of the whole divine essence, without any division, alienation, or change.”

– Louis Berkhof, Systematic Theology (Grand Rapids, 1949), pp. 93-94.