だが

Conjunction (used in writing and formal speech only) (Intermediate ㊥ 18)

A conjunction that expresses something that is contrasted with what is expressed in the previous sentence.

Equivalent: But; however; yet; nevertheless

日本の経済力は伸びている。だが、いつまで続くかは分からない。: Japanese economic power is growing, but we can't tell how long it will last.
都会の生活は便利だ。だが、ストレスが多すぎる。: Urban life is convenient. But there are too many stresses.
私は彼女とは初めて会った。だが、前から知っていたような親しみを感じた。: I met her for the first time; but I felt close to her as if I had known her for a long time.
山本は医者に何度も煙草を辞めるように言われた。だが、辞める気はないらしい。: Yamamoto was told by his doctor to quit smoking, but he doesn't seem to have any intention of quitting.
あの人には才能がある。だが、その才能を使っていない。: He is talented, but he is not using his talents.
今日の試験のために寝ないで勉強した。だが、さっぱり出来なかった。: I studied hard for today's exam without sleeping, but I couldn't do it at all.
妹はよく勉強するし、頭もいい。だが、成績はなぜかよくない。: My younger sister studies hard and she is intelligent, but somehow her grades are not good.

Formation

S1 informal	だが、S2 informal
	あの人の話は面白い。だが、内容がない。	His talk is interesting, but there is no content

Notes

だが is not used in spoken Japanese unless it is followed by ね as in (1).

A: あの男はなかなか切れるな。
That guy is really sharp, isn't he?

B: だがね、奴は性格が悪いんだ。
But, he has a bad character, you know.

In spoken Japanese it is usually replaced either by けれど(も) or by でも. The formal version ですが can be used in both spoken and written Japanese.

A: 仕事はお忙しいでしょう。
Your job must keep you busy.

B: ええ、{でも/ですが/けれども}、面白いんです。
Yes, but it is interesting.

日本へ行きたくて仕方がないんです。{でも/ですが/けれども}、お金がないから、行けません。
I'm dying to go to Japan. But I don't have money, so I can't go there.

【Related Expression】

The first difference between だが and が/けれど(も) /のに/しかし/だけど/でも is the way they combine two sentences. だが, だけど, しかし and でも are always used as a sentence-initial conjunction, but が and のに are normally used as a non-sentence-initial conjunction, and けれど(も) is used either as a sentence-initial conjunction or a non-sentence-initial conjunction.

Sentence-initial conjunctions:

a.	Sentence1。だがSentence2。	*Sentence1だがだが、Sentence2。
b.	Sentence1。だけどSentence2。	*Sentence1だけど、Sentence2。
c.	Sentence1。しかしSentence2。	*Sentence1しかし、Sentence2。
d.	Sentence1。でもSentence2。	*Sentence1でも、Sentence2。

Non-sentence-initial conjunctions:

e.	Sentence1が、Sentence2。	???Sentence1。がSentence2。
f.	Sentence1のに、Sentence2。	*Sentence1。のにSentence2。

(Non-)Sentence-initial conjunction:

Sentence1けれど(も)、Sentence2。

Sentence1。けれど(も)、Sentence2。

The second difference concerns semantic difference. が and けれど(も) can be used to in two senses of 'but' and 'and.'

[1]

今東京に来ています{が/けれど/*のに}、東京は、やはり、活気がありますね。
I'm in Tokyo now, and I feel that Tokyo is full of energy, after all.

For the difference between けれど(も) and のに, see のに. (⇨ のに㊦) Among the four sentence-initial conjunctions, the most colloquial is でも, followed by だけど and the least colloquial one is だが, followed by しかし.