The thing is, most of us want to do "the right thing" and be considerate and helpful, etc. As such, it seems like giving your current manager an advance "heads up" would be the moral thing to do. But... the reality is, you never know how that is going to be received. It may be appreciated and you may continue to work normally until you find something new. But there is always the risk that your current employer will choose - either out of a sense of retaliation, for for some other reason - to terminate you immediately if you declare "I'm planning to move on."
So you have to weigh the risks, relative to your situation. Would you be fucked if you were let go immediately? Then definitely don't say anything. Do you have a year of living expenses saved up, and you live in your car with almost no bills at all? Then it probably doesn't matter. Reality is probably somewhere in between, so you'll have to evaluate your own circumstances.
Beyond that, remember that business is business, and (almost) everybody involved understands that. If you leave, their may be some bruised feelings, but your current employer should understand your need to do what's right for yourself. If they don't, well, that just illustrates even more so that leaving is the right decision. But as long as you give sufficient notice (two weeks is kinda considered "standard" but you might want to do more depending on the situation) and are respectful and professional in how you conduct things, there's no reason for any acrimony or bad blood as a result of your leaving.