Automatic expandable editor

Basically I want an input field, which expands whenever the user puts too much text in it. There are several approaches out there trying to achieve this. The problem exists in web developement too and it's pretty basic (as seen by an user).

I went with the most logical (well, for me) approach I found. Extend the Changed-event.

private void OnTextChanged_Grow(object inSender, TextChangedEventArgs inEventArgs)
{
      InvalidateMeasure();
}

But this heavily affects the performance! The power needed to invalidate the view each time the user presses a key is just too much.

Is there any other clean way to do it? Maybe even a change to the design / architecture?

Thanks in advance.