That's not really how child support works, at least not in my state. Both parents could have 50/50 physical custody, and the higher earner is still paying child support to the other parent. It's so they can maintain the same sort of standard of living in BOTH households.
Here's some worksheets for Maryland so you can see where they are coming from with the calculation:
http://www.dhr.state.md.us/CSOCGuide/App/selectWorksheet.do
Just for an example, I picked the joint physical custody work sheet- Mother making $2,000 per month, Father making $10,000 per month. For nights with each parent I did 183 for Mother, 182 for Father. Calculation shows Father pays $1,143.67 in child support.