In four orders delivered late Tuesday night, Koh said that a California jury's August verdict stands, but that Apple failed to prove that Samsung's infringement of its utility and design patents was intentional.
Apple had asked Koh to award an additional $400 million for wilful infringement to compensate for its loss of market share going forward.
But Koh said that Apple's arguments were "inconsistent".
She wrote: "First, [Apple argues] that money cannot compensate Apple for the harm its lost market share may cause going forward, and second, that the Court should award $400 million to compensate Apple for lost market share. If an amount cannot be calculated to compensate for this loss, then it is unclear why $400 million would be an appropriate award."
Ars Technica author Joe Mullin said that Koh's order shows an attempt to limit the "crushing" effects of Apple's victory.
All four orders are available on Ars Technica. The decision is likely to be appealed.
Apple and Samsung are also battling in Japan over Samsung's August win in the Tokyo District Court.
