I'd have to say I was the most "sleep deprived" during first trimester. I was so sick, couldn't eat/drink.sleep etc, that I could barely function. I had to have a pump (similar to an insulin pump) to give me anti nausea meds just so I could keep bread and water down.
I can say that even when the babies were little I wasn't sleep deprived. DH and I took turns when the babies were little (honestly I don't get why any DH WOULDN'T take turns taking care of their child) and as the night feedings got fewer and farther between we each got longer stretches of sleep.
Sleep is VERY important to our family, the kids sleep 10-12 hours at night, an the babies take one 2-3 hour nap during the day, I can't imagine what life would be like without sleep.