Why am I so angry when I'm tired?

I don't understand it. I'm normally not a happy person but when I haven't slept for more than two or three hours in a 36-48 hour period I get really, unreasonably angry. I'd never hurt anyone because of it but it is one of the things driving a wedge between my wife and I. I don't get much sleep because I work and I have the only license so she can't drive and I have to drive her to run errands and take the kids to school and such which leaves me with about 3 hours of sleep a day for about five to six days and I am constantly upset for the entire week. I can hide it from the kids but the wife picks up on it and we tend to argue a lot more during the work week like a lot more. Could there be some kind of chemical deficiency in my brain that takes all my patience like beyond the normal irritation caused by sleeplessness?