Hi XC.6800!
I am an undergraduate student ^_^. Also, i am newbie in IC design, i focus on analog IC design.
"what knowledge is need for a beginner to design his/her own IC."
- I follow the courses about analog IC design of UC Berkeley, i can easily find them in the internet, each course includes: lecture notes, video, homeworks, test, also recommended book chapters or papers for problems. I think learn by this way is good to me.
"What IC is usually designed by undergraduate student."
- First, i simulate the circuits in the books to understand more about each small block, then i build the larger circuit, for example: bandgap, operational amplifier, comparator, flash ADC...Also, i have to connect small blocks together to get "IC". Actually, when i connect them, there are some new problems appear, but i have to read papers a lot to solve them. I designed successfully IC LDO by this way.
I will design another one with the same these steps.
ps: (I think digital IC and analog IC have the different way to reach the design problems).
That is all of my experience until now.
Hope this help!