Here's a link:
http://www.babycenter.com/0_how-much-sleep-does-your-chil...
A baby this age usually naps 2-3 times a day.
A baby not sleeping well, can be due to many reasons, even just new development, which happens each month.
1) at 3 months old, they have a growth spurt...in which their intake needs INCREASES, and feeding increases as well. IS your son, getting enough intake daily? If not, this is one reason they cannot sleep well... because their intake is NOT keeping pace with their growth/weight gain and they will then basically always be hungry.
So, make sure he is getting fed on demand, at proper intake amounts, and has a full tummy. MANY babies will simply not sleep well, because they are not getting enough calories for their system, which is growing quickly.
2) Is he ill or getting sick? This is another reason a baby cannot sleep.
3) Are you always on the go with him, or do you allow him to nap at home in the same place (ie: his crib), or since he may be on the go all the time at his sleepy-times... he CANNOT get a SOLID rested nap for it's full length. ie: some babies CANNOT get a LONG solid nap/deep sleep, because they are in a stroller or on the go. My kids, would never get a good normal solid nap, if I was out with them... they were not "portable" nappers... but would ONLY nap well, AND REGULARLY if they were home in their crib. So at their nap times, I ALWAYS was home.
The thing is, as a baby grows each month, their "needs" changes too, INCLUDING sleep patterns and needs. Some babies, just need to be put to nap regularly in a place that is not transient... you need to cue into their environment too, for napping. ie: as an adult, could YOU nap/sleep WELL and SOLIDLY for it's full length, if someone were wheeling you around amidst a mall or on the go for errands? Same for a baby... you provide them with a suitable sleep environment... so that they can sleep well and solidly and for a proper amount of time undisturbed
4) His "napping" for ONLY 30 minutes, is NOT a "nap." It is reflecting that he goes to sleep... but then his sleep is interrupted or disturbed and his REM deep sleep patterns are not being let happen and thus, he wakes up. Some kids may SEEM to be able to sleep anywhere... BUT THEIR "QUALITY" OF SLEEP is not good... so, you may need to reassess "how" and "where" you put him to nap... I personally, would consistently only put him to nap at home, in his crib (or with you)... therefore providing him with a static place for sleep... that is undisturbed. IN THE LONG RUN....this will also form a consistent nap pattern in him. And when he gets older, he will learn that naps happen at the same time and same place... because it will "cue" him about that.
He is too young for any "sleep training" BUT, by providing him with a consistent place/time for naps... it really helps a baby/child.
5) Don't wait until he is "over-tired" before putting him to nap. An over-tired baby/child actually CANNOT sleep well and they will wake more. So, know his tired cues, and put him to nap then. After waking, a baby typically gets tired after about 2-3 hours of "awake" time. So this is how you can gauge it.
6) a baby's need for naps is important... it contributes to their immune system, their development, their brain development, and for restoring their body. So, you baby is not really napping... only 30 minutes.
Or, some babies start teething early.
I don't know if you are breastfeeding or not... but, Is your baby a good feeder? Does he latch on properly? Is your breastmilk production ample enough? If "no" to any of these questions, I doubt he is getting enough intake. MANY times a baby also "cluster-feeds" meaning they NEED to feed even every hour, especially at growth-spurt periods.
7) Per his age... I suspect he is at a growth spurt time... and when a baby changes developmentally this ALSO causes them to have a hard time sleeping... but it will pass. Because, they are in transition developmentally and growing.
8) ALso, some babies cannot sleep/nap if they are over-stimulated prior, and not allowed to wind-down first... we need to help them nap/sleep by making the atmosphere calm first and have a routine of it.
If anything, ask your Pediatrician.
BUT, keep in mind that a baby and child's sleep-patterns are NOT static, it ALWAYS changes per their growth and changing needs. Even whenever they hit "milestones" a baby will often get a kink in their ability to sleep/nap.
Just some ideas,
all the best,
Susan