The crank is what everything runs off of. It is what spins the rest of the acessories. So if it is smaller then less belt will travel across it when it turns one full revolution.
The acessories are dependant on how fast the crank is spinning them so they are opposite. The bigger pulley you put on them the slower that ascessory spins. The smaller the acessory pulley the faster that acessory spins.
You have to think of the circumference of the pulley, not the diameter. Just a little change in diameter makes a big difference in circumference.
Remember Math class.
If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter (pronounced Pi) to represent this value. The number goes on forever. However, using computers, mathematicians have been able to calculate the value of to thousands of places.
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Pulley diameter VS circumference:
6 inch diameter pulley (stock) = 18.84955591 inches of belt travel.
4 inch diameter pulley (street underdrive) = 12.56637061 inches of belt travel.
3 inch diameter pulley (race underdrive) = 9.42477796 inches of belt travel.
So if you put a street pulley kit on your car the 4 inch crank pulley is slowing the alternator down already by approximately 33%. Then you add a bigger alternator pulley as well and it spins even slower. So you are really spinning the alternator down twice! Hence low charge.
Actually depending on how short your belt was the tensioner will take up an inch or so of belt.
I hope this helps.