"Can't get any TV" related question

Didn't want to highjack the ongoing thread.

Does each individual analog TV inside a residence need it's own 
converter?

I live about 45 miles from strong transmitting towers, and my house 
has big UHF/VHF antenna outside on the roof which brings in analog 
stations very well.  I'll never subscribe to cable or any DTV 
offering.

But, the antenna cable is split, outdoors, before it even comes into 
the house.  One line, closest to the antenna, goes straight through 
into a lower level den (tri-level house).  I'm pretty sure the 27" 
Sony Trinitron analog TV there will need it's own converter.

Then it gets complicated.  The other cable comes into the house from 
the outside splitter, up the outside wall and into an upper level 
bedroom.  (I didn't wire this!)  There used to be a TV there, but not 
currently.  However the inline amplifier that boosted the signal from 
the long cable run from the antenna is still there.  Then the cable 
dives into the walls, trots across the attic heading south and ends up
as far as it could possibly go to a mid-level office, living room wall
terminating connector.

From that that terminating connector there lives yet another in-line 
amplifier and another splitter (visualize a "Y" output) which feeds a 
2 yr. old, small 15" Sharp LED EDTV in an office, and a larger old 
analog TV in the living room.  I don't think the Sharp EDTV has HD 
tuner or capability.

Now to review:  That's three TVs sucking the life out of one large 
antenna, but it works with the amplifiers positioned as described!

Do I need three converters?  Or could one converter be placed at the 
lower level (Den, Sony 27" etc.) and a second placed BEFORE the second
distant "Y" split, thus feeding the final two TVs?  I have two 
coupons, but haven't purchased yet.    

Sorry for the complex question, but I tried to describe what I'm 
living with.

 
-- 
Barbara