Would an RF amplifier be required for an indoors antenna connected via coaxial cable to an outdoor directional antenna (900/1800 MHz)
Good question, but unfortunately this doesn't work very well for covering any useful volume.

The problem is that the path loss between the indoor antenna and the phone is surprisingly large, even though you're only a few feet away. Put another way, the fraction of the transmitted signal that is intercepted by the receiver is very very small.

I'll try some numbers to check this. If the signal outdoors (on your phone) is about -75 dBm, then you need to add the following:  


Good Outdoor antenna: +8 dB
Coax cable: -6 dB
Indoor antenna: + 2 dB
Indoor path loss to your phone, 900 MHz, 6 feet: -37 dB

And optionally, also add:
at 1800 MHz: -6 dB 
Holding phone on the wrong side of your head: -20 dB 
Walk another 6 feet away: -6 dB


The total effect of this system, in the best case, leaves you with 33 dB less signal than you had outdoors, which is -108 dBm, not enough to make a call, and it quickly gets worse.

The exact numbers are full of assumptions and can be debated, but the indoor pathloss is the killer.

Commercially available repeaters have 60 dB bi-directional amplifiers in them, that's a power gain of 1 million times. They also need sharp filters to prevent oscillation, and other circuits to stop them interfering with the cell network.

The site you link to shows a reasonable antenna that can be constructed without measurement equipment. But it depends on coupling directly into the back of the 3G modem or phone. This is probably only a few dB path loss between antenna and 3G stick, which tips the balance. Or you might have a phone or stick with an actual RF connector, first prize.

So I'm sorry but if you want to walk around indoors, on the phone, you really need that 60 dB amplifier.