Passive repeaters can be very effective in fixing gross shadowing problems. By this I mean it is worth doing in those situations where there is something specific that is heavily blocking the signal path between your phone and the cell tower. So, for example, if you have a ridge in the way, or are inside a metal building, or you are underground in a car parkade, then perhaps a passive reflector or passive repeater may be helpful. They are less helpful and sometimes a waste of time when simply used to bring signals down from 20 feet above your house's roof into the family room.
Let's look at an example. Let's say that your building is a wooden house, located a bit too far from the cell tower, say 10 miles. We'll assume the weakest path is inbound and that you use a CDMA phone. Your phone's EIRP is perhaps about 20 dBm and the path loss to the tower is about 130 dB from the family room. The tower's antenna system might have net gain, say 10dBi, and the site receiver sensitivity may be around -106 dBm. Your inbound signal is pretty marginal, at around -100 dBm so it will not be reliable.
Now, let's say that you set up a passive repeater. The indoor antenna type depends on where you want coverage. If you want it all around one floor, then a quarter wave monopole mounted against the ceiling in the center of the building might be appropriate, or within the most-used room. Such an antenna might have 1 dBi gain and you might be separated from it by, on average, maybe 15 feet distance, shall we say? So the path loss from your phone to that antenna might be about 48 dB. That antenna picks up about 20 - 48 +1 = -27 dBm which is then routed up to your yagi on the roof with cable loss of about 5dB (assuming a 60 foot run). So the yagi is re-radiating -32 dBm with a gain towards the tower of 12dBi, giving a net EIRP of -20 dBm. The yagi is up higher, say at 50 feet, so its path loss to the tower is 110 dB instead of 130dB. So your signal hits the cell tower at -20-110=-130 dBm, enjoys a 10dB gain through the antenna system and hits the receiver at -120 dBm. That is 20 dB lower than the example without the passive repeater. What will happen is that the energy from your phone will hit the cell site at a stronger level than from the passive repeater and the two will interfere with each in a modest way, providing a bit more multipath distortion than would otherwise exist. The result would be that you might not perceive any change at all in reliability of coverage.
This illustrates that the passive repeater suffers quite a bit of loss and is best used where you are trying to make up for a blockage that is costing you 40 dB or more.
(Apologies to Duffy for not converting all the dB values to non-dB values, but that is just way too much work)