Captain Pit Bull,
I think what BarryCuda was alluding to is the way ACAS/TCAS should be used, not the machanical or electrical theory behind the system.
It is purely an aid to assist pilots in the visual detection of intruder A/C via a TA (in the first instance) and in the second instance, it is an aid to help avoid collision via an RA.
Some pilots - and I would like to stress, it's not too many, believe that TCAS is an instrument that can also be used to give them a picture of what is going on around them. When being told about traffic by ATC, the phrase "we have it on TCAS" means nothing - it might be the wrong A/C!!
In the vertical sense, it can help the situational awareness, but in a horizontal sense ACAS/TCAS is very unreliable in azimuth. It's misuse has caused incidents in the past, when A/C that were on headings to miss each other by 5 or more miles have actually had an airprox because one of the sets of crew decided to turn the A/C on the strength of the information they saw on the display.
It is a good system, it is not infallable, it has caused incidents in TC airspace where several A/C are in the same vicinity.