You've taken a very complex topic and reduced it down to a very simple question.  As a result, there won't be an easy answer.

Using relays to control electrical blocks is quite an old topic, going back at least to the 1930's or 40's.  Check out my post from two years ago for some hints:

     Block Wiring (12/1/21) | Mellow Hudson Mike

Actually the whole thread that this post comes from is good reading.  It explains how two-train operation works.

By the way relays aren't analog.  They're switches, and as such only have two states, "off" and "on".  For this reason they are much more like modern digital devices (0 and 1) than not.

Mike

Hi Sally joe boyd, 

looks like you recently joined the forum, so welcome!  I am not much of an expert on two train block operation, I do have "reenberg's Wiring Your Lionel Layout, Vol. 2: Intermediate Techniques " which was published in 1993. It has a lot of good information. Including how to wire two train operations with block signals. There are used copies available on Amazon, probably ebay as well.

The author, Peter Riddle, notes that Lionel trains us alternating current (AC) to power trains, while most relays are direct current (DC).  The ones for AC are more expensive. So, you would need to add a full wave bridge rectifier to convert AC to DC.  There are many styles of relays, typically you will need a 24-volt AC DPDT (double pole, double throw) or a 12-volt version. I have not bought a relay since Radio Shack closed in my area, others on a Forum probably have so hopefully someone will chime in. 

Best, Dave 

@Mellow Hudson Mike posted:

You've taken a very complex topic and reduced it down to a very simple question.  As a result, there won't be an easy answer.

Using relays to control electrical blocks is quite an old topic.  Check out my post from two years ago for some hints:

     Block Wiring (12/1/21) | Mellow Hudson Mike

Actually the whole thread that this post comes from is good reading.  It explains how two-train operation works.

By the way relays aren't analog.  They're switches, and such only have two states "on" and "off".  For this reason they are much more like digital devices than not.

Mike

Hi Mike, that is fantastic!  Glad you responded. 

If you are looking for auto control of two trains on the same track, you will need detectors as well as relays.

@BOB WALKER posted:

If you are looking for auto control of two trains on the same track, you will need detectors as well as relays.

In the post I mentioned detectors are discussed, starting with the old-fashioned isolated outside rail we enjoy as one of the few important benefits of having 3 rails.  If you're into O Scale however, with only 2 rails, then physical detectors of some sort, optical, infrared, current sensing, etc., will indeed be necessary.

Mike

In my work with automated layout control in my 3rail layout, I used IR detectors. I cannot be certain that isolated rail sections would have worked, but will look at it again.

One method is to use a Z-Stuff Infrared detector and Z-Stuff relay.

There's a Youtube video that shows this.

It's all described in a 2018 post here:   https://ogrforum.ogaugerr.com/...trains-on-1-mainline