I am trying to put together a "simple" circuit that will control a relay/transistor when the voltage from a source changes from 12.5vdc to 13.5vdc. Was thinking zener, MOSFET, etc .. what would work best/be simple?

 

You need a 'comparator' look into the LM339 or LM393 . This link will get you started;
http://home.cogeco.ca/~rpaisley4/Comparators.html

 

I "think" the problem I would have with a comparator is that I only have the ONE voltage to look at .. the one that changes from 12.5 to 13.5. I could see using one if I had two different voltages .. a steady 12.5 and the the one that varies to compare. But maybe I don't understand comparators well enough.

 

So, what's this for? Making sure the car's engine is running before switching on HIDs?

 

Semper Fi .. I am a Viet Nam vet .. thanks for your help.

 

The comparator method is valid. As you say a reference is required, but almost certainly much less than 12.5V.

Due to the doubt over the intended application it may be best not to say more pending moderator's decision.

 

"Comparator Voltage Monitor", now the internet search engine is your best friend...

 

A comparitor is best to monitor voltage levels and trigger when voltages change, but for fine thresholds like you are suggesting, you really need a stable reference. Typically a zener diode connected in series with a resistor would suffice, but alternately you can use a low voltage regulator IC such as 7805 (I recommend the T03 case style) which would work marvelously with a 12v input.

 

Since others are giving advice, so far without management intervention, I would point out that the charging circuits of such things as self-starting generators are prone to horrid surges. These could easily fry a 7805, even in a big case style. Additional anti-surge protection would be required before the regulator.

Note that it is also much, much safer to use a low reference voltage, so that the battery input can be well attenuated to feed the comparator. Additional clamping may be needed part-way along the input voltage potential dividing chain.

All of this may not be easy, especially when just beginning to get to grips with the basics.