On the attachment the Narrow band output graph illustrates the output of the O2 sensor relative to the A/F mixture. When the oxygen sensor reaches operating temperature it generates a voltage, the voltage on a narrow band sensor puts out between .1 and .9 volts, but at an oscillating pulse most likely because of the pulsating exhaust gasses in the manifold. You can prove this by holding a propane torch or lighter to the sensor end and heating it. With a multimeter attached put the flame to the sensing element. The flame consumes the oxygen around the sensing element and heats it. After a few seconds the voltage will slowly rise until it peaks to around .96 volts. When the sensor is in the exhaust the exhaust pulses cause a fluctuation in the signal the ECU then averages these to come up with the current A/F ratio and changes the Pulse Width of the injector to either add or reduce the fuel being injected. With the simulator one can choose what A/F ratio you want to the ECU to think it's running at by changing the output voltages. This will hold the signal steady at one voltage so the ECU doesn't lean or Richen the mixture. Basically it will think the fuel being burned is staying the same and won't try to adjust the PWM. This is good because then you can tune it with a piggyback tuner and when it goes closed loop it won't lean your mixture back out.
This video is a bit weird, but does a good job of explaining how the simulator works:
If you have some basic soldering skills, can read schematics and an understanding of electronics it's easy to build.
If you want to buy the stuff to make your own check out:
Jameco Electronics - Electronic Components Distributor
or
www.digikey.com
If this prospect scares you or makes you go cross eyed just buy one here. These units look pretty nice because they use all surface mounted components.
http://www.o2simulator.com/o2-simulator-c-76/universal-o2-simulator-singledual-output-p-184.html
It's really easy to connect, one wire goes to the positive terminal on the battery post, one on the negative and the output goes to the O2 sensor plug.
Note: This thread is only for information purposes. I have no affiliation with any of these companies. What you choose to do with the information is up to you.