Digital IO – PIR Sensor – Arduino for Beginners

what is the maximum distance betweeen the transmitter and the receiver?

http://www.ingenstech.com/6-digital-io-pir-sensor-arduino-beginners/

PIR doesn't have a transmitter and receiver as such, since it's all in one housing. It's not like an IR beam from a transmitter to a reflector or receiver that gets broken. It sets up a sort of "ir field" for want of a better word, and senses a disturbance.

This page at adafruit explains how they work.

thanks will look to it