How to make a FSK Rfid Tag that works at 125 kHz?

I am trying for some time to make my own rfid reader following the ideas on the DIY FSK RFID Reader. My primary problem now is that i do not have a specific rfid tag to test the reader so i decided to make my own using also an arduino uno. The only information on the internet which i found is at FSK MODULATED SIGNAL. I really need to know how to write the code to transmit the id from the tag to the reader. I mention again that the tag needs to work at a 125 kHz frequency and needs to use FSK modulation.

Solution

You won't be able to send data to the Reader without special hardware, just adding a wave on some antenna doesnt work for RFID systems with passive tags.

Reason is, RFID-Tags do not actively 'send' waves to the reader, instead they 'modify' (modulate) the reader's field by producing load on the antenna.

Imagine when the tag had an LED switching on and off while receives energy from the reader's RF field by inductive coupling. The reader will notice a change in it's own field when the LED on the TAG turns on/off as the more/less power is drained from the RF field.

This method is used for the TAG -> Reader communication, which is nice for several reasons:

TAG gets power from inductive coupling anyways, modulating the signal through load is alot more power efficient than using power for actively sending.
Smaller/Easier/Cheaper, needs less hardware on the TAG, might even need a separate antenna for sending
Harder to snoop communication as the modulation is harder to detect from distance

tl;dr

A bare ardouino doesn't have the required hardware onboard to modulate the reader's RF field.

Sidenote: transponders are not expensive, you get them for a few bucks. The LF transponders based on T55x7 are really nice for playing around as the can be configured for various modulations (PSK/FSK/etc in different modes), bitrates and more, however the usually come with Manchester modulation enabled by default.