analog to digital conversion using operational amplifier
It is not an A/D converter - it is just an amplifier.

To transmit to the card T1 is turned on and off by the microprocessor to create a 125kHz signal at R1, the antenna (L1) resonates with C2 to create a signal that is picked up by the card.

The card will detect this signal and modulate it by modifying the resonant antenna within the card, as it does so it will affect the amplitude of the 125 kHz signal at L1.

Diode D1 detects the 125kHz signal across the antenna, as the intensity of the signal changes so does the voltage across R5 fluctuate.

This small signal is amplified by IC2A by about 12 times.  It is then amplified again by T2, the way that T2 is biased will cause it to limit the signal so only the negative peaks at IC2a pin 1 will cause the transistor to come out of saturation.

The output of T2 then passes through IC2B, by now the signal will be either high or low and so will be a digital signal that is sensed by the microprocessor to read the card data.