"Transistor Q1 is connected to TxD, and the goal is to borrow a negative voltage connection for Q1. Conditions make this converter to work only half-duplex, so that a negative voltage is always present when transmitting data from TTL level to RS232 level."
It will only work if both sides aren't trying to send at the same time.
The circuit from the Single Sided Serial Arduino uses a capacitor to hold a negative charge for the conversion. I'd recommend using that instead:
http://arduino.cc/en/uploads/Main/ArduinoSeverinoSchematic.png
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