I am not the first person to build an IR blaster for a RaspberryPI, and I sure won't be the last. Thanks to the LIRC gpio module, the circuit required is super simple:

One side is the transmitter - 3 IR LEDs in series, with a 56ohm resistor, driven by a bog-standard BC547 transistor.

The LEDs I used have a 1.2V at 20mA. forward voltage, so the three in series drop 3.6V. R2 needs to drop 1.4V (to add up to 5V). R = V/I, so R2 needs 70 ohm. For some reason, I picked a 56 ohm resistors, so the LEDs will get driven a little harder at 25mA, which is still well with in their spec (They max out at 50mA).

The transmitter side is even easier - the device does all the work, so there is just a pull down resistor on the signal leg. I picked GPIO 17 and 18 at random - any GPIO line will work, and you can configure it in software.