How to calculate bias resistor values to drive IR diode

Question

I'm creating a circuit to do communications via a digital serial infrared link. My requirements are for the link to support relatively high speeds (maximum serial bit rate is 4,000,000 bps or 4Mbps) and for it not to draw a unreasonable amount of power; both requirements derive from the fact that I'm intending to drive this with a Raspberry Pi. The driver for this is a UART TX line directly from the Pi. I've chosen the Kingbright APTD3216F3C-P22 IR transmitter and a BC817-40 as the driver transistor (mostly because I have a lot of them leftover from an earlier project!). If it matters, this will be on FR4 PCB with 0402 resistors.

Calculations

Here are my calculations for the various resistors. When the transistor is on, I want to drive 15mA of current through D1. Since the forward voltage drop across D1 is about 1.2V, and \$V_{CEsat} \le 0.7V\$, and the supply is 3.3V, I calculate the value of R3:

$$ R3 = \frac{(3.3 - 1.2 - 0.7)\text{V}}{15\text{mA}} = 93\Omega \approx 100\Omega$$

For R1, I am driving it with 3.3V and \$250 \le h_{FE} \le 600\$ for this transistor, so I calculate the resistor from the required base current times a factor of ten to make sure it's driven into saturation:

$$R1 = \frac{V_{in}}{10I_B} = \frac{3.3\text{V}}{150\text{mA}/250} = 5.5\text{k}\Omega \approx 5.6\Omega$$

To accommodate the higher speeds with clean transitions, I have R2 and used the rule of thumb that it should be about 10x R1. (Is there a better way to calculate that?)

When I do a SPICE DC sweep of Vin, however, the transition isn't very sharp, so I'm inclined to decrease R1 and increase R2, but I'm not sure what values to choose without just guessing.

Questions

1. Are my calculations correct and reasonable?
2. How should I increase the switching speed of the transistor?
3. Is there a better design method? How should I choose the resistor values?

Schematic

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

When I asked "Is there a better design method?" that was not a rhetorical question. I'd be grateful if someone could show a better design method in an answer.

This should be a better (higher speed) driver because you are not forcing the BJT to operate in saturation (it takes vital nanoseconds to come out of saturation): -

If it's still not fast enough you might consider using a faster transistor because the BC817 is unity hFE at 100 MHz (aka \$F_T\$) - go for something like 1 GHz.

Another improvement in speed can be got by not fully turning the transistor off i.e. biasing the base a bit so that the IR LED receives (say) 3 or 4 mA when the logic input is at 0 volts. This is similar to how laser diodes are driven - full light extinction is prevented.

I also see nothing in the IR LED data sheet that tells you how quick it can turn on and off - this would significantly concern me. I see that it has a capacitance of 90 pF and that's OK when turning on the LED but not so great when turning it off.