How to calculate the current in a PWM LED driver circuit

[nathanpc]

I've been fascinated by the simplicity of the driver circuit based in the YX8018 in the prominent solar garden lights, they were able to simplify the circuit a lot in a simple boost topology by just running at fixed frequency and using the LED as the output rectifier. I was interested in building my own circuit using a 555 timer driving a small transistor, just to learn more about the topology, but in my research I was not able to find a equation, or at least a simpler explanation between the frequency, input voltage, and inductor value to be able to calculate the output current to the LED. Could someone help me understand how I can calculate the output current given these parameters?

The closer I got to an answer was by reading the SLVA372C App Note, in the equations section, the inductor ripple current:

Il = (Vin * D) / (f * L)

Plugging the values I tested on my solar light's circuit:

Il = (1.5 * 0.5) / (200000 * 330 * 10^-6)
Il = 0.0107

But when I measured the current to the LED using my DMM I got 6.3mA.

[TerminalJack505]

Those equations look similar to ones I used in this post.

I  don't think they will work in your case, however, since you need a constant output current and the equations are for a constant output voltage.

Since you are basically operating the converter as an open loop (that is, no feedback) you should probably just pick some particular fixed parameters (switching frequency, inductor size, etc.) and then tweak the duty cycle until you get the desired result.  This is something that you would need to do anyway since there will be variations in the parameters and there's no control loop to compensate for the variations.  This likely won't satisfy your intellectual curiosity but will help you get the project done.

For another example of using the 555 to drive LEDs with a constant current, see the attached.  This circuit has the advantage of having a control loop.  It could be easily modified to allow for dimming as well.