It's a blocking oscillator.
Related ideas:
http://seventransistorlabs.com/Images/LED_Light2.pngThis uses a coupling transformer to drive the switching transistor at constant hFE (15t/3t = 5 hFE); it acts like an SCR. The on-pulse is terminated by core saturation, which turns off the transistor quickly. The remainder of the circuit is an error amplifier (controlling LED current) and variable astable, regulating average current by varying frequency (off time, and therefore duty cycle).
http://seventransistorlabs.com/tmoranwms/Circuits_2010/RegBO.pngThis is a fairly standard blocking oscillator, with feedback winding, bias current, bypass capacitor, etc. The prototypical circuit is:
![](http://seventransistorlabs.com/tmoranwms/Circuits_2010/Blocking_Oscillator.png)
Add bias control or current detection to control frequency and/or pulse width, and therefore power; and add diodes, secondaries, etc. for power output. (Running it "open circuit" as shown will generate a huge voltage spike, which may be tall enough to damage the transistor.)
This example uses an inverting feedback method, so that, as the opto is turned on more strongly, more power is delivered (notice the negative clamping diode will push more positive base current when it's loaded). This requires an additional inverter in the error amplifier circuit (on the right), and saves bias current (the idle performance of this circuit is very good -- one pulse every so often, just enough to keep it going; minimum bias current being defined by the 1M bias resistor), but has poor startup performance (too low of a load resistance and it won't start up at all, simply ticking away quietly).
With no emitter resistor, and enough turns on the transformer to avoid saturation, switch-off is hFE limited: the base coupling/bypass capacitor is eventually charged by the base current, so that during the pulse, base current is falling over time, while collector current is rising. Eventually, the transistor comes out of saturation, collector voltage shoots up, and base voltage is quickly reversed (this type of circuit can only exhibit hard switching, i.e., collector current drops after collector voltage rises).
Circuits like this have been used over the years in televisions (injection-locked sweep generators, since the introduction of analog TV in the 30s, until analog finally went away, relatively recently), power supplies (e.g., Apple II, most VCRs/DVD players), and occasional internet curiosities ("Joule Thief", usually repeating the same poorly designed circuit).
Your LED light appears to be another example. Its attributes will include base current limited switching (emitter resistors also help to keep this consistent, but usually a transistor is added there to speed up turn-off at a defined current threshold), constant peak current behavior, modest switching performance (better than a resistor, sure, but not great, as this circuit style is concerned), relatively poor line regulation (since switch current is limited, but not LED current), and poor thermal drift (because hFE varies with temperature).
Switching frequency isn't easy to calculate from principles (indeed, the circuit can exhibit burst, quasi-periodic and chaotic behaviors that are very difficult to understand), but if we assume they know what they're doing (making a clean, periodic, full wave blocking oscillator), it will be defined more or less jointly by the base RC time constant, the inductor value and supply voltage, and transistor hFE.
Tim