Buck-Boost converters and the details of the inductor (field collapse)

[RJSV]

   I've been bugged by questions about the Buck-Boost circuit that is included in the commonly seen yard or 'garden' light.
Knowing the voltage is boosted by the collapse of the magnetic field wasn't enough ...it seems to be pulses coming in, as approx. 10 usec. out of every 50 (microseconds, or about a 20 khz repetition rate.)

   Of course I should dig out the scope, but meanwhile I'm curious about the numbers, like what is the peak voltage at the critical point in the circuit, which is what is commutated to ground, or negative common, for that 10 usec. pulse.
   Voltage would start at zero, as Buck-Boost switch opens, but then what ?  What peak voltage would end up applied to the LED, needing some 2.8 volts to illuminate.

   The inductor is usually blue colored, about size of 1/2 watt resistor.

[RJSV]

   Schematic shows, (I assumed 4 milli-amps) what might be some 'steady-state' or d.c. value , however, it's actually a pulse, 10 usec. connecting the coil, to ground and charging up the field
Then, switch opening point is where things start happening but I'm not sure what form of voltage rise starts up, and what peak can be expected (for a given inductance).

[soldar]

I am not sure what you are asking. The inductance stores energy and then dumps it into the LED. If the LED is 2.8 V then that is what you will see.