I'm want to create a LED pulse with a simple circuit.
I choose to use a NE555. I found a lot of schematics on the Internet, but often without any explanation, and I don't like to create a cricuit without understanding it.

The NE555 is a very cheap, popular and useful precision timing device that can act as either a simple timer to generate single pulses or long time delays or as an oscillator.
It works at 9V.

Most of the time, to blink a LED, the NE555 is operated as an astable multivibrator with two resistors, one capacitor and one NPN. The timing is adjusted by changing the value of the resistors and the capacitor.

As I want to pulse a LED, I found on Instrucables another circuit, quite simple but without any explanation.

I was expecting to see the load driven by the NPN on the collector side, but if the load is between V_CC and the NPN collector, the NPN will be in saturation mode, and the LED will not pusle.

This circuit is quite different than any other schematics that I found, as the pin 2 is directly linked to the pin 6.
Moreover, the output is followed by a RC filter.

NE555 highlights

To understand the behavior of this circuit, it's interesting to look at the simplified schematics of the NE555.

And look at the following pins (with CONT at 2/3 V_CC):

THRES / pin 2 (input): Start of timing input. TRIG < 1/2 CONT sets output high and discharge open
TRIG / pin 6 (input): End of timing input. THRES > CONT sets output low and discharge low
OUT / pin 3 (output): High current timer output signal

RC Filter

And a quick reminder on RC filters.

Series circuit (as used in the LED pulse circuit):

Capacitor voltage (Vc) when Vin is set:

With

τ = RC

NPN in active mode

On the following schematics, we have:

U_R + U_C = V_CC
i_R = i_C + i_b

When U_C increases, i_C decreases, and when the capacitor is fully charged, i_B is almost equal to i_R.

To be able to manage the current flow through the LED, the NPN in used in active mode.

That's why the LED and the resistor are placed after the emitter, and the collector is directly linked to V_CC.

Therefore:

V_C > V_B > V_E

In active mode:

i_C = βi_B
i_C = αi_E
α = β / (β + 1)
and β is at least 35 for the 2N2222

I want around 16mA in my LED at peak.

i_C = βi_B with β = 35
i_B = 16 * 10^-3 / 35 ≈ 0.5mA
So R = V_R / i_R
R = (2/3 * V_CC) / i_R = (2/3 * 9) / (0.5 * 10^-3) = 12kΩ

With τ = RC, and I want τ = 1s
So C = 1 / R = 83µF

After the maths, I played with a real circuit and decided to use

R = 10kΩ
C = 100µF

Combining the three circuits

So:

When the pin 2 is below 1/3 Vcc, pin 3 will be set at HIGH.
The capacitor will charge at 2/3 Vcc in approximately τ seconds
The pin 6 will be above 2/3 Vcc and set pin 3 at LOW
The capacitor voltage will slowly go aroung 1/3 Vcc and the loop begins !

Remark: Output will never be higher than 2/3 Vcc, and lower than 1/3 Vcc (except at the power-up). The resistor and the capacitor will define the time needed to goes up to 2/3 Vcc and down to 1/3 Vcc.

The current flowing to the base is limited by the resistor.
The current flowing into the LED is limited by another resistor.

I tried to probe the results with my cheap DSO138.

Please note that my DSO doesn't seems to be well calibrated on ground

Output (pin 3) voltage

We can see the LOW / HIGH change.
The output in LOW level (0V) is shorter than in HIGH level (9V) as it's quicker to discharge the capacitor from 2/3 Vcc to 1 / 3 Vcc than charge it.

Capacitor voltage

We can see that the capacitor charges and discharges between 1/3 Vcc (3V) to 2/3 Vcc (6V).

I don't know if we have to take into account V_BE which should be around 0.7V when NPN is in saturation mode.

Limit the current through the resistor

Now than the LED is ready to get powered, it's time to compute the second resistor value:

V_LED = 3.2V
V_R = 9 - 3.2 = 5.8V
R = V_R / i_R = 5.8 / (16 * 10^-3) ≈ 360Ω

As I don't have any 360Ω resistor, I will use a 330Ω resistor.

Final schematics

Result in video

Next step: I want to include this montage into a Tardis, but only power up the circuit when there is some lights in the room (the Tardis will be put in a bathroom whithout any window).