It seems that many "Joule Thief" circuits depend on a clunky (bulky and heavy) toroid or "donut" that has to be carefully wound with copper wire. But now there are several very small 4 legged ICs available that do the job using only a simple inductor, single cell battery and a LED. In effect, the 4 legged IC replaces the clunky toroid.
I came across these ICs when I disassembled some solar powered yard lights. I looked for a toroid but only found a four legged IC and a part that looked like a resistor but actually was a very physically small inductor (coil). Both of these parts along with wire attachment points were soldered to a small circuit board. I was able to remove parts, attach wires to them and assemble them on a Radio Shack type of "Breadboard" to test and better understand this circuit.
But then I created a very crude and minimal circuit to better understand some of the key parts of a "Joule Thief."
I used a Yellow LED that requires 2 volts (or a little more). My 1.5 volt "Rocket Battery" has been worn down to 1.4 volts. As a result, the LED is off and is not even close to conducting any current. Points A and B on the inductor coil L are at pretty much the same voltage, 1.4 volts compared to "ground" or the minus of the battery.
When the switch is pushed and and held ON, briefly, current flows through the coil and creates a magnetic field around the coil. Points A and B are still positive with point A being slightly more positive than point B.
But when the switch is released and turned OFF, the magnetic field suddenly collapses and creates a 1.4 volt voltage with a reverse polarity. This means that point B is now 1.4 volts higher (more positive) than point A. It is as if the coil has become like a temporary battery connected in series with the actual battery, presenting 2.8 volts to the LED. The LED reacts to this by flashing on for a very short moment. Pushing the switch again repeats this cycle. If I could push the switch rapidly enough, the LED would appear to be solidly ON.
The pictures that follow will reveal how simple it would be to recreate this. The coil or inductor is 12 feet of 24 gage wire wrapped (200 turns) around a 1/4 inch diameter soft iron nail.
A crude "Joule Thief" circuit was created and hooked up as shown but no current is flowing.
Now the switch is held down and current is flowing through the coil. The switch only has to be turned on momentarily to create a magnetic field. Also, the switch is shorting out the LED.
But when the switch is released and turned off, the LED lights very briefly.
Again, if I could only turn on and off the switch in a very rapid manner, I would have a working "Joule Thief" like circuit.
And it turns out that the IC I mentioned at the beginning of all of this does just that. This IC turns the LED on and off somewhere between 50,000 and over 100,000 times a second, making the LED appear solidly ON.
With the QX5252F IC connected as shown, Pin 4 on the IC very rapidly connects and disconnects to Pin 3, the negative on the battery, causing the LED to repeatedly flash similar to the crude "Joule Thief" already mentioned. But here the LED flashes so rapidly that the LED appears completely ON, more so than some florescent lights that have a flicker to them.
The picture here reveals the QX5252F IC at work, keeping the LED flashing so rapidly that it appears to be solidly ON.
The bulky, handwound coil-on-a-nail can be replaced with the tiny inductor shown between the IC and an LED.
Although the IC "Joule Thief" seems to work with my crude, handwound coil on a nail, I actually use a very small 330 (orange-orange-brown) inductor that has the size and appearance of a small 1/2 watt resistor.
So you can see that all of the parts of the circuit using the QX5252F IC would fit on a small circuit board with the whole apparatus taking up much less room and having much less weight than a circuit using a Toroid with two copper windings on it.
Although the toroid or "iron donut" has served us well and deserves much respect, the tiny inductor along with the QX5252F IC may very well serve as an advancement to some of the readers here.
Note: If the battery is replaced by a rechargeable battery, a solar cell can be connected to "Unused" Pin 1 and Pin 3 on the IC. During the day, the IC will turn off the LED while also trying to charge the battery, depending on sunlight. During the night, the IC will turn on the LED. But this is another story since this operation takes us away from our "Joule Thief" discussion...