From Gemini:
The following guidelines break down how to tune and adjust each component:
1. The Core & Windings (The Transformer)
* The 1:1 Baseline: For standard builds, use a bifilar winding (twisting two wires together and wrapping them simultaneously). Aim for 10 to 15 turns around a small ferrite toroid core.
* More Turns vs. Fewer Turns:
- Adding more loops increases inductance and reduces the operating frequency, which typically improves efficiency and lowers battery drain.
- If you need a significantly higher voltage boost (e.g., driving an array of LEDs), move to an asymmetric ratio like 1:5 or 1:10 (primary to feedback).
* Wire Thickness: Use thicker magnet wire (e.g., 24–26 AWG) for the primary winding to reduce DC resistance and limit current loss.
* Salvage Tip: Excellent small toroidal cores can be harvested from dead compact fluorescent lamp (CFL) bulbs or old computer power supplies.
2. The Resistor (R₁)
* The 1kΩ Standard: A 1kΩ resistor is the universal starting point for a 1.5V input.
* Increasing for Efficiency: If your transistor is running hot or you want the battery to last as long as possible, increase the resistor up to 2.2kΩ or 6.8kΩ. Higher resistance drops the input current draw, stretching out battery life at the cost of a slightly dimmer LED.
* Lowering for Low Voltages: If you want the circuit to keep stealing energy down to ultra-low thresholds (below 0.5V), you can drop the resistor below 1kΩ (even down to a few ohms), but monitor the transistor so it doesn't overheat.
3. Transistor Selection
* Key Specs: Look for general-purpose NPN BJTs with high DC current gain (h_FE) and a low collector-emitter saturation voltage (V_CE_sat).
* Top Choices: The 2N4401 and BC337 often outperform the standard 2N3904 or 2N2222 in efficiency because they feature a lower saturation voltage, letting them "pump" more cleanly at ultra-low battery levels.
* The Temperature Rule: The transistor should always remain cool to the touch. If it exceeds roughly 60°C, increase your base resistor to safely throttle the current.
4. The LED Load
* Wiring Configurations: Always connect multiple LEDs in series rather than parallel. Parallel setups suffer from current hogging (where one LED steals all the power and burns out early) unless you add individual balancing resistors.
* Voltage Rule: For every 1.5V battery added to the input, you can reliably string another 3V white/blue LED in series on the output.
Sorry I can't help you with calculations here.
I can give you my joule thief circuit that I've used to build dozens of them over the years.
It's a really good one. Will light up brightly with near-dead cells.
I wind the transformers on small (1/8" or so) ferrite rods using 32 gauge magnet wire.

(I based this on designs I found on Colin Mitchell's "Talking Electronics" site; see
this page for Joule Thief specifics.)
YIKES! I have never heard of "Joule Thief" but I can tell you that the original schematic design will not work with any old ferrite core for the "transformer."
The circuit is sort of a self oscillating flyback. For that, you need to have energy storage in the core...that is done with either a discrete or distributed gap in the core. A gap in an inductor core is analagous to the gap between capacitor plates....it is where the energy is stored!!
So for the most part a ferrite core will need some sort of calculated gap for energy storage and the correct inductance. Core materials such as powdered iron, or Permalloy (Molyperm) or Kool Mu have a distributed gap. Powdered iron is the cheapest but least efficient (more power loss) but might be worth experimenting with. For easy work in the lab, I really like ferrites with round center legs (such as PQ shapes) and PQ2020 might be good unless you find and want something smaller. Grinding a gap in the PQ core assembly requires the right equipment, but a spacer gap made with polyester film often works well enough for me.
YIKES! I have never heard of "Joule Thief" but I can tell you that the original schematic design will not work with any old ferrite core for the "transformer."
Well, what can I tell you?
Not only do all mine work, they all work very well, with the kind of transformer you insist won't work.
Couple pics of one of my homemade transformers:


I used to break up salvaged transformers with ferrite cores and use the pieces for my cores.
The circuit is sort of a self oscillating flyback.
Close; technically it's a blocking oscillator.
Here's a closeup of one of my units:

This one is in a loupe. The JT circuit drives 4 high-brightness LEDs in series/parallel. Very bright.
YIKES! I have never heard of "Joule Thief" but I can tell you that the original schematic design will not work with any old ferrite core for the "transformer."
The circuit is sort of a self oscillating flyback. For that, you need to have energy storage in the core...that is done with either a discrete or distributed gap in the core. A gap in an inductor core is analagous to the gap between capacitor plates....it is where the energy is stored!!
So for the most part a ferrite core will need some sort of calculated gap for energy storage and the correct inductance.
Whilst a closed loop ferrite like an E-core or toroidal core requires a gap or distributed gap, a solenoid ferrite core naturally has a massive air gap from one end of the solenoid to the other.
A joule thief does not require a gapped transformer because it operates as a resonant blocking oscillator that naturally prevents core saturation.