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My first Joule Theif - Questions Galore :)

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Two transistors invert the signal twice which makes the input the same phase as the output so they can oscillate. The single transistor with a tapped inductor has its input the same phase as its output due to the phase reversal in the tapped inductor.
 
I would guess the efficiency is only about 60%. Nearly half the battery's power is wasted.
Probably even less than 60% because the transistors CE voltage drop is high relative to the low input voltage.
I tried this circuit using a 3V supply and 5 white LEDs in series. I put a schotty diode and cap on the output to avoid problems with peak LED current. This also made it easier to measure the LED current accurately. Here's what I measured:
Input = 3.18V @ 135ma
Output = 15.6V @ 15.2ma
Efficiency = 55%
I wish I had taken a picture of the transistor waveforms, but from memory I seem to recall the transistor's CE saturation voltage was around 0.4V
 
Just because it's simple it doesn't mean it can't be efficient.

My switching regulator circuit had the same three simple parts for the oscillator. The only difference was crude voltage regulation was achieved by adding a transistor to ground the base of the switching regulator when the output exceeded a certain voltage set by a zenner and potential divider.

The problem is the choice of core, ferrite suppresion beads probably won't be very efficeint because they have a very low Q. Don't fordet they're actually designed to dissipate high frequency signals not store energy.
 
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