Joule thief : number of turns around the ferrite core

[Corvinus96]

Hi everyone,

I have to build a simple Joule thief circuit for school. Here it is :(http://upload.wikimedia.org/wikipedia/commons/8/83/Joule_thief.png). The resistance of the resistor is fixed to 1 kOhms, the voltage across the "dead battery" is about 1.5V, the transistor needs about 0.7V to open and finally, the led needs 2.0V to light up. So I have to figure out (not experimentaly) the number of turns around each inductor so that the led has enough voltage across it to light up at best... and that's where I'm stuck with calculations. With all the formulas that I know : Lenz's law, Ohm's law, etc... I feel like the problem is quite hard to solve (but maybe I can get a good approximation). Does anyone have an idea on how to solve my problem?

Thanks in advance,

 

[berkeman]

Hi everyone,

I have to build a simple Joule thief circuit for school. Here it is :(http://upload.wikimedia.org/wikipedia/commons/8/83/Joule_thief.png). The resistance of the resistor is fixed to 1 kOhms, the voltage across the "dead battery" is about 1.5V, the transistor needs about 0.7V to open and finally, the led needs 2.0V to light up. So I have to figure out (not experimentaly) the number of turns around each inductor so that the led has enough voltage across it to light up at best... and that's where I'm stuck with calculations. With all the formulas that I know : Lenz's law, Ohm's law, etc... I feel like the problem is quite hard to solve (but maybe I can get a good approximation). Does anyone have an idea on how to solve my problem?

Thanks in advance,

Welcome to the PF.

The circuit does not look like it will work without some modifications. Where did you get it? What is the overall goal of this school project?

 

[Corvinus96]

I got it from wikipedia (the circuit of the school is exactly the same), I think you get more info on how the circuit works there : http://en.wikipedia.org/wiki/Joule_thief . By what is the overall goal of the school project, do you mean what is the purpose of the circuit? If so, the circuit can generate "more voltage" (in fact, in convert DC to AC with higher amplitude) to light up a led that is connected to a "dead battery" that is, a battery that does not have enough voltage to light up the led if you connect it directly to the led.

 

[Rive]

... I have to figure out (not experimentaly) the number of turns around each inductor...

As I understand it it does not really matters. The principle of it's operation based on the saturation of the ferrite, and then the discharge of the stored energy through the LED - the number of turns (within a wide range) would determine only the operating frequency.

 

[Corvinus96]

Sounds right! But then how do you determine the minimum number of turns around the coil for the LED to light up :/ ?

 

[NascentOxygen]

Search on google, see how others have done it. You will probably hear the core squeal when it's operating.

 

[Corvinus96]

http://upload.wikimedia.org/wikipedia/commons/8/83/Joule_thief.png

Ok so today they talked about what we had to do to figure out the solution (more or less). They want us to mathematically solve it and then check the results experimentaly. So they said that they want us to figure out a relation between the frequency of the led and the number of turns around the coil (the inductance and the number of turns in each inductor is supposed to be equal)...and in order to do that, we have to solve for the voltage V1(t) (left) and V2(t) (right) across each inductor as a function of time (in both cases when the circuit is "charging" and "discharging"). Then finding the roots of these functions will give the time it took to charge and discharge and so 1 over that is the frequency. Okay... so I managed to solve for the voltage across the right-hand inductor when the circuit is discharging. It was easy because the current does not pass in the transistor at that moment. But I'm stuck with the "charging part". Here is my equation for V1 for example : V1(t) = L*∂(I1)/∂t - L*∂(I2)/∂t where I1 is the current that goes is the left-hand inductor and I2 the one in the right-hand inductor and L the inductance of the coils. The problem is that I can't solve this as a differential equation because I do not know how to express I2! I1 is the voltage across the resistor divided by its resistance but there is no resistor in the other wire! Another problem is that because the current does not go in the led, it seems like the voltage V2(t) equals the battery voltage and the V1(t) = -V2(t) does not work :/ .Anyone have an idea?