ac - What is the output voltage of this 555 timer high voltage circuit?

I'm trying to calculate the theoritical output voltage of the following 555 timer high voltage circuit.
It claims to output up to 20kV, however results I get give only 12kV.

(source)

---

Here is how I did it:

According wikipedia, frequency in 'astable mode' is given by :

For this circuit :

\$f = \frac{1}{0,69 \cdot 0,00000001 F \cdot 33000\Omega} = 4391 Hz\$

I calculated the output of the transformer to be 125 times (1000 / 8) higher than input. Since 12v is given as input, output should be 1500v (not sure about this)

Then I draw the circuit in circuit lab:

^{simulate this circuit – Schematic created using CircuitLab}

And I ran a time domain simulation (Stop Time = 30m, Time Step = 20u)

The output stabilizes at 12kV:

What is wrong? Did I miss something or are the results given by this circuit a little too optimistic?

Answer

Two notes:

• 
  
  

  the impedance transformation is the square of its turns ratio, the voltage transformation is the turns ratio itself. Hence your 1k/8r transformer will have a voltage transformation of sqrt(125) = ~ 11. But ...

  
  


• 
  

  the voltage transformation calculated this way applies to a sine wave, not to the on-off switching done in this case. Theoretically there is no limit to the voltage you can generate with this method, even on the primary (8r) side. For that reason circuits like this often use a zener diode at the primary side, to prevent damage to the transistor.