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?

• I don't think you missed anything, a Greinacher voltage double cell is not particularly known for its efficiency. That is the same reason I was rounding down all figures in our chat conversation – jippie Apr 28 '13 at 14:56
• You used 1N4148 diodes in your simulation which are generic purpose/low voltage diodes. They won't survive 1500V. Neither will a 1N4007, but it is closer to spec. – jippie Apr 28 '13 at 14:59

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.

• Thanks for your answer. Is there a way to calculate the theoretical output voltage of a transformer "excited" by a square wave ? (for a given input voltage and frequency, knowing primary and secondary resistance of transformer) – tigrou May 2 '13 at 12:59
• Yes, infinite. It will operate more or less as a switched-mode voltage converter. – Wouter van Ooijen May 3 '13 at 17:23

That isn't the correct formula for frequency for this circuit configuration.

Since you have the timing resistor connected to the output (pin 3) rather than Vcc, the correct formula would be:

$f = \frac{1}{ln(2) \cdot C \cdot 2 \cdot R} = \frac{1}{0.693 \cdot 0.01 {\mu}F \cdot 2 \cdot 33k\Omega} = 2186 Hz$