The Cockcroft-Walton voltage multiplier is a popular method of generating high DC voltage using diodes and capacitors. It is used in particle accelerator, older CRT TV, electron microscope, x-ray, photocopier machines, mosquito bats zappers etc. Here the Cockcroft-Walton voltage multiplier is explained using animation of the Cockcroft-Walton voltage multiplier circuit. Proteus professional circuit animation software is used which you can download here: Free Electronics Download Hub.
This circuit is a Cockcroft-Walton Voltage Quadrupler (a 4-stage diode-capacitor multiplier). It converts an AC input voltage ($V_{in}$) into a high-voltage DC output using alternating charge transfer across the capacitors.
Assuming the AC input source $V_1$ has a peak voltage of $V_m$ (where $V_m = \sqrt{2} \cdot V_{rms}$):
Circuit Operation
Negative Half-Cycle 1 (Initial Stage):
When the top side of $V_1$ goes negative and the bottom side goes positive, diode $D_1$ becomes forward-biased (conducts). Capacitor $C_1$ charges through $R_1$ and $D_1$ up to the peak input voltage $V_m$.
$$V_{C1} = V_m$$Positive Half-Cycle 1:
When the input reverses, $D_1$ turns off and $D_2$ becomes forward-biased. The input voltage $V_m$ adds in series with the voltage already stored across $C_1$ ($V_m$). This combined voltage ($2V_m$) charges $C_2$ through $D_2$.
$$V_{C2} = V_{C1} + V_m = 2V_m$$Negative Half-Cycle 2:
$D_2$ turns off and $D_3$ turns on. The charge from $C_2$ transfers to $C_3$, charging $C_3$ up to a peak differential voltage of $2V_m$.
$$V_{C3} = 2V_m$$Positive Half-Cycle 2 (Final Steady State):
$D_3$ turns off and $D_4$ turns on. The combined potential across the upper capacitors transfers charge to $C_4$, charging $C_4$ up to $2V_m$.
$$V_{C4} = 2V_m$$
Voltage Calculations
Assuming ideal diodes ($V_D \approx 0\text{V}$) and an input peak voltage of $V_m$:
Initial Output Voltage (After 1st full cycle):
The first stage doubling occurs across $C_2$.
$$V_{out, initial} = V_{C2} = 2V_m$$Final Steady-State DC Output Voltage (Across $C_2 + C_4$):
The total quadrupled output voltage is tapped across the series combination of the lower capacitors ($C_2$ and $C_4$).
$$V_{out, final} = V_{C2} + V_{C4} = 2V_m + 2V_m = 4V_m$$
Example Numerical Calculation:
If $V_1 = 100\text{V}_{rms}$ (or $V_c = 100\text{V}$ peak input amplitude):
Peak Voltage ($V_m$): $100\text{V}$
Initial Voltage ($V_{C2}$): $2 \times 100\text{V} = 200\text{V}$
Final Quadrupled Voltage ($V_{total}$): $4 \times 100\text{V} = 400\text{V}$
The following video shows animation of Cockcroft-Walton Voltage Multiplier Circuit.
