Voltage Multipliers, Inc. - Multiplier Regulation Voltage

DC Output Voltage drops as DC Output Current is increased. Regulation is the drop in DC Output Voltage from the ideal at a specified DC Output Current (assuming AC Input Voltage and AC Input Frequency are constant). A close approximation for series half-wave multipliers can be expressed as follows:

V_reg=[I(N³+(9N²/4)+(N/2)]

12FC

N=number of stages
F=AC input frequency (Hz)
C=capacitance per stage (Farads)
I=DC output current (Amps)

Example:
Calculate the Regulation Voltage of a 6 stage multiplier with 1000pF capacitors, 50kHz Input Frequency (sine wave), 1mA DC output current, 20kV DC output voltage as follows:

V_reg=[1*10^-3(6³+((9*6²/4)+(6/2))]

12(50,000)(1*10^-9)

V_reg=500 volts

This would require increasing the input voltage 167Vp-p to maintain 20kV DC output voltage at 1mA.

An equivalent parallel multiplier would require each capacitor stage to equal the total series capacitance of the AC capacitor bank. In the above case, the 3 capacitors in the AC bank would equal 1000pF/3 or 333pF. The parallel equivalent would require 333pF capacitors in each stage. However, each successive stage would require a higher voltage capacitor.

Note: Regulation voltage is not to be confused with power losses dissipated in a multiplier. Power losses are primarily Vf losses in the diodes and rarely result in excessive multiplier temperatures.