Charge Pump Output Voltage

Vout = N × Vin − N × Vf

Quick answer

This calculator solves Vout = N × Vin − N × Vf for Output Voltage. With Multiplier Stage Count 0.5, Input Voltage 26.4 V, Diode Forward Voltage 56.4 V, the result is -15 V. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Output Voltage (V)
—

Formula

Vout = N × Vin − N × Vf

Description

A charge pump (voltage multiplier) uses capacitors and diodes to generate a DC output voltage that is a multiple of the input voltage without using inductors. During each half cycle, capacitors are charged in parallel and then reconnected in series, stacking their voltages. Each diode in the chain drops one forward voltage Vf, reducing the ideal output. Charge pumps are used for generating gate drive voltages, EEPROM programming voltages, and in applications where magnetic components are undesirable or where very low noise is required.

Variables

  • Vout — Output voltage under no load (V)
  • N — Number of multiplier stages
  • Vin — Input voltage per stage (V)
  • Vf — Forward voltage drop per diode (V)

Practical Notes

Output impedance increases with N, limiting the available output current. Each stage adds capacitor ESR and diode drop losses. Practical charge pumps are efficient only at light loads (typically < 100 mA). Switched-capacitor voltage converters (like the ICL7660) implement a 1-stage inverter or doubler with regulated output. Use Schottky diodes (Vf = 0.2-0.3V) instead of silicon (Vf = 0.6-0.7V) for better efficiency.

Symbols and units

Symbol Meaning Default unit Accepted units
Vout Output Voltage V pV, nV, µV, mV, V, kV
N Multiplier Stage Count — —
Vin Input Voltage V pV, nV, µV, mV, V, kV
Vf Diode Forward Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Multiplier Stage Count 0.5, Input Voltage 26.4 V, Diode Forward Voltage 56.4 V
  2. 2. The relation: Vout = N × Vin − N × Vf
  3. 3. Substitute: N = 0.5, Vin = 26.4 V, Vf = 56.4 V
  4. 4. Result: Output Voltage = -15 V

Worked examples

Minimum range

Given: Multiplier Stage Count 0.025, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V

Result: Output Voltage = -20.6 mV

Low range

Given: Multiplier Stage Count 0.25, Input Voltage 7.26 V, Diode Forward Voltage 15.5 V

Result: Output Voltage = -2.06 V

Typical

Given: Multiplier Stage Count 0.5, Input Voltage 26.4 V, Diode Forward Voltage 56.4 V

Result: Output Voltage = -15 V

High range

Given: Multiplier Stage Count 0.8, Input Voltage 0.506 kV, Diode Forward Voltage 1.08 kV

Result: Output Voltage = -0.4592 kV

Maximum range

Given: Multiplier Stage Count 8, Input Voltage 5.06 kV, Diode Forward Voltage 10.8 kV

Result: Output Voltage = -45.92 kV

Solving for each variable

Solve for Output Voltage

Multiplier Stage Count 0.025, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V → -20.6 mV

Solve for Multiplier Stage Count

Output Voltage 0.33 V, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V → -0.4005

Solve for Input Voltage

Output Voltage 0.33 V, Multiplier Stage Count 0.025, Diode Forward Voltage 1.55 V → 14.75 V

Solve for Diode Forward Voltage

Output Voltage 0.33 V, Multiplier Stage Count 0.025, Input Voltage 0.726 V → -12.47 V

How Output Voltage changes with Multiplier Stage Count

Multiplier Stage Count (input) Output Voltage (result)
0.05 -1.5 V
0.125 -3.75 V
0.25 -7.5 V
0.375 -11.25 V
0.5 -15 V
0.75 -22.5 V
1 -30 V
2 -60 V
3.5 -105 V
5 -150 V

The same result in other units

Unit Value
mV -15000
V -15
kV -0.015

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Frequently asked questions

How do you calculate Charge Pump Output Voltage?

Use Vout = N × Vin − N × Vf. With Multiplier Stage Count 0.5, Input Voltage 26.4 V, Diode Forward Voltage 56.4 V, Output Voltage works out to -15 V.

What is the formula for Charge Pump Output Voltage?

The formula is Vout = N × Vin − N × Vf. A charge pump (voltage multiplier) uses capacitors and diodes to generate a DC output voltage that is a multiple of the input voltage without using inductors.

How do you find Multiplier Stage Count when you know the other values?

Rearrange for Multiplier Stage Count: with Output Voltage 0.33 V, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V, Multiplier Stage Count is -0.4005.

How do you find Input Voltage when you know the other values?

Rearrange for Input Voltage: with Output Voltage 0.33 V, Multiplier Stage Count 0.025, Diode Forward Voltage 1.55 V, Input Voltage is 14.75 V.

What units does Charge Pump Output Voltage use?

Output Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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