Buck Output Ripple (with ESR)

ΔVout = ΔIL · (ESR + 1/(8·fs·Cout))

Quick answer

This calculator solves ΔVout = ΔIL × (ESR + 1/(8 × fs × Cout)) for Output Ripple. With Ripple Current 20 mA, Capacitor ESR 50 mΩ, Switching Frequency 100 kHz, Output Capacitance 100 µF, the result is 1.25 mV. It solves in 5 directions, so you can enter the values you have and get the one you need.

Calculator

Output Ripple (mV)
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Formula

ΔVout = ΔIL × (ESR + 1/(8 × fs × Cout))

Description

The output ripple of a buck converter has two parts: a resistive term from the ripple current flowing through the capacitor’s equivalent series resistance (ESR), and a capacitive term from the charge it stores and releases. At typical frequencies the ESR term usually dominates, which is why low-ESR capacitors matter more than raw capacitance for ripple.

Variables

  • ΔVout — Output ripple voltage (V)
  • ΔIL — Inductor ripple current (A)
  • ESR — Capacitor equivalent series resistance (Ω)
  • fs — Switching frequency (Hz)
  • Cout — Output capacitance (F)

Practical Notes

For ceramic capacitors the ESR term is tiny and the 1/(8·fs·Cout) capacitive term dominates; for electrolytics the ESR term dominates. Add the two in worst case, or RSS them for a typical estimate.

Symbols and units

Symbol Meaning Default unit Accepted units
dVout Output Ripple mV pV, nV, µV, mV, V, kV
dIL Ripple Current mA pA, nA, µA, mA, A, kA
ESR Capacitor ESR mΩ mΩ, Ω, kΩ, MΩ
fs Switching Frequency kHz Hz, kHz, MHz, GHz
Cout Output Capacitance µF pF, nF, µF, mF, F

Step by step

  1. 1. What you know: Ripple Current 20 mA, Capacitor ESR 50 mΩ, Switching Frequency 100 kHz, Output Capacitance 100 µF
  2. 2. The relation: ΔVout = ΔIL × (ESR + 1/(8 × fs × Cout))
  3. 3. Substitute: dIL = 20 mA, ESR = 50 mΩ, fs = 100 kHz, Cout = 100 µF
  4. 4. Result: Output Ripple = 1.25 mV

Related quantities from the same inputs

  • P = V × I = 25 µW

Worked examples

Minimum range

Given: Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF

Result: Output Ripple = 1.25 V

Low range

Given: Ripple Current 1 mA, Capacitor ESR 1 mΩ, Switching Frequency 1 kHz, Output Capacitance 1 µF

Result: Output Ripple = 125 mV

Typical

Given: Ripple Current 20 mA, Capacitor ESR 50 mΩ, Switching Frequency 100 kHz, Output Capacitance 100 µF

Result: Output Ripple = 1.25 mV

High range

Given: Ripple Current 0.5 A, Capacitor ESR 0.5 Ω, Switching Frequency 0.5 MHz, Output Capacitance 1 mF

Result: Output Ripple = 0.2501 V

Maximum range

Given: Ripple Current 5 A, Capacitor ESR 5 Ω, Switching Frequency 5 MHz, Output Capacitance 10 mF

Result: Output Ripple = 25 V

Solving for each variable

Solve for Output Ripple

Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF → 1.25 V

Solve for Ripple Current

Output Ripple 10 mV, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF → 0.8 µA

Solve for Capacitor ESR

Output Ripple 10 V, Ripple Current 100 mA, Switching Frequency 100 kHz, Output Capacitance 100 µF → 99.99 Ω

Solve for Output Capacitance

Output Ripple 10 mV, Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz → 12.5 µF

Solve for Switching Frequency

Output Ripple 10 mV, Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Output Capacitance 100 nF → 12.5 kHz

How Output Ripple changes with Ripple Current

Ripple Current (input) Output Ripple (result)
2 mA 125 µV
5 mA 0.3125 mV
10 mA 0.625 mV
15 mA 0.9375 mV
20 mA 1.25 mV
30 mA 1.875 mV
40 mA 2.5 mV
80 mA 5 mV
140 mA 8.75 mV
0.2 A 12.5 mV

The same result in other units

Unit Value
nV 1250000
µV 1250
mV 1.25
V 0.00125

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Frequently asked questions

How do you calculate Buck Output Ripple (with ESR)?

Use ΔVout = ΔIL × (ESR + 1/(8 × fs × Cout)). With Ripple Current 20 mA, Capacitor ESR 50 mΩ, Switching Frequency 100 kHz, Output Capacitance 100 µF, Output Ripple works out to 1.25 mV.

How do you calculate buck converter output ripple esr capacitance?

Rearrange for Output Ripple: with Ripple Current 1 mA, Capacitor ESR 1 mΩ, Switching Frequency 1 kHz, Output Capacitance 1 µF, Output Ripple is 125 mV.

What is the formula for Buck Output Ripple (with ESR)?

The formula is ΔVout = ΔIL × (ESR + 1/(8 × fs × Cout)). The output ripple of a buck converter has two parts: a resistive term from the ripple current flowing through the capacitor’s equivalent series resistance (ESR), and a capacitive term from the charge it stores and releases.

How do you find Ripple Current when you know the other values?

Rearrange for Ripple Current: with Output Ripple 10 mV, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF, Ripple Current is 0.8 µA.

How do you find Capacitor ESR when you know the other values?

Rearrange for Capacitor ESR: with Output Ripple 10 V, Ripple Current 100 mA, Switching Frequency 100 kHz, Output Capacitance 100 µF, Capacitor ESR is 99.99 Ω.

What units does Buck Output Ripple (with ESR) use?

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

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