Decoupling Capacitor Impedance

Z = 1 / (2πfC)

Quick answer

This calculator solves Z = 1 / (2πfC) for Impedance. With Target Frequency 10 MHz, Capacitance 100 nF, the result is 0.1592 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Impedance (Ω)
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Formula

Z = 1 / (2πfC)

Description

In power distribution network design, decoupling capacitors must present low impedance at the frequencies where the IC draws transient current. This is the same capacitive reactance formula but applied in the PDN context to determine whether a capacitor provides adequate bypassing at the target frequency. The PDN impedance target is typically derived from the allowable voltage ripple divided by the maximum transient current. Multiple capacitor values are used in parallel to cover different frequency ranges.

Variables

  • Z — Capacitor impedance at target frequency (Ω)
  • f — Target frequency (Hz)
  • C — Capacitance (F)

Practical Notes

Real capacitors have ESR and ESL that limit their effectiveness at high frequencies. A 100nF ceramic capacitor is effective up to about 100 MHz, above which its parasitic inductance dominates. Use multiple capacitor values (10µF, 1µF, 100nF, 10nF) in parallel to maintain low impedance across a wide bandwidth. Place capacitors as close as possible to the IC power pins.

Symbols and units

Symbol Meaning Default unit Accepted units
Z Impedance Ω mΩ, Ω, kΩ, MΩ
f Target Frequency MHz Hz, kHz, MHz, GHz
C Capacitance nF pF, nF, µF, mF, F

Step by step

  1. 1. What you know: Target Frequency 10 MHz, Capacitance 100 nF
  2. 2. The relation: Z = 1 / (2πfC)
  3. 3. Substitute: f = 10 MHz, C = 100 nF
  4. 4. Result: Impedance = 0.1592 Ω

Nearest standard component values

Series Nearest value Error
E12 150 mΩ 5.8%
E24 0.16 Ω 0.53%

Worked examples

Minimum range

Given: Target Frequency 100 kHz, Capacitance 100 pF

Result: Impedance = 15.92 kΩ

Low range

Given: Target Frequency 1 MHz, Capacitance 1 nF

Result: Impedance = 0.1592 kΩ

Typical

Given: Target Frequency 10 MHz, Capacitance 100 nF

Result: Impedance = 0.1592 Ω

High range

Given: Target Frequency 100 MHz, Capacitance 1 µF

Result: Impedance = 1.592 mΩ

Maximum range

Given: Target Frequency 1 GHz, Capacitance 10 µF

Result: Impedance = 0.01592 mΩ

Solving for each variable

Solve for Impedance

Target Frequency 100 kHz, Capacitance 100 pF → 15.92 kΩ

Solve for Target Frequency

Impedance 1 Ω, Capacitance 100 pF → 1.592 GHz

Solve for Capacitance

Impedance 1 Ω, Target Frequency 100 kHz → 1.592 µF

How Impedance changes with Target Frequency

Target Frequency (input) Impedance (result)
1 MHz 1.592 Ω
2.5 MHz 0.6366 Ω
5 MHz 0.3183 Ω
7.5 MHz 0.2122 Ω
10 MHz 0.1592 Ω
15 MHz 106.1 mΩ
20 MHz 79.58 mΩ
40 MHz 39.79 mΩ
70 MHz 22.74 mΩ
100 MHz 15.92 mΩ

The same result in other units

Unit Value
mΩ 159.2
Ω 0.1592
kΩ 0.0001592

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Frequently asked questions

How do you calculate Decoupling Capacitor Impedance?

Use Z = 1 / (2πfC). With Target Frequency 10 MHz, Capacitance 100 nF, Impedance works out to 0.1592 Ω.

What is the formula for Decoupling Capacitor Impedance?

The formula is Z = 1 / (2πfC). In power distribution network design, decoupling capacitors must present low impedance at the frequencies where the IC draws transient current.

How do you find Target Frequency when you know the other values?

Rearrange for Target Frequency: with Impedance 1 Ω, Capacitance 100 pF, Target Frequency is 1.592 GHz.

How do you find Capacitance when you know the other values?

Rearrange for Capacitance: with Impedance 1 Ω, Target Frequency 100 kHz, Capacitance is 1.592 µF.

What units does Decoupling Capacitor Impedance use?

Impedance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Power Distribution formulas →
Decoupling Capacitor Impedance Capacitor Ripple Current (Buck) Bulk Capacitor Hold-Up Energy Buck Input Capacitor RMS Ripple Boost Output Capacitor RMS Ripple

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