Capacitor Impedance with ESR
Z = √(ESR² + Xc²)
Quick answer
This calculator solves Z = √(ESR² + Xc²) for Total Impedance. With ESR 50 mΩ, Capacitive Reactance 1.03 kΩ, the result is 1.03 kΩ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A real capacitor has equivalent series resistance (ESR) that prevents its impedance from ever reaching zero. The total impedance is the vector sum of the resistive ESR component and the reactive capacitance component. At low frequencies, Xc dominates and the impedance is mostly capacitive. Near the self-resonant frequency, Xc and ESL cancel, leaving only ESR as the minimum impedance. Below this minimum, the capacitor acts capacitive; above it, the parasitic inductance (ESL) dominates and the component behaves as an inductor.
Variables
- Z — Total capacitor impedance (Ω)
- ESR — Equivalent series resistance (Ω)
- Xc — Capacitive reactance at the frequency of interest (Ω)
Practical Notes
Ceramic capacitors have very low ESR (1-10 mΩ), making them excellent for high-frequency bypassing. Electrolytic capacitors have ESR from 10 mΩ to several ohms, which limits their effectiveness at high frequencies but provides damping in power supply output filters. Low-ESR electrolytics are specifically designed for switching power supply output filtering.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Z | Total Impedance | Ω | mΩ, Ω, kΩ, MΩ |
| ESR | ESR | mΩ | mΩ, Ω, kΩ, MΩ |
| Xc | Capacitive Reactance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: ESR 50 mΩ, Capacitive Reactance 1.03 kΩ
- 2. The relation: Z = √(ESR² + Xc²)
- 3. Substitute: ESR = 50 mΩ, Xc = 1.03 kΩ
- 4. Result: Total Impedance = 1.03 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1 kΩ | 2.9% |
| E24 | 1 kΩ | 2.9% |
Worked examples
Minimum range
Given: ESR 0.1 mΩ, Capacitive Reactance 2.2 Ω
Result: Total Impedance = 2.2 Ω
Low range
Given: ESR 1 mΩ, Capacitive Reactance 22 Ω
Result: Total Impedance = 22 Ω
Typical
Given: ESR 50 mΩ, Capacitive Reactance 1.03 kΩ
Result: Total Impedance = 1.03 kΩ
High range
Given: ESR 0.5 Ω, Capacitive Reactance 10.3 kΩ
Result: Total Impedance = 10.3 kΩ
Maximum range
Given: ESR 5 Ω, Capacitive Reactance 103 kΩ
Result: Total Impedance = 103 kΩ
Solving for each variable
Solve for Total Impedance
ESR 0.1 mΩ, Capacitive Reactance 2.2 Ω → 2.2 Ω
Solve for ESR
Total Impedance 10 Ω, Capacitive Reactance 4.7 Ω → 8.827 Ω
Solve for Capacitive Reactance
Total Impedance 1 Ω, ESR 0.1 mΩ → 1 Ω
How Total Impedance changes with ESR
| ESR (input) | Total Impedance (result) |
|---|---|
| 5 mΩ | 1.03 kΩ |
| 12.5 mΩ | 1.03 kΩ |
| 25 mΩ | 1.03 kΩ |
| 37.5 mΩ | 1.03 kΩ |
| 50 mΩ | 1.03 kΩ |
| 75 mΩ | 1.03 kΩ |
| 100 mΩ | 1.03 kΩ |
| 0.2 Ω | 1.03 kΩ |
| 0.35 Ω | 1.03 kΩ |
| 0.5 Ω | 1.03 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 1030000 |
| Ω | 1030 |
| kΩ | 1.03 |
| MΩ | 0.00103 |
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<p><a href="https://vbatpower.com/formulas/capacitor-esr-impedance/">Capacitor Impedance with ESR</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Capacitor Impedance with ESR?
Use Z = √(ESR² + Xc²). With ESR 50 mΩ, Capacitive Reactance 1.03 kΩ, Total Impedance works out to 1.03 kΩ.
How to calculate esr from impedance for a capacitor?
Rearrange for Total Impedance: with ESR 1 mΩ, Capacitive Reactance 22 Ω, Total Impedance is 22 Ω.
What is the formula for Capacitor Impedance with ESR?
The formula is Z = √(ESR² + Xc²). A real capacitor has equivalent series resistance (ESR) that prevents its impedance from ever reaching zero.
How do you find ESR when you know the other values?
Rearrange for ESR: with Total Impedance 10 Ω, Capacitive Reactance 4.7 Ω, ESR is 8.827 Ω.
How do you find Capacitive Reactance when you know the other values?
Rearrange for Capacitive Reactance: with Total Impedance 1 Ω, ESR 0.1 mΩ, Capacitive Reactance is 1 Ω.
What units does Capacitor Impedance with ESR use?
Total Impedance is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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