Capacitor ESR Equivalent Circuit
A real capacitor is not a pure capacitance. It behaves as an ideal capacitor (C) in series with a small resistance (ESR) and a small inductance (ESL). ESR dominates at low-to-mid frequencies, causing power loss and ripple voltage. At high frequencies, ESL takes over.
At low frequencies: Xc dominates (capacitor behaves as expected). At mid frequencies: ESR dominates (impedance floor). At high frequencies: ESL dominates (capacitor becomes an inductor).
ESR Capacitor Calculator
Every capacitor has internal resistance — the ESR — caused by electrode foils, electrolyte, lead wires, and internal connections. ESR wastes power as heat, adds ripple voltage to the output, and limits filtering effectiveness. This calculator takes capacitance, ESR, and frequency and returns total impedance, dissipation factor, quality factor, and phase angle. Add ripple current to see the heat generated and the ripple voltage produced.
Formulas
|Z| = √(ESR² + Xc²) — total impedance
D = ESR / Xc — dissipation factor (lower is better)
Q = 1 / D = Xc / ESR — quality factor (higher is better)
θ = −arctan(Xc / ESR) — phase angle (ideal = −90°)
P = Irip² × ESR — ESR power loss (heat)
Vrip = Irip × ESR — ripple voltage from ESR
Calculator Inputs
C (Capacitance) — pF through farads. Determines Xc at the operating frequency.
ESR — from the data sheet, in mΩ or Ω. Typical ranges: 1–5 mΩ (high-quality ceramics), 10–100 mΩ (polymer and low-ESR electrolytics), 50–500 mΩ (standard electrolytics), 10–100 mΩ (supercapacitors).
f (Frequency) — operating, switching, or ripple frequency. At low frequencies Xc dominates and the capacitor behaves normally. At higher frequencies ESR becomes a larger fraction of |Z| and eventually sets the impedance floor.
Irip (Ripple Current) — optional. RMS ripple current from a switching regulator or rectifier. Enables power loss and ripple voltage outputs.
Worked Example — Switching PSU (1000 µF, 200 mΩ, 100 kHz, 2 A)
|Z| = √(200² + 1.59²) = √(40000 + 2.53) ≈ 200 mΩ
D = 200 / 1.59 = 125.8 — very high, ESR completely dominates
Q = 0.008 — extremely low
θ = −0.46° — nearly resistive (ideal would be −90°)
P = 2² × 0.200 = 0.8 W — heat inside the capacitor
Vrip = 2 × 0.200 = 400 mV — ESR ripple on the output
At 100 kHz, the 1.59 mΩ capacitive reactance is negligible — the capacitor looks like a 200 mΩ resistor. The 400 mV ripple voltage is entirely ESR-driven. The capacitive ripple contribution (I / (2πfC) ≈ 3.2 mV) is 125× smaller. This is why ESR is the dominant spec for switching power supply output capacitors — capacitance barely matters at the switching frequency.
0.8 W of internal heating shortens electrolytic capacitor life. Every 10 °C temperature rise roughly halves the lifespan. Switching to a 50 mΩ polymer capacitor cuts heat to 0.2 W and ripple to 100 mV. To understand the power dissipation in detail, see our Electrical Power Calculator.
Worked Example — RF Decoupling (100 nF Ceramic, 5 mΩ, 10 MHz)
|Z| = √(0.005² + 0.159²) ≈ 0.159 Ω
D = 0.005 / 0.159 = 0.031 — excellent
Q = 31.8 — good for decoupling
θ = −88.2° — near-ideal capacitive behaviour
At 10 MHz with a quality ceramic, ESR is negligible. The capacitor behaves almost ideally — Xc dominates impedance, dissipation factor is well under 0.05, and the phase angle is close to −90°. This is why MLCC ceramics are the default choice for RF and high-frequency decoupling.
Worked Example — Supercapacitor (10 F, 50 mΩ, 1 Hz, 5 A)
|Z| = √(50² + 15.9²) = √(2500 + 253) ≈ 52.5 mΩ
D = 50 / 15.9 = 3.14 — high, ESR dominates even at 1 Hz
Q = 0.32
P = 5² × 0.050 = 1.25 W
Vrip = 5 × 0.050 = 250 mV
Even at 1 Hz, the supercapacitor’s ESR contributes more to impedance than the reactance. 1.25 W of continuous heating in a sealed package is significant — supercapacitor temperature limits are typically 65–85 °C. ESR is the main selection criterion for supercapacitors in high-ripple applications.
How Frequency Changes the Picture
A capacitor’s impedance has three frequency regions:
Mid frequency — ESR dominates. Xc has dropped below ESR. Impedance hits a floor and stays flat (|Z| ≈ ESR). This is where most switching power supplies operate.
High frequency — ESL (equivalent series inductance) takes over. Impedance starts rising again. The capacitor becomes an inductor. This is why you need small ceramics in parallel with large electrolytics — the ceramic covers the high-frequency range where the electrolytic has gone inductive.
The calculator covers the first two regions (capacitive and ESR-dominated). ESL effects require the full three-element model. For fundamental RC timing behaviour, see the RC Time Constant Calculator.
Dissipation Factor and Quality Factor
Dissipation Factor (D = ESR / Xc)
The fraction of stored energy lost as heat per cycle. D below 0.05 is good. D between 0.05 and 0.2 is acceptable for bulk filtering. D above 0.2 means significant ESR losses — consider a lower-ESR part.
Quality Factor (Q = 1 / D)
The inverse of dissipation factor. Q above 50 is desirable for RF resonant circuits and precision filters. Q of 10–50 is fine for general decoupling. Q below 5 means the capacitor is lossy — adequate for energy storage or bulk bypass but not for frequency-selective circuits.
ESR by Capacitor Type
MLCC ceramic (C0G/NP0) — 1–5 mΩ. Lowest ESR. Best for RF, timing, and precision.
MLCC ceramic (X5R/X7R) — 2–20 mΩ. Low ESR. Standard for decoupling and filtering.
Polymer electrolytic — 10–50 mΩ. Low-ESR alternative to aluminium electrolytics. Preferred for switching PSU outputs.
Standard aluminium electrolytic — 50–500 mΩ. Highest ESR in common use. Adequate for low-frequency filtering (50/60 Hz rectifiers) but poor at switching frequencies.
Supercapacitor — 10–100 mΩ. ESR is the main performance limiter despite the enormous capacitance.
Why ESR Matters in Power Supplies
In a switching regulator, output ripple has two components: capacitive ripple (V = I / (2πfC), reduced by larger capacitance) and ESR ripple (V = I × ESR, reduced only by lower ESR). At typical switching frequencies (100 kHz–1 MHz), ESR ripple dominates by 10–100×. Adding more capacitance does not help — only lower ESR reduces the ripple. This is why power supply design specs focus on ESR rather than capacitance for output filtering.
Performance Status
Yellow — dissipation factor 0.05 to 0.2. Acceptable for power supply filtering but not ideal for precision timing, RF, or low-noise circuits.
Red — dissipation factor above 0.2. High ESR losses. Switch to a lower-ESR capacitor type or add parallel capacitors to reduce effective ESR.
Frequently Asked Questions
Last updated: March 2026