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Calculate capacitive reactance, total impedance with ESR, and view impedance vs frequency.
Xc = 1/(2πfC) — Capacitive Reactance vs Frequency
| Frequency | Xc |
|---|---|
| 50.00 Hz | 31.83 Ω |
| 100.0 Hz | 15.92 Ω |
| 1.000 kHz | 1.592 Ω |
| 10.00 kHz | 159.2 mΩ |
| 100.0 kHz | 15.92 mΩ |
| 1.000 MHz | 1.592 mΩ |
A capacitor’s impedance drops with frequency: Xc = 1/(2πfC). At DC it’s an open circuit (infinite impedance), while at high frequencies it approaches a short circuit. This frequency-dependent behavior is what makes capacitors essential for filtering, coupling, and decoupling in electronic circuits.
Real capacitors have ESR (Equivalent Series Resistance) from their leads, electrodes, and electrolyte. ESR sets a floor on impedance — no matter how high the frequency, the impedance can never drop below ESR. The total impedance is |Z| = √(Xc² + ESR²). At the frequency where Xc equals ESR, the capacitor transitions from capacitive to resistive behavior.
For bypass (decoupling) capacitors, low ESR is critical. Ceramic capacitors (MLCC) have ESR in the milliohm range, making them ideal for high-frequency decoupling near IC power pins. Aluminum electrolytics offer large capacitance but higher ESR (0.01–1Ω), so they handle low-frequency bulk filtering. A common design practice places both in parallel: a 10µF–47µF electrolytic for bulk and a 100nF ceramic close to the IC.
Capacitive Reactance (Xc)
Xc = 1 / (2πfC)Total Impedance |Z|
|Z| = √(Xc² + ESR²)The garden-variety 0.1 µF you bypass every IC with. How much reactance does it actually present at a 1 MHz switching edge?
Xc = 1/(2π × 1×10⁶ × 100×10⁻⁹) = 1.59 Ω
A bulk reservoir cap on a power rail, holding up the supply against a 100 kHz buck converter ripple.
Xc = 1/(2π × 100×10³ × 10×10⁻⁶) = 0.159 Ω
An audio coupling cap passing a 1 kHz tone. The reactance here is what sets the low-frequency rolloff with the next stage's input resistance.
Xc = 1/(2π × 1×10³ × 1×10⁻⁶) = 159 Ω
The Xc = 1/(2πfC) formula treats a capacitor as ideal. It isn't. Every real part has a small series resistance (ESR) from the plates and leads, and a tiny series inductance (ESL) from the loop the current has to travel. The full impedance is the vector sum:
Impedance of a real capacitor
Z = √(ESR² + (Xc − XL)²), where XL = 2πf·ESLAt low frequency Xc dominates and the part behaves. Climb in frequency and Xc shrinks while XL grows — at some point they cancel.
The frequency where Xc and XL are equal is the self-resonant frequency (SRF). Below it the part is capacitive; above it the ESL wins and your capacitor acts like an inductor.
Self-resonant frequency
f_SRF = 1 / (2π√(ESL·C))Here's where people get burned: a 10 µF cap can be useless at 10 MHz because it's sailed past its self-resonant frequency and is behaving like a coil. That's exactly why you parallel a small 100 nF (low ESL, high SRF) with the bulk 10 µF on a power rail — each part owns a frequency band. The big one handles low-frequency bulk current; the little one keeps impedance low where the big one has already gone inductive.
Two caps marked "1 µF" can behave nothing alike depending on the dielectric. The DC-bias gotcha alone catches people every week: an X7R MLCC can lose 50–80% of its rated capacitance when you run it near its rated voltage. If you need the capacitance to actually be the capacitance, that matters.
| Dielectric | Strengths | Watch out for |
|---|---|---|
| C0G / NP0 | Rock-stable over temp and voltage, very low loss | Only small values (pF to a few nF). I'd reach for a C0G in a filter or timing circuit, not an X7R. |
| X7R (class 2 MLCC) | Much denser — more capacitance per package | Loses capacitance with DC bias and temperature. Derate hard if you're near rated voltage. |
| Electrolytic / tantalum | Bulk capacitance, cheap microfarads | High ESR, low SRF — useless above a few hundred kHz on their own. Pair with ceramics. |
Related: LC resonance uses the same XL = XC crossover that defines a cap's SRF. See RC filter for how reactance sets a cutoff, and RLC circuit for the full resistance-reactance picture. Reference: Equivalent series resistance (Wikipedia).
Did you know? At audio frequencies (20 Hz–20 kHz), a 100 µF electrolytic capacitor has an impedance of 8 Ω down to 0.08 Ω — useful as a bypass. At 100 MHz, the same cap may actually look inductive due to its parasitic series inductance (ESL), making a 100 nF ceramic cap far better for decoupling.