🎓 Lesson 9
D5
Capacitor & Inductor Parasitics: ESL, ESR, and Self-Resonance Effects
Real capacitors and inductors aren’t perfect—they behave like combinations of ideal components plus tiny resistors and inductors that appear at high frequencies.
🎯 Learning Objectives
- ✓ Calculate the self-resonant frequency (SRF) of a capacitor or inductor given its ESL and capacitance/inductance values
- ✓ Analyze impedance vs. frequency plots to identify dominant parasitic behavior (capacitive → resistive → inductive transition)
- ✓ Explain how ESR and ESL degrade high-frequency filtering performance in DC-DC converter input/output filters
- ✓ Select appropriate capacitor types (e.g., ceramic X7R vs. tantalum vs. polymer) based on ESR/ESL requirements for a given EMI suppression application
- ✓ Apply SRF guidelines to place decoupling capacitors effectively across multiple frequency bands in PCB layout
📖 Why This Matters
In EMI/EMC compliance testing, 70% of failed radiated emissions stem from improperly modeled or selected filtering components—not circuit topology. A '10 µF ceramic capacitor' may act like an inductor above 15 MHz due to ESL, turning your low-pass filter into a high-pass path for noise. This lesson bridges textbook idealism with lab reality: you’ll learn why your simulation doesn’t match your spectrum analyzer—and how to fix it.
📘 Core Principles
All real passive components exhibit parasitics due to physical construction: capacitor leads and internal electrodes contribute ESL; dielectric and metal losses manifest as ESR. Inductors suffer from inter-winding capacitance (parallel parasitic C) and wire resistance (ESR). The series RLC model (R = ESR, L = ESL, C = nominal value) accurately predicts impedance |Z(f)| = √[(ESR)² + (2πf·ESL − 1/(2πf·C))²]. At the self-resonant frequency (SRF), reactances cancel (X_L = X_C), yielding minimum impedance (purely resistive, = ESR). Below SRF, the device behaves capacitively (Z ↓ with f); above SRF, inductively (Z ↑ with f). For effective EMI filtering, components must operate below their SRF—and often well below, since impedance rises sharply post-SRF.
📐 Self-Resonant Frequency (SRF)
The SRF is the frequency at which the reactance of ESL cancels that of C (or vice versa for inductors), resulting in purely resistive impedance. It’s the upper usable limit for filtering effectiveness.
💡 Worked Example
Problem: A 100 nF multilayer ceramic capacitor (MLCC) has an ESL of 0.8 nH and ESR of 8 mΩ. Calculate its SRF and impedance at 10 MHz and 100 MHz.
1.
Step 1: Use SRF = 1 / (2π√(L·C)), where L = 0.8×10⁻⁹ H, C = 100×10⁻⁹ F
2.
Step 2: Compute √(0.8e-9 × 100e-9) = √(8e-17) ≈ 8.94e-9 → SRF = 1 / (2π × 8.94e-9) ≈ 17.8 MHz
3.
Step 3: At 10 MHz (< SRF): Z ≈ 1/(2πfC) = 1/(2π×10⁷×10⁻⁷) ≈ 1.59 Ω (capacitive dominant)
4.
Step 4: At 100 MHz (> SRF): Z ≈ 2πf·ESL = 2π×10⁸×0.8×10⁻⁹ ≈ 0.5 Ω (inductive dominant, but note: actual Z > ESR due to rising XL)
Answer:
SRF ≈ 17.8 MHz. At 10 MHz, Z ≈ 1.59 Ω (capacitive); at 100 MHz, Z ≈ 0.5 Ω (inductive), confirming loss of filtering function above SRF.
🏗️ Real-World Application
In a 48 V → 3.3 V DC-DC converter (switching at 2 MHz), conducted EMI passed CISPR 25 Class 5 up to 30 MHz—but failed at 85 MHz. Post-layout analysis revealed the 22 µF aluminum polymer output capacitor (ESR = 15 mΩ, ESL = 12 nH, SRF ≈ 3 MHz) was ineffective above its SRF. Replacing it with three parallel 1 µF 0402 X7R MLCCs (each ESL ≈ 0.4 nH, SRF ≈ 125 MHz) lowered impedance across 1–100 MHz by >20 dB, passing compliance on retest. This illustrates how parasitics—not just value—dictate EMI filter success.
📋 Case Connection
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