Decoupling Capacitor Impedance

Decoupling Capacitor Impedance

A real capacitor's impedance is not just 1/(2πfC). It includes:

• ESR (Equivalent Series Resistance): resistive losses
• ESL (Equivalent Series Inductance): inductive parasitics

Total impedance at frequency f:

Z = √(ESR² + (2πf·ESL - 1/(2πf·C))²)

At the self-resonant frequency, the capacitive and inductive reactances cancel, leaving only ESR — the minimum impedance point.

The capacitor is only effective as a decoupler near its resonant frequency where Z is minimized.

Frequency Regions

• f < SRF: capacitive — Z decreases as f increases
• f = SRF: Z = ESR (minimum impedance)
• f > SRF: inductive — Z increases as f increases

Your Task

Implement capImpedance(f_MHz, C_nF, ESR_ohm, ESL_nH) returning impedance in ohms.

Then find the frequency of minimum impedance for a 100nF, 50mΩ ESR, 1nH ESL capacitor by evaluating at 1, 10, and 16 MHz.