Pi-Filter Attenuation

A = 20 × log10(1/(ω² × L × C))

Calculator

Result
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Formula

A = 20 × log₁₀(1/(ω² × L × C)) dB

Description

A pi-filter (CLC) consists of two capacitors with an inductor between them, forming a third-order low-pass filter. Well above the resonant frequency, the attenuation increases at 60 dB/decade (third-order rolloff). The formula gives the approximate attenuation at a given frequency assuming the frequency is well above the filter cutoff. Pi-filters are extensively used in power supply filtering, EMI suppression, and DC bus filtering. The name comes from the schematic resembling the Greek letter π.

Variables

  • f — Frequency at which attenuation is calculated (Hz)
  • L — Series inductance (H)
  • C — Shunt capacitance on each side (F, assumed equal)

Practical Notes

The result is in dB (negative values indicate attenuation). This approximation is valid only well above the filter resonant frequency. Near resonance, the response depends heavily on component Q and damping. For practical EMI filters, the actual attenuation may be 10-20 dB less than calculated due to component parasitic coupling, PCB layout parasitics, and insufficient grounding. Always verify filter performance with measurements.

Related Formulas

RC Low-Pass Filter RC High-Pass Filter Bandpass Bandwidth Filter Rolloff Rate Notch Frequency Butterworth Q Factor

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