Pi-Filter Attenuation
A = 20 × log10(1/(ω² × L × C))
Quick answer
This calculator solves A = 20 × log₁₀(1/(ω² × L × C)) dB for A. With Frequency 100 kHz, Inductance 100 µH, Capacitance (each) 100 µF, the result is -71.93.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | kHz | Hz, kHz, MHz, GHz |
| L | Inductance | µH | nH, µH, mH, H |
| C | Capacitance (each) | µF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Frequency 100 kHz, Inductance 100 µH, Capacitance (each) 100 µF
- 2. The relation: A = 20 × log₁₀(1/(ω² × L × C)) dB
- 3. Substitute: f = 100 kHz, L = 100 µH, C = 100 µF
- 4. Result: A = -71.93
Worked examples
Minimum range
Given: Frequency 100 Hz, Inductance 100 nH, Capacitance (each) 100 nF
Result: A = 168.1
Low range
Given: Frequency 1 kHz, Inductance 1 µH, Capacitance (each) 1 µF
Result: A = 88.07
Typical
Given: Frequency 100 kHz, Inductance 100 µH, Capacitance (each) 100 µF
Result: A = -71.93
High range
Given: Frequency 0.5 MHz, Inductance 0.47 mH, Capacitance (each) 1 mF
Result: A = -133.3
Maximum range
Given: Frequency 5 MHz, Inductance 4.7 mH, Capacitance (each) 10 mF
Result: A = -213.3
How A changes with Frequency
| Frequency (input) | A (result) |
|---|---|
| 10 kHz | -31.93 |
| 25 kHz | -47.84 |
| 50 kHz | -59.89 |
| 75 kHz | -66.93 |
| 100 kHz | -71.93 |
| 150 kHz | -78.97 |
| 0.2 MHz | -83.97 |
| 0.4 MHz | -96.01 |
| 0.7 MHz | -105.7 |
| 1 MHz | -111.9 |
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<p><a href="https://vbatpower.com/formulas/pi-filter-atten/">Pi-Filter Attenuation</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Pi-Filter Attenuation?
Use A = 20 × log₁₀(1/(ω² × L × C)) dB. With Frequency 100 kHz, Inductance 100 µH, Capacitance (each) 100 µF, A works out to -71.93.
What is the formula for Pi-Filter Attenuation?
The formula is A = 20 × log₁₀(1/(ω² × L × C)) dB. A pi-filter (CLC) consists of two capacitors with an inductor between them, forming a third-order low-pass filter.
Related Concepts
All Filters formulas →Need more features?
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