Calculator KB-06
LC Filter Calculator
Calculate an LC low-pass filter, for example to reduce ripple at the output of a DC-DC converter.
Result
In brief: Calculate a low-pass LC filter: cutoff frequency, characteristic impedance, Q factor, attenuation at the switching frequency, and find L or C. Example: Cutoff frequency: 5.033 kHz.
Calculation example
| Inductance L | 10 µH |
|---|---|
| Capacitance C | 100 µF |
| Load resistance | 5 Ω |
| Ripple frequency | 150 kHz |
| Input ripple | 100 mV |
| Required cutoff frequency | 5 kHz |
| Cutoff frequency | 5.033 kHz |
|---|---|
| Characteristic impedance | 316.2 mΩ |
| Loaded Q factor | 15.81 |
| Attenuation at the ripple frequency | 887.3 times (59 dB) |
| Output ripple | 0.113 mV |
| Required L for this C | 10.13 µH |
| Required C for this L | 101.3 µF |
How it is calculated
Z0 = √(L / C)
Q = R / Z0
|H(f)| = 1 / √((1 − (f/f0)²)² + (f / (Q·f0))²)
This is a second-order filter: above the cutoff frequency, attenuation increases by 40 dB per decade, or 100 times for every 10-fold increase in frequency.
What to look for
- Choose a cutoff frequency at least 10 times lower than the ripple frequency for noticeable suppression.
- When Q is greater than 1, a resonant peak appears at the cutoff frequency: instead of attenuating the signal, the filter amplifies it there. A resistor that lowers Q can help, as can a capacitor with significant ESR.
- An output filter on a converter can affect its stability if feedback is taken after the filter. Usually, feedback is taken before the filter.
- This is an ideal calculation: at high frequencies, the capacitor's ESR and ESL and the inductor's interwinding capacitance come into play, so only ceramic capacitors placed close to the output can suppress short spikes. The inductor must handle the load current without saturating.
Frequently asked questions
How do I calculate an LC filter’s cutoff frequency?
f₀ = 1 / (2π · √(L · C)). With 10 µH and 100 µF, it’s about 5 kHz. At 150 kHz, an ideal filter attenuates ripple almost 900 times, or about 59 dB.
How do I choose L and C to reduce DC-DC ripple?
Set the cutoff frequency at least 10 times lower than the switching frequency. The inductor must handle the load current without saturating, and the capacitor should have low ESR.
Why are there still “spikes” after the filter?
Short transients occur in the megahertz range, where the capacitor’s inductance and the inductor’s interwinding capacitance matter more. A 100 nF ceramic capacitor right at the output and short traces help.
