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LC filter calculator

Resonant frequency, characteristic impedance and Q of a second-order LC low-pass driving a resistive load, with the magnitude response.

Presets
µH
nF
Ω
Resistance across C. Sets the damping.
kHz
Resonant frequency f0
159.2kHz
The -3 dB point equals f0 only at Q = 0.707; here the gain at f0 is 0.0 dB.
VinL10 µHC100 nFR load10 ΩVoutf0159.2 kHzQ1
Series L from a zero-impedance source, C to ground, load R across C.
Characteristic impedance sqrt(L/C)
10 Ω
Q = R / Z0
1
Response is peaked: it rises above the passband near f0.
Gain at f0
0 dB
Gain at the frequency of interest
-31.82 dB
Load for Q = 0.7071 (Butterworth)
7.071 Ω
LC low-pass magnitude response
-60-40-20010,000100,0001,000,00010,000,000Frequency (Hz)Gain (dB)
  • LC low-pass
  • Frequency of interest
Method

How this is calculated

f0 = 1 / ( 2π · sqrt( L · C ) )
Z0 = sqrt( L / C )
Q = R / Z0 = R · sqrt( C / L )
H(f) = 1 / ( 1 − (f / f0)² + j · (f / f0) / Q )
Gain at f0 = Q
Circuit
Series L from the source, shunt C to ground, load R across C. This is the SLOA049D second-order low-pass standard form with K = 1.
Q
Q = 0.7071 is maximally flat (Butterworth). Above that the response peaks just below f0; the gain at f0 itself is 20 · lg(Q) dB, which is above 0 dB once Q passes 1. Lower Q rolls off earlier and has no peak.
Assumes
A zero-impedance source and ideal parts. Inductor DC resistance and capacitor ESR add damping and lower a high Q.
Roll-off
40 dB per decade above f0, from the square of the frequency ratio.
Sources
FAQ

Questions

1/(2π × sqrt(10 µH × 100 nF)) = 159.2 kHz. The characteristic impedance is sqrt(L/C) = 10 Ω, so a 10 Ω load gives Q = 1.

With a light load, R is much larger than sqrt(L/C) and Q is high. The gain at f0 equals Q: a Q of 10 is a 20 dB peak. Damp it with a load closer to 0.7 times Z0, or with an RC snubber across C.

R = 0.7071 × sqrt(L/C) gives Q = 0.7071, the Butterworth response: no peak and −3 dB at f0. For 10 µH and 100 nF that is 7.07 Ω.

Well above f0, 40 dB per decade. Ten times f0 is about −40 dB, compared with −20 dB for a single RC stage at the same ratio.

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