LC Filter Calculator

For a simple LC filter, the cutoff frequency is:

f_c = 1 / (2π√(L×C))

L is in henries and C is in farads. The answer is in hertz.

Example: L = 1 µH and C = 100 pF gives f_c ≈ 15.9 MHz.

For a ladder filter with many parts, each element is scaled from a prototype table, so the whole chain still hits the same −3 dB point.

An RC filter uses a resistor and a capacitor. An LC filter uses an inductor and a capacitor.

• Loss: RC filters burn signal power in the resistor. LC filters store energy instead, so they pass the wanted band with much less loss.
• Sharpness: LC filters cut much harder for the same order.
• Size and cost: RC is cheap and tiny. Inductors are bigger and cost more.
• Use: RC is fine for slow audio and DC smoothing. LC rules in radio and power work.

Each order adds about 6 dB per octave, or 20 dB per decade.

• 1st order: 6 dB/octave (20 dB/decade)
• 3rd order: 18 dB/octave (60 dB/decade)
• 5th order: 30 dB/octave (100 dB/decade)
• 7th order: 42 dB/octave (140 dB/decade)

An octave means double the frequency. A decade means ten times the frequency. This is the far-out slope, not the shape right at the corner.

Pick the order from how much you must block and how far away the stop band sits.

Rough steps:

1. Find the ratio of the stop frequency to the cutoff frequency.
2. Find how many dB of blocking you need there.
3. Divide the dB needed by 20 dB per decade of that ratio.

Example: you need 40 dB down at ten times the cutoff. 40 ÷ 20 = order 2 for Butterworth. Need 40 dB at only twice the cutoff? That takes about order 7.

Chebyshev and Elliptic shapes reach the same goal with a lower order.

Match the shape to the job:

• Butterworth: general use, flat passband, no surprises.
• Chebyshev Type I: you need a sharp cut and can accept small passband ripple.
• Elliptic: the sharpest cut with the fewest parts, if ripple in both bands is fine.
• Bessel: square waves, pulses, and data lines that must keep their shape.
• Legendre: you want a steep cut but zero passband ripple.

50 Ω is a compromise. In coax cable, the lowest loss is near 77 Ω, and the highest power handling is near 30 Ω. 50 Ω sits between them and works well for both.

Because nearly all radios, test gear, antennas, and connectors use 50 Ω, filters are designed for it too. Video and TV gear often uses 75 Ω instead, since long cable runs favor low loss.

Insertion loss is how much signal you lose by putting the filter in the path. It is shown as |S21| in dB.

• 0 dB means everything passes.
• −3 dB means half the power is gone, which marks the cutoff.
• −40 dB means only 0.01% of the power gets through.

A perfect LC filter has almost no loss in the passband. Real coils and caps add a few tenths of a dB.

Return loss tells how much signal bounces back instead of going through.

• Below −20 dB: very good, only 1% of power reflects (SWR about 1.22).
• −15 dB: good for most work (SWR about 1.43).
• −10 dB: the usual minimum, 10% reflects (SWR 2.0).
• Above −6 dB: a poor match, fix it.

Bad return loss usually means the source or load impedance does not match the filter design value.

Q measures how lossy a part is. Low Q means more hidden resistance.

Low inductor Q will:

• Add insertion loss in the passband
• Round off the sharp corner at cutoff
• Make notches shallower
• Flatten ripple peaks

Inductors usually have Q of 30 to 100, while capacitors often reach 200 to 1000. So the coils cause most of the loss. Narrow band-pass filters suffer the most, since they circulate energy many times.

Group delay is how long a signal takes to get through the filter. It is measured in seconds, often nanoseconds.

If all frequencies take the same time, the wave shape stays intact. If some are slower, the shape smears. That ruins square waves and digital data.

Sharp filters like Elliptic and Chebyshev have big delay bumps near cutoff. Bessel filters have almost flat delay, so they keep pulses clean, but they cut much more gently.

Both give the same frequency response. Choose by what suits the circuit.

• Shunt-first (cap to ground first): uses fewer inductors in a low-pass filter. Cheaper and smaller.
• Series-first (coil in line first): better when the source cannot handle a capacitor load, or when DC must be blocked.

In RF work, most people pick the layout with fewer inductors, since coils cost more, take more room, and are lossier.

You resonate every element at the center frequency.

• Series inductor becomes a series L and C.
• Shunt capacitor becomes a parallel L and C.

Scale the first value using the bandwidth instead of the cutoff, then find its partner with:

C = 1 / (ω₀² × L)

Here ω₀ = 2πf₀, and f₀ = √(f_low × f_high). A band-pass filter has twice as many parts as the low-pass it came from.

Use the geometric mean, not the plain average:

f₀ = √(f_low × f_high)

Example: 80 MHz and 120 MHz gives f₀ = √9600 ≈ 98 MHz, not 100 MHz.

The geometric mean is used because filter response is symmetric on a log scale, not a linear one.

For a band-pass or band-stop filter, Q is:

Q = f₀ / BW

BW is the bandwidth, f_high minus f_low.

A high Q means a narrow band. Q above about 20 is hard to build, because part tolerances and coil losses start to dominate. Keep Q under 10 to 20 for a design that works with real parts.

It depends on the E-series you use:

• E6 (20%): big shifts, ripple grows, match gets worse.
• E12 (10%): usable for rough filters.
• E24 (5%): fine for most designs.
• E96 (1%): nearly the same as the exact math.

Keep each part within about 5% of the ideal value. Parts near the input and output matter most for return loss. Sharp filters like Elliptic are the fussiest.

Yes, but the filter must be designed for it. A standard ladder assumes a set ratio between the two ends.

If the real load does not match, you get:

• Worse return loss
• More ripple in the passband
• A cutoff that shifts a little

Even-order Chebyshev filters naturally need unequal ends. Butterworth and odd-order Chebyshev filters want equal ends.

Common causes:

• Self-resonance: every real inductor has stray capacitance and stops acting like a coil above its SRF. Pick parts with an SRF well above your highest frequency of interest.
• Lead and trace inductance: capacitor leads add series inductance and create a notch, then the cap acts like a coil.
• Poor ground: shared ground paths let signal sneak past the filter.

Use short traces, a solid ground plane, and parts rated well beyond your band.

Check these five things:

1. Value and tolerance: 5% or better for most filters, 1% for sharp ones.
2. Self-resonant frequency: at least 3 to 5 times your top frequency.
3. Q: higher is better. Use wirewound or air-core coils for RF, not ferrite beads.
4. Current and voltage rating: check peak values, which run higher inside resonant branches.
5. Temperature stability: use C0G/NP0 capacitors, never X7R or Y5V, in tuned circuits.

The −3 dB point is where the filter passes half the input power. Voltage there is about 70.7% of the input.

This is the standard definition of cutoff frequency, since the half-power point is a clean, repeatable spot on the curve.

Some specs use −1 dB or −0.5 dB instead, especially for Chebyshev filters where the ripple value sets the band edge.

Yes. Passive LC filters are reciprocal, so the response is the same either way. |S21| equals |S12|.

What can change is the match at each end. If the source and load impedances are different, the input return loss (S11) and output return loss (S22) will not match, even though the signal loss through the filter stays the same.