Ferrite bead filter calculator

A bead and a capacitor are not automatically a filter. This computes the bead's impedance across frequency from its equivalent circuit, the attenuation it gives at the frequency you care about — and the resonance it forms with the capacitor, where an undamped pair amplifies noise instead of removing it.

Fig 1 — the filter amplifies by 9.1 dB at 99.2 kHz before it attenuates; at 10.0 MHz it gives 69 dB.

Bead inductance (nH)

Bead AC resistance (Ω)

Bead parasitic C (pF)

Bead DC resistance (mΩ)

Downstream capacitance (µF)

Capacitor ESR (mΩ)

Load current (A)

Noise frequency (MHz)

Attenuation at 10 MHz: 69.1 dB · bead is 15.0 Ω and inductive there
Resonant peak: +9.1 dB of gain at 99.2 kHz — the filter amplifies here
Filter resonance: 103 kHz · Q = 2.82
Bead self-resonance: 188 MHz at 130 Ω — resistive here, capacitive above
DC penalty: 25.0 mV dropped · 12.5 mW burned at 0.5 A

This filter makes noise worse at 99.2 kHz, by 9.1 dB. An undamped bead and ceramic are an LC tank; if a converter's switching frequency or a load step lands near that peak, the filter is the problem. Damp it with ESR — a polymer or electrolytic in parallel with the ceramic — or move the resonance with more capacitance.

How this is calculated

Standard: Würth ANP045 — Behind the Magic of High Frequency SMT Chip Bead Ferrites (equivalent circuit and the three regions); TI SLYT740 and SNVA871 — output-noise filtering in practice

$Z_{bead} = R_{DC} + \left( j\omega L \;\|\; R_{AC} \;\|\; \frac{1}{j\omega C_{par}} \right)$: The equivalent circuit ANP045 specifies and SLYT740 repeats: an inductance, an AC resistance and a parasitic capacitance in parallel, with the DC resistance in series. Inductive below self-resonance, resistive at it, capacitive above.
$f_{SRF} : \; \operatorname{Im}\{Z_{bead}\} = 0$: Self-resonance, where the reactance crosses zero and the impedance peaks at roughly R_AC. Only near here does a bead dissipate interference as heat rather than store and re-radiate it.
$H(f) = \frac{Z_{C}}{Z_{bead} + Z_{C}}, \qquad Z_C = R_{ESR} + \frac{1}{j\omega C}$: The filter is a divider between the bead and the downstream capacitor. Attenuation in dB is −20·log₁₀|H|; where |H| exceeds 1 the network has gain.
$f_0 = \frac{1}{2\pi\sqrt{LC}}, \qquad Q = \frac{\sqrt{L/C}}{R_{DC} + R_{ESR}}$: The bead is an inductor below its self-resonance, so with the capacitor it forms an LC tank. Q above about 0.7 means a visible peak — and a ceramic’s few mΩ of ESR damps almost nothing.
$V_{drop} = I \cdot R_{DC}, \qquad P = I^2 R_{DC}$: What the bead costs when it is doing nothing: a permanent drop and dissipation at the load current.

Assumptions

The load is high impedance. A real load draws current and damps the resonance; this is the pessimistic case, which is the right default for a quiet rail feeding an ADC or a PLL.
The bead model is linear and un-derated. Real bead impedance falls substantially with DC bias — ANP045 and SLYT740 both stress this — so at a large fraction of the rated current the true attenuation is well below what is shown. Use the vendor’s bias-derated curve.
Impedance is also temperature dependent: ANP045 measures it falling as the part heats.
One bead and one capacitor. Multiple capacitors in parallel each add their own resonance, and the tool models only the lumped value entered.
A bead never belongs in a feedback path or on a rail whose regulator senses after it — the added impedance is inside the loop, and stability is not modelled here.

What a ferrite bead and capacitor actually filter

A ferrite bead is sold as a part that removes noise, and the schematic symbol encourages the belief that adding one can only help. It can hurt. A bead is inductive over most of its range, and an inductor followed by a low-ESR ceramic capacitor is an undamped LC tank — a circuit whose entire purpose is to resonate. Below its resonance the pair does nothing; at the resonance it amplifies; only well above it does the filtering people bought it for begin.

This tool draws that whole picture. The bead comes from the equivalent circuit Würth ANP045 specifies and TI SLYT740 repeats — an inductance, an AC resistance and a parasitic capacitance in parallel, with the DC resistance in series — so the three regions ANP045 names fall out naturally: inductive below self-resonance, resistive at it, capacitive above. Then the bead and the downstream capacitor are combined as a divider, and the response is swept from 1 kHz to 1 GHz so the peak, if there is one, cannot hide.

Two numbers decide everything. Where the resonance sits, and how much resistance is available to damp it — which on an all-ceramic rail is the bead's DC resistance plus a handful of milliohms, and is nowhere near enough.

Bead and capacitor chart: where the filter peaks

The worked example's bead into the ceramic values a rail actually gets, computed by the calculator above. The resonance moves down and the peak shrinks as the capacitor grows, because Q is √(L/C) over the loop's resistance, and the bead's DC resistance plus the capacitor's ESR is all the resistance there is. The last column is what the filter does at 10 MHz, which is the job it was fitted for.

Ceramic C	Resonance f₀	Q	Peak gain	Attenuation at 10 MHz
1 µF	325 kHz	8.91	+18.7 dB	59 dB
2.2 µF	219 kHz	6.01	+15.5 dB	65 dB
4.7 µF	150 kHz	4.11	+12.3 dB	68 dB
10 µF	103 kHz	2.82	+9.1 dB	69 dB
22 µF	69.3 kHz	1.90	+5.9 dB	69 dB
47 µF	47.4 kHz	1.30	+3.0 dB	70 dB

Every row still peaks. A larger capacitor lowers the peak slowly, from 19 dB at 1 µF to 3 dB at 47 µF, and moves it through exactly the frequencies where a switching regulator's fundamental sits. The fix is damping, which the section on where the model stops being valid works through.

Worked example: a 130 Ω bead into 10 µF of ceramic

The defaults are the bead model this site's ferrite article is drawn from — 240 nH, 130 Ω of AC resistance, 3 pF, 50 mΩ DC — feeding 10 µF of ceramic with 5 mΩ of ESR.

bead SRF   = 1 / (2π√(240 nH × 3 pF))       = 187.6 MHz  at ≈130 Ω
filter f₀  = 1 / (2π√(240 nH × 10 µF))      = 102.7 kHz
Q          = √(240 nH / 10 µF) / 55 mΩ
           = 0.1549 / 0.055                 = 2.82

           →  +9 dB of gain at 103 kHz

at 10 MHz  bead is 15 Ω, capacitor 5.3 mΩ  →  69 dB of attenuation

Read the third line again: this filter makes noise at 103 kHz roughly three times worse. That frequency is not academic — it is squarely where a switching converter's ripple lives. The classic failure is fitting a bead to clean up a rail, measuring at the switching frequency, and finding more ripple than before.

Two fixes, both visible in the tool. Damp it: put a polymer or electrolytic in parallel with the ceramic so the filter has some ESR to work against — a few hundred mΩ takes Q below 0.7 and the peak vanishes. Or move it: ten times the capacitance drops f₀ by √10 and damps by √10 as well, since Q = √(L/C)/R.

Where the bead filter model stops being valid

The largest caveat is bias current. Bead impedance falls sharply as DC current approaches the rated value — ANP045 devotes a measurement methodology to it, and SLYT740 reports a bead disappointing in exactly this way because a high output current had collapsed its AC resistance. The model here is un-derated, so it flatters any bead carrying real current. Take the impedance curve at your operating current from the vendor's tool, and enter those parameters.

The load is assumed to be high impedance, which is pessimistic: a real load draws current and damps the peak. That is the right default for the case beads are used in — a quiet rail feeding an ADC, a PLL or an oscillator — but a bead feeding a hungry digital load will peak less than shown.

A bead also does not belong on every rail. Inside a regulator's feedback path it adds impedance the loop must deal with; on a rail whose sense point is before the bead, load current turns the DC resistance into an unregulated drop. And for common-mode noise on a differential pair, a bead in each leg is the wrong part — that is a common-mode choke's job.

Common ferrite bead mistakes

Fitting a bead and a ceramic and measuring only at high frequency. The damage is at the LC resonance, typically a few tens to a few hundred kHz, which is where the switching ripple already was.
Choosing the bead by its headline number. "600 Ω" is the impedance at 100 MHz; at the frequency of your actual noise it may be a few ohms, and at your actual bias current, fewer.
Using a bead above its self-resonance. Past that point it is a capacitor, and it passes the noise it was installed to stop.
Putting a bead in series with a high-current rail and forgetting the DC resistance. Tens of milliohms at amps is a real drop and real heat, for a part most people never budget for.
Relying on the bead instead of layout. A bead in the return path of a loop that should not exist does not fix the loop — seewhy a bead is not a resistor.