Butterworth (Maximally Flat) Band-Stop Filter Calculator

A band-stop filter passes everything except a band around the center frequency. The Butterworth type keeps both passbands perfectly flat with no ripple, so it disturbs nearby operating channels as little as possible. Enter the center frequency, stopband width and order to get the LC notch values and response plot.

No passband rippleOrder 1–10Type 1 / Type 2 topologiesL in nH · C in pF

① Input Parameters

Order n (resonators)1–10Center frequency f0MHzBandwidth BWMHzImpedance ZoΩ

BW is the −3 dB width of the stopband; a higher order gives a deeper stopband with steeper edges.

② Results

#	Type 1		Type 2
#	L (nH)	C (pF)	L (nH)	C (pF)
1
2
3
4
5
6
7
8
9
10

Each row is one resonator (L and C both resonate at f0). Type 1: odd rows = series-arm parallel LC, even rows = shunt series LC; Type 2 is the reverse. Only the first n rows are shown.

Circuit Diagram

Type 1: odd sections are parallel LC resonators in the series arm (high impedance at f0, blocking the signal); even sections are series LC resonators to ground (a short to ground at f0). Type 2 is the reverse. For even n the last section is the other resonator type.

Frequency Response (current inputs)

Inductor LCapacitor CGroundCenter frequency f0Band edges

Ideal response: A(Ω) = 10·log(1 + Ω²ⁿ); Ω = (BW/f0) ÷ (f/f0 − f0/f). The orange lines are the −3 dB points bounding the stopband.

How to Use

Enter the order n (number of resonators, 1–10).
Enter the center frequency f0 of the band to reject and the −3 dB stopband width BW in MHz, plus the impedance Zo.
Click Calculate. The table lists L (nH) and C (pF) for every resonator of Type 1 and Type 2.
Pick one topology, choose standard values, then measure the notch position on a network analyzer and fine-tune.

Theory & Formulas

The Butterworth low-pass prototype values depend only on the order:

g_k = 2 · sin( (2k − 1)π / 2n ), k = 1 … n

The low-pass to band-stop transformation turns each series inductor into a parallel LC resonator in the series arm (open at f0) and each shunt capacitor into a series LC resonator to ground (short at f0):

ω₀ = 2π · f₀, Δω = 2π · BW
Series-arm parallel resonator: L = g_k·Z_o·Δω / ω₀²　C = 1 / ( g_k·Z_o·Δω )
Shunt series resonator: L = Z_o / ( g_k·Δω )　C = g_k·Δω / ( Z_o·ω₀² )

Response

Ideal response A = 10·log(1 + Ω²ⁿ) with Ω = (BW/f0) ÷ (f/f0 − f0/f). Attenuation peaks at f0 and the two −3 dB points are BW apart. Every resonator satisfies L·C = 1/ω₀².

Design Tips

Real notch depth is limited by component Q and is typically a few tens of dB; increase the order for more rejection.
The narrower the stopband, the wider the spread of values – check that all parts are available and mind their self-resonant frequencies.
Operating channels should lie outside the −3 dB points (orange lines) with margin for component tolerance.
If you need steeper stopband edges and can accept ripple, use the Chebyshev BEF.

FAQ

When do I need a band-stop filter?: When the interferer sits inside or very close to the band you need, so a low-pass or high-pass cannot separate them – e.g. suppressing a nearby strong transmitter or your own transmit frequency at a receiver.
How do Type 1 and Type 2 differ?: Same frequency response. Type 1 starts and ends with parallel resonators in the series arm, Type 2 with series resonators to ground; choose by part availability and layout.
Why is my measured notch shallower than theory?: Inductor and capacitor losses (finite Q), parasitics and ground inductance make the notch shallower and wider; high-Q parts and short ground paths help.

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