When you need to isolate a specific frequency band — say, the 300 Hz to 3 kHz voice band, or a tone-decoder's narrow window — passive RC filters get you partway but lack gain and have poor selectivity. The Multiple Feedback (MFB) bandpass filter is the workhorse single-op-amp topology for moderate-Q applications.

The MFB bandpass uses one op-amp with two capacitors and three resistors arranged so that feedback occurs through both a capacitor and a resistor. It inverts the signal, provides voltage gain at center frequency, and rolls off at 6 dB/octave on both sides. It's preferred over Sallen-Key for bandpass because it produces a true bandpass response with a single stage and is less sensitive to op-amp gain-bandwidth limitations at modest Q values (Q ≤ 10).

The standard design equations (with C1 = C2 = C):

• Center frequency: f₀ = 1 / (2π·C·√(R1‖R3 · R2))
• Gain at f₀: A₀ = −R2 / (2·R1)
• Quality factor: Q = 0.5·√(R2 / (R1‖R3))
• Bandwidth: BW = f₀ / Q

R1 sets the input impedance and gain. R2 is the feedback resistor and sets gain together with R1. R3 is the "Q-tuning" resistor — it lets you adjust Q without changing f₀ much (a key practical advantage).

Real-world example: A DTMF tone decoder needs to detect 1209 Hz (the column tone for keys 1, 4, 7, *). Target Q = 8, gain = 10 (20 dB). Pick C = 10 nF (good general-purpose film cap value). Then:

• R2 = Q / (π·f₀·C) = 8 / (π·1209·10nF) ≈ 210 kΩ → use 220 kΩ
• R1 = R2 / (2·A₀) = 220k / 20 = 11 kΩ → use 11 kΩ
• R3 = R1 / (4Q² − 2A₀) ≈ 11k / (256 − 20) ≈ 47 Ω

That tiny R3 value is a warning sign — at Q = 8 with gain = 10, you're pushing the topology. Rule of thumb: keep Q² × gain ≤ 100·(GBW/f₀) for your op-amp. A TL072 (GBW ≈ 3 MHz) at 1.2 kHz handles this easily; an LM358 (GBW ≈ 1 MHz) would already be marginal.

Use 1% resistors and C0G/NP0 or film capacitors — center frequency shifts directly with component tolerance, and Q amplifies any mismatch. Cascade two identical stages for sharper skirts (Q effectively rises by √2 in the combined response).