passband filter calculator

What this passband filter calculator does

A passband (or band-pass) filter is designed to let a specific frequency range pass while attenuating frequencies below and above that range. This calculator is made for fast early-stage design work. It helps you move from target frequencies to useful engineering values in one step.

Given f_L and f_H, it computes:

• Center frequency (f₀) using the geometric mean
• Bandwidth (BW) as the difference between upper and lower edges
• Quality factor (Q) to show filter selectivity
• Optional gain conversion from dB to linear ratio
• Optional series RLC estimate if capacitor value is supplied

Core formulas used

1) Center frequency and bandwidth

f₀ = √(f_L × f_H)
BW = f_H − f_L

The geometric mean better represents center behavior in many band-pass designs, especially on logarithmic frequency scales.

2) Quality factor (Q)

Q = f₀ / BW

A larger Q means a narrower, more selective passband. A lower Q means a broader passband.

3) Optional gain conversion

A_v = 10^{(Gain dB / 20)}

This is useful for active filter stages where passband gain is part of the target response.

4) Optional series RLC starting values

If you enter capacitor value C (in nF), the calculator estimates:

• L = 1 / (ω₀²C)
• R = 1 / (ω₀CQ)

where ω₀ = 2πf₀. These are practical first-pass values to begin simulation and refinement.

How to use it effectively

1. Enter lower and upper passband edge frequencies in Hz.
2. Click Calculate to get f₀, BW, and Q.
3. If needed, include gain in dB and/or capacitor in nF for additional outputs.
4. Use the computed values in SPICE or your preferred circuit tool.
5. Tune for real component tolerances and source/load impedance effects.

Worked example

Suppose your target passband is from 1 kHz to 5 kHz.

• f_L = 1000 Hz
• f_H = 5000 Hz
• f₀ = √(1000×5000) ≈ 2236 Hz
• BW = 5000 − 1000 = 4000 Hz
• Q ≈ 2236 / 4000 = 0.559

This is a relatively broad band-pass response. If you need tighter selectivity, narrow the bandwidth relative to center frequency.

Practical design tips

Component tolerance matters

Even 5% capacitors and inductors can shift the final passband noticeably. Use tighter tolerances for precision designs.

Source and load impedance can reshape response

Real-world source and load conditions can detune your expected cutoff frequencies and flatten or peak the passband.

Use this as a starting point, then simulate

For production designs, always verify in simulation (AC sweep, Monte Carlo tolerance runs) before hardware build.