About

Signal processing often requires isolating a specific range of frequencies while attenuating those outside that range. A Band-Pass Filter allows signals between a lower cut-off frequency (f_L) and an upper cut-off frequency (f_H) to pass, rejecting DC components and high-frequency noise. This tool aids engineers and audio technicians in component selection for passive filter designs.

Getting the values of Resistors, Capacitors, and Inductors correct is crucial. An incorrect Center Frequency (f_c) can distort audio signals or cause data loss in communication protocols. This calculator handles standard and scientific notation (e.g., 4.7k, 10u) to streamline the design of both simple RC series filters and resonant RLC circuits.

Formulas

For a Series RLC Band-Pass Filter, the resonance occurs when inductive and capacitive reactances cancel out. The Center Frequency is calculated as:

f_c = 12π√LC

The Quality Factor (Q) determines the sharpness of the peak:

Q = 1R √LC

The cut-off frequencies define the bandwidth (BW = f_c / Q):

f_L,H = f_c √1 + (12Q)² ± 12Q

Reference Data

Parameter	Symbol	Unit	Formula Relationship
Resistor	R	Ω (Ohms)	Determines Bandwidth / Q
Capacitor	C	F (Farads)	Reactance X_C ∝ 1/f
Inductor	L	H (Henries)	Reactance X_L ∝ f
Center Frequency	f_c	Hz	Geometric Mean of f_L, f_H
Lower Cut-off	f_L	Hz	-3dB Point (Low)
Upper Cut-off	f_H	Hz	-3dB Point (High)
Quality Factor	Q	Dimensionless	Selectivity of the filter
Bandwidth	BW	Hz	f_H − f_L

Frequently Asked Questions

An RC (Resistor-Capacitor) filter is passive and simple but generally has a lower Quality Factor (Q), meaning the band-pass curve is wider and less selective. An RLC (adding an Inductor) allows for resonance, creating a much sharper peak and higher selectivity (High Q) around the center frequency.

This calculator supports engineering notation suffixes. You can type "10u" for 10 microfarads, "4.7k" for 4.7 kilo-ohms, or "100p" for 100 picofarads. The tool automatically converts these to standard base units (Farads, Ohms, Henries).

The -3dB points (or cut-off frequencies) represent the boundaries where the output power drops to half of the maximum pass-band power. This corresponds to the voltage dropping to roughly 70.7% of the maximum voltage.

No. This tool is designed for passive Series RLC or cascaded RC topologies. Active filters (using Op-Amps) require different formulas involving gain bandwidth products and feedback resistors.