Band-Pass Filter Calculator

Band-pass filtering became an engineering necessity with the birth of frequency-division multiplexing in long-distance telephony. George Campbell at AT&T filed his seminal filter patent in 1915 describing how cascaded reactive networks could separate several simultaneous voice channels onto one pair of copper wires by assigning each channel a distinct frequency band. The mathematics of synthesizing a desired pass-band from R, L, and C elements was formalized through the 1920s and 30s by Wilhelm Cauer in Germany, Otto Brune at MIT, and Sidney Darlington at Bell Labs — a body of work still taught as "network synthesis" today.

The first radio receivers in the 1900s–1920s used simple LC tank circuits as crude band-pass filters tuned to a single station frequency. The superheterodyne architecture invented by Edwin Armstrong in 1918 moved the selective filtering to a fixed intermediate frequency, which allowed much tighter, more selective band-pass stages (crystal filters, ceramic filters, mechanical filters) that no tunable LC tank could match. Every modern AM/FM radio, TV, and cell phone still uses this basic architecture: convert to an IF, then band-pass filter with a fixed-frequency high-Q element.

The simple RC-RC passive band-pass in this calculator sits at the low-complexity end of the filter family. It's fine for voice telephony (300–3400 Hz), ECG front-ends, and basic audio splitting. For selective RF, steep audio equalizers, or biomedical filters demanding low insertion loss, you'd move to LC resonators, Sallen-Key active filters, biquads, or digital FIR/IIR implementations — all descendants of the same Campbell/Cauer/Darlington theory.

Enter the desired lower and upper −3 dB cutoff frequencies and a common capacitance value; this tool solves for the two resistors in an RC-RC cascade (one high-pass stage, one low-pass stage) and reports center frequency, Q-factor, and bandwidth. The frequency response plot shows gain in dB versus log frequency.

One practical note: the two RC stages load each other through the intermediate node, which broadens the response slightly beyond the ideal product of the two transfer functions. For a perfect passive design, buffer between stages with an op-amp follower; or just live with the slight Q reduction — for most signal-band applications it's unnoticeable. Everything runs in your browser; no values are sent to a server.