Bandpass Filter Calculator

Bandpass Filter Calculator results give the center, Q and part values for an LC ladder, a passive RC pair or an MFB op-amp stage, plus the stopband loss at a frequency you specify.

Bandpass Filter Calculator for LC, RC and Op-Amp Designs

A bandpass filter lets one range of frequencies through and blocks what lies above and below it. The right build depends on the job, so an RF band filter, a voice-band audio filter and a tone detector need very different parts.

Radio amateurs and RF builders use the LC mode for receiver front ends and transmitter cleanup on bands from 1.8 to 440 MHz. Audio and sensor designers use the RC and op-amp modes for signals from a few hertz to tens of kilohertz.

The Bandpass Filter Calculator handles all three. It returns the center frequency, bandwidth and Q, every component value, and a check of how much the design passes or blocks at any frequency you test.

Three Filter Types in the Bandpass Filter Calculator

LC Passive (RF) takes the lower and upper band edges in MHz, a Butterworth or Chebyshev response, an order from 2 to 9 and the system impedance in ohms. The accordion sets whether the ladder starts with a shunt resonator (Pi) or a series one (T), and the frequency to check for attenuation.

RC Passive (Audio) takes the lower and upper cutoffs in hertz and the first resistor. Active MFB (Op-Amp) takes the two -3 dB edges, the gain wanted at center and one capacitor value used for both capacitors.

Center Frequency, Bandwidth and Q

Every bandpass filter is centered on the geometric mean of its two edges, not the midpoint. The bandwidth is the difference between the edges, and Q is the center divided by that bandwidth.

$$f_0=\sqrt{f_L\times f_H}$$

$$Q=\frac{f_0}{f_H-f_L}$$

In the Bandpass Filter Calculator, the 88 to 108 MHz FM broadcast band gives a center of 97.488 MHz rather than 98 MHz, with a Q of 4.87 and a 20.5% fractional bandwidth. Tuning every resonator to the arithmetic midpoint is the common mistake, and it skews the passband toward the upper edge.

LC Ladder Values From the Lowpass Prototype

The LC mode starts from a normalized lowpass prototype whose element values g are listed in standard tables, such as the RF Cafe Chebyshev prototype table. A 5th-order 0.1 dB Chebyshev uses 1.1468, 1.3712 and 1.9750, mirrored about the middle.

Each prototype element becomes a resonator tuned to the center, using the fractional bandwidth FBW, which is the bandwidth over the center. Series arms get an inductor and capacitor in series, and shunt arms get them in parallel.

$$L_{series}=\frac{g\times Z_0}{{\omega }_0\times FBW}$$

$$C_{shunt}=\frac{g}{{\omega }_0\times FBW\times Z_0}$$

The default FM band filter in a 50 Ω Pi layout starts with a 14.60 nH and 182.5 pF shunt resonator, followed by a 545.6 nH and 4.885 pF series resonator. Its largest coil is 64 times its smallest, which the fourth card reports as the inductor spread.

That spread grows fast as the band narrows. The same design at 1% bandwidth needs a coil ratio over 25,000 to 1, and CERN's analog electronics course notes point out that very narrow filters suit coupled resonators, while very wide ones are easier as a lowpass and highpass in cascade.

Even orders of a Chebyshev filter cannot have equal source and load impedances, as the RF Cafe table notes. The Bandpass Filter Calculator warns when an even order is picked, so choose 3, 5, 7 or 9 to keep both ends at 50 Ω.

Stopband Attenuation and Chebyshev Ripple

To check a frequency outside the band, the Bandpass Filter Calculator maps it back to the prototype with Ω = (f/f0 - f0/f)/FBW. A Butterworth response then loses the following amount in decibels, where N is the order.

$$A=10{\log }_{10}\left(1+{\Omega }^{2N}\right)$$

Chebyshev filters trade a small passband ripple for a steeper skirt. At 144 MHz, the default 5th-order 0.1 dB Chebyshev blocks 66.1 dB, against 59.1 dB for a 5th-order Butterworth, 30.7 dB for a 3rd-order Chebyshev and 101.5 dB for a 7th-order one.

The band edges of a Chebyshev design are ripple edges, not -3 dB points. The default filter is 20 MHz wide at its 0.1 dB edges but 22.694 MHz wide at -3 dB, which the third card shows.

These figures assume lossless parts. Real coils and capacitors add passband loss, so the alert asks for component Q well above ten times the filter's loaded Q, or about 49 for the FM band design.

Passive RC Bandpass for Audio

The RC mode chains a high-pass stage and a low-pass stage, each with its own corner from the simple RC formula. The second stage uses ten times the first resistor so it loads the first one less.

$$f_c=\frac{1}{2\pi RC}$$

For a 300 to 3,400 Hz voice band with a 10 kΩ first resistor, that gives a 53.05 nF high-pass capacitor and a 0.468 nF low-pass capacitor. The two stages still interact, so the real -3 dB edges land at 256 Hz and 3,986 Hz, with 0.80 dB of loss at the 1,010 Hz center.

When the edges drift like this, the Bandpass Filter Calculator's alert suggests pre-warped corner values that bring the real edges back onto your targets. For a narrow band such as 800 to 1,200 Hz, the edges spread to 389 and 2,469 Hz, and no RC choice fixes that, so the tool points you to the MFB mode.

Active MFB Bandpass With One Op-Amp

The multiple-feedback (MFB) circuit uses one op-amp, two equal capacitors and three resistors. Audio designer Rod Elliott gives the design equations in his MFB bandpass article, where G is the gain at center.

$$R_1=\frac{Q}{G\times 2\pi f_{0}C}$$

$$R_2=\frac{Q}{(2Q^2-G)\times 2\pi f_{0}C}$$

$$R_3=\frac{Q}{\pi f_{0}C}$$

For 800 to 1,200 Hz with 10 nF capacitors and unity gain, the center is 979.8 Hz with a Q of 2.45. That gives R1 of 39.8 kΩ, R2 of 3.62 kΩ and R3 of 79.6 kΩ, which the cards round to E96 and E24 values.

The gain must stay below 2Q², or R2 turns negative, which caps this example at a gain of 12. The output is inverted, and the eCircuitCenter MFB bandpass guide notes the circuit is useful up to a Q of about 20, which is where the tool starts to warn.

The Bandpass Filter Calculator's fourth card also gives a minimum op-amp gain-bandwidth of ten times the center gain times the center frequency, about 9.8 kHz for the default. That follows the Analog Devices MT-218 MFB design tutorial, which asks for open-loop gain at the center at least 20 dB above the filter's peak response.

With less gain than that, the tutorial warns of Q multiplication, where the real response peaks higher and narrower than designed. For gain stages around the filter, the Op Amp Gain Calculator works out the feedback resistors.

Bandpass Filter Questions

Should I choose a Butterworth or Chebyshev bandpass filter?

Choose Butterworth for the flattest passband, and Chebyshev for faster rejection outside the band. A 0.1 dB ripple is barely measurable, yet at the same 5th order it adds about 7 dB of rejection at 144 MHz for the FM band filter.

Larger ripple settings such as 0.5 or 1 dB give still steeper skirts. The trade-off is more ripple across the passband, so keep the ripple small where the signal level must stay even across the band.

What does 2nd order mean for a bandpass filter?

In the LC mode, the order is the number of resonators, so a 2nd-order LC filter has two LC pairs and four parts. More resonators give steeper skirts, as the 3rd, 5th and 7th order figures above show.

A single MFB stage is a 2nd-order bandpass with one resonance. Each side rolls off at 20 dB per decade, so steeper audio filters cascade two or more stages.

How do I design a narrow bandpass filter?

Narrow bands push each design type to its limit. For the 5th-order 0.1 dB LC design, the coil spread passes 100 to 1 below about 16% bandwidth, and the tool then suggests a coupled-resonator design instead.

For audio, a single MFB stage handles a Q up to about 20. Beyond that, two stagger-tuned stages hold their center better than one high-Q stage, since part tolerances shift a high-Q center the most.