Calculator Inputs
Example Data Table
| Scenario | Input Basis | Key Inputs | Center Frequency | Bandwidth | Q |
|---|---|---|---|---|---|
| Audio tone selection | Cutoff analysis | fL = 500 Hz, fH = 5000 Hz | 1.581 kHz | 4.5 kHz | 0.351 |
| Sensor noise isolation | Center and Q | f0 = 2 kHz, Q = 2.5 | 2.000 kHz | 800 Hz | 2.500 |
| Series RLC prototype | RLC synthesis | L = 10 mH, C = 100 nF, R = 50 Ω | 5.033 kHz | 795.775 Hz | 6.325 |
Formula Used
From cutoff frequencies:
Center frequency: f0 = √(fL × fH)
Bandwidth: BW = fH − fL
Quality factor: Q = f0 / BW
From center frequency and quality factor:
Bandwidth: BW = f0 / Q
fL = f0 × [√(1 + 1 / 4Q²) − 1 / 2Q]
fH = f0 × [√(1 + 1 / 4Q²) + 1 / 2Q]
For a series RLC band pass network:
f0 = 1 / [2π√(LC)]
BW = R / (2πL)
Q = (1 / R) × √(L / C)
At resonance, XL = XC and the response peaks near the center frequency.
This calculator reports center frequency, bandwidth, lower cutoff, upper cutoff, Q, fractional bandwidth, damping ratio, and frequency-domain reference values. The generic analysis modes work for many active and passive band pass responses, while the synthesis mode specifically matches a series RLC implementation.
How to Use This Calculator
Choose the calculation mode that matches your design stage. Use cutoff analysis when you already know both edge frequencies. Use center frequency and Q when you are verifying a target response. Use the RLC option when you have component values and want resonance details.
Enter positive values only. Click Submit to display the result card above the form. Review the derived response data, then use the CSV or PDF buttons to save the output for reports, design notes, or client documentation.
For the most stable engineering workflow, keep all units consistent. This page expects hertz for frequency, millihenry for inductance, nanofarad for capacitance, and ohms for resistance.
Frequently Asked Questions
1. What does a band pass filter do?
A band pass filter passes frequencies inside a selected range and attenuates frequencies below and above that range. It is widely used in audio, sensors, communications, and instrumentation.
2. What is center frequency?
Center frequency is the resonant or peak-response point of the passband. For many filters, it is the geometric mean of the lower and upper cutoff frequencies.
3. What does Q mean in filter design?
Q, or quality factor, indicates how selective the filter is. A higher Q means a narrower bandwidth around the center frequency and sharper frequency discrimination.
4. Why are lower and upper cutoffs important?
These frequencies define the useful passband limits. They help engineers verify whether the filter admits the desired signal while rejecting nearby unwanted frequencies.
5. When should I use the RLC mode?
Use the RLC option when you already know inductance, capacitance, and resistance values. It is useful for prototype checks and resonance-based circuit analysis.
6. Can this calculator help with active filters?
Yes. The cutoff and center-frequency modes are generic response calculators, so they can be used to analyze many active or passive band pass targets.
7. What is fractional bandwidth?
Fractional bandwidth is bandwidth divided by center frequency. It shows how wide the passband is relative to its resonant location and is useful for comparing different designs.
8. Why does the calculator show damping ratio?
Damping ratio gives another view of selectivity and transient behavior. In second-order systems, it is directly related to Q, making it useful during control and filter tuning.