Frequency Response Online Calculator

Calculator Form

Frequency Sweep Table

Example Data Table

Formula Used

Angular frequency:
ω = 2πf

Gain ratio:
Gain = |Vout / Vin|

Gain in decibels:
Gain dB = 20 log10(Gain)

Output amplitude:
Vout = Vin × Gain

RC low pass:
|H| = 1 / √(1 + (ωRC)²)
Phase = -tan⁻¹(ωRC)
fc = 1 / (2πRC)

RC high pass:
|H| = ωRC / √(1 + (ωRC)²)
Phase = 90° - tan⁻¹(ωRC)
fc = 1 / (2πRC)

RL low pass:
|H| = R / √(R² + (ωL)²)
Phase = -tan⁻¹(ωL / R)
fc = R / (2πL)

RL high pass:
|H| = ωL / √(R² + (ωL)²)
Phase = 90° - tan⁻¹(ωL / R)
fc = R / (2πL)

Series RLC band pass:
|H| = R / √(R² + (ωL - 1 / ωC)²)
f0 = 1 / (2π√LC)
Q = √(L / C) / R
Bandwidth = f0 / Q

How To Use This Calculator

1. Select the response model that matches your circuit or physics example.
2. Enter resistance, capacitance, inductance, and their correct units.
3. Add the test frequency for the main result.
4. Enter input amplitude if you need output amplitude.
5. Set sweep start, sweep end, and number of points.
6. Choose logarithmic sweep for wide frequency ranges.
7. Press the calculate button to show results above the form.
8. Use CSV or PDF buttons to save your report.

Article: Calculating Frequency Response Online

What Frequency Response Means

Frequency response describes how a system reacts across frequency. It shows gain, phase shift, cutoff behavior, and resonance. In physics, this idea appears in circuits and acoustics. It also appears in vibration, sensors, and control systems. A signal may pass strongly at one frequency. It may weaken at another. The graph tells that story clearly.

Why Gain And Phase Matter

Gain compares output amplitude with input amplitude. A gain above one means amplification. A gain below one means attenuation. Decibel gain makes large ranges easier to read. Phase shows timing shift between input and output. A negative phase means the output lags. A positive phase means the output leads. Together, gain and phase explain stability. They also explain filtering and signal quality.

Common Physical Models

Simple filters are useful teaching models. An RC low pass keeps low frequencies. It reduces high frequencies. An RC high pass does the reverse. RL filters behave similarly. Inductance controls their frequency response. A series RLC band pass becomes strongest near resonance. The resonant frequency depends on inductance and capacitance. Resistance controls damping, peak width, and quality factor.

Using This Tool For Study

This calculator accepts resistance, capacitance, inductance, input amplitude, and ranges. It computes angular frequency, gain ratio, decibel gain, and output amplitude. It also computes phase angle and cutoff frequency. Resonant frequency, quality factor, and bandwidth appear when supported. The sweep table helps compare many points quickly. It is useful before plotting. It also helps lab reports and homework checks.

Interpreting Results Carefully

Frequency response values depend on the assumed output point. For RC and RL filters, the model name states behavior. For RLC circuits, the band pass model uses resistance output. Real components have tolerance, heating, parasitic resistance, and limits. Therefore, calculated values should support analysis. They should not replace measured data. Use consistent units. Check every input before exporting reports.

Good Laboratory Practice

Start with expected component values. Then compare calculated points with measured points. Watch the slope near cutoff. Note phase movement near resonance. Use more sweep points for narrow peaks. Save exports after checking units. Add notes about probes, sources, and loads. This makes results clearer for future review. Record assumptions beside each exported result.

FAQs