Frequency Response Online Calculator

Calculate gain, phase, cutoff, resonance, bandwidth, impedance, and Bode response for RC, RL, RLC, and custom transfer function systems online with clear visual results.

Calculator Inputs


Component Values

Custom Transfer Function

Descending powers of s. Example: 1, 10.
Example: 1, 2, 100 for s² + 2s + 100.
Separate values with commas or semicolons.
Complex example: -10+20j; -10-20j.

Frequency Sweep and Display

Formula Used

Angular frequency: ω = 2πf
Magnitude: |H(jω)| = √(Re(H)² + Im(H)²)
Gain: GdB = 20 log10|H(jω)|
Phase: φ = atan2(Im(H), Re(H))
RC cutoff: fc = 1/(2πRC)
RL cutoff: fc = R/(2πL)
RLC resonance: f0 = 1/(2π√LC)
Series RLC quality factor: Q = 2πf0L/R
Bandwidth: BW = R/(2πL) = f0/Q
Group delay: τg = −dφ/dω

Frequency response describes how a system changes sinusoidal signals across frequency. Magnitude shows amplification or attenuation, while phase shows timing displacement. These measures reveal bandwidth, resonance, stability, and practical operating limits.

How to Use This Calculator

  1. Select an RC, RL, RLC, or custom response model.
  2. Enter the evaluation frequency and required component values.
  3. Choose a sweep range, spacing method, and sample count.
  4. For custom systems, enter coefficients or zero-pole-gain data.
  5. Select Calculate Response to generate values and Bode plots.
  6. Copy, print, or export the calculated data as needed.

Example Data

ModelRCLSuggested SweepExpected Behavior
RC low-pass1 kΩ0.1 µF10 Hz to 100 kHzAbout 1.59 kHz cutoff
RL high-pass100 Ω10 mH10 Hz to 100 kHzAbout 1.59 kHz cutoff
RLC band-pass50 Ω0.1 µF10 mH100 Hz to 100 kHzPeak near 5.03 kHz
Custom second-order1 Hz to 10 kHzUse numerator 100 and denominator 1, 10, 100

Frequently Asked Questions

What is frequency response?

Frequency response shows system gain and phase across frequencies. It reveals where signals pass, weaken, peak, or shift. Engineers use it to evaluate filters and control systems.

What does a negative decibel value mean?

A negative decibel value means the output is attenuated. Zero decibels represents a magnitude ratio of one. Positive values indicate amplification relative to the selected input.

What is the cutoff frequency?

Cutoff usually marks the half-power response point. Its amplitude is approximately 0.707 of the passband value. This corresponds to about negative three decibels.

Why use a logarithmic frequency sweep?

Logarithmic spacing covers many frequency decades efficiently. It gives balanced visibility across low and high frequencies. Bode plots normally use this horizontal scale.

What is resonance in an RLC circuit?

Resonance occurs when inductive and capacitive reactances cancel. The series circuit impedance then becomes mainly resistive. Response strength depends strongly on resistance and topology.

What does the quality factor represent?

Quality factor measures resonance sharpness and energy storage. Higher values produce narrower bandwidth and stronger selectivity. Lower values create broader and more damped responses.

Can I enter a custom transfer function?

Yes, enter polynomial coefficients in descending powers. You may also enter zeros, poles, and gain. Complex values can use forms such as -3+4j.

How are stability margins estimated?

Phase margin uses the approximate zero-decibel crossover frequency. Gain margin uses the approximate negative-180-degree phase crossover. Results depend on the selected frequency sweep range.

Why is group delay unavailable sometimes?

Group delay requires phase change around the evaluation frequency. It cannot be estimated at sweep endpoints reliably. Expand the sweep range around the chosen frequency.

Are component tolerances included?

The calculator uses the exact entered component values. Manufacturing tolerances and parasitic effects are not automatically modeled. Consider worst-case analysis for production circuit design.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.