Frequency Response & Stability Simulators

How to Use

1. Select filter topology (Butterworth, Chebyshev, or Bessel) from the dropdown
2. Set cutoff frequency (Hz) and filter order (2–8) using numeric inputs
3. Enter system input signal frequency range (0.1–10 kHz) to sweep the magnitude and phase response
4. Run simulation; view Bode plot, pole-zero map, and step-response overshoot
5. Export stability margin data (gain margin in dB, phase margin in degrees) for control system verification

Worked Example

Design a 4th-order Butterworth low-pass filter with cutoff at 500 Hz for a robotic servo motor feedback loop. Applying the simulator: cutoff fc=500 Hz, order n=4. At 100 Hz (−3 dB point), magnitude = −3.01 dB, phase = −45°. At 5 kHz (10× cutoff), attenuation = −80 dB, phase ≈ −360°. Gain margin = 12 dB, phase margin = 58°—sufficient stability for 0.2 kg payload with 50 rad/s natural frequency.

Practical Notes

1. Butterworth filters suit servo control (maximally flat passband); Chebyshev allows steeper rolloff but introduces ripple and phase distortion—avoid for precision trajectory tracking
2. Verify nyquist stability by checking pole locations remain in left half-plane; simulator flags instability if any pole Re > 0
3. Cross-reference phase margin ≥ 45° and gain margin ≥ 6 dB for industrial robotic arms operating at ±10% load variation
4. Filter delay (group delay) at cutoff ≈ 1/(2πfc × n); account in real-time closed-loop sampling at 1 kHz and above