What Is the Bode Gain & Phase Margin Stability Calculator?
Bode margins quantify how close a feedback loop is to the critical -1 point (180° lag and unity gain) in the frequency domain.
How Does the Bode Gain & Phase Margin Stability Calculator Work?
Evaluates complex transfer function magnitude and phase across frequency to identify crossover points.
Bode Gain & Phase Margin Stability Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
ext{PM} = 180^circ + angle G(jomega_{ ext{gc}}), quad ext{GM(dB)} = -20 log_{10} |G(jomega_{ ext{pc}})|
Classical frequency-domain definitions of Gain Margin and Phase Margin.
How to Use the Bode Gain & Phase Margin Stability Calculator
- Enter forward gain K and three real pole frequencies in rad/s.
Step-by-Step Example Calculation
Feedback Control Loop Tuning
Input Values:
staticGainK:25
poleP1RadS:2
poleP2RadS:8
poleP3RadS:30
Worked Steps: Phase Margin = 52.1° at w_gc = 4.2 rad/s, Gain Margin = 11.4 dB at w_pc = 12.8 rad/s (Closed-loop Stable).
Understanding Your Result
Displays Phase Margin in degrees, Gain Margin in dB, and whether closed-loop response is stable.
Factors That Affect the Result
- Higher loop gains push crossover to higher frequencies, eroding Phase Margin toward instability.
When Should You Use This Calculator?
- Tuning PID controllers, servo amplifiers, and power electronic compensators.
Assumptions & Limitations
- Applies to minimum-phase open-loop transfer functions with unity feedback.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard frequency response numerical solver.