Enter control loop data
Example data table
| Case | Magnitude at phase crossover | Frequency | Computed gain margin | Interpretation |
|---|---|---|---|---|
| Drive loop A | -8.5 dB | 42 Hz | 8.5 dB | Healthy reserve for many tuned loops. |
| Thermal loop B | 0.55 ratio | 3.2 rad/s | 5.19 dB | Borderline margin. Review controller gain carefully. |
| Position loop C | -14.0 dB | 65 Hz | 14.0 dB | Robust reserve with more tuning headroom. |
Formula used
Linear gain margin: GMlinear = 1 / |L(jωpc)|
Decibel gain margin: GMdB = 20 log10(GMlinear) = -MagnitudedB at ωpc
Margin after proposed gain change: GMnew = GMdB - 20 log10(1 + ΔG/100)
Buffered margin: GMbuffered = GMdB - uncertainty allowance
The phase crossover frequency ωpc is the frequency where loop phase reaches -180 degrees. Gain margin measures how much open-loop gain can increase before the system reaches the stability boundary at that frequency.
The calculator also estimates how much additional gain remains while still preserving a target margin after accounting for uncertainty. This helps compare current tuning with a more conservative engineering limit.
How to use this calculator
- Choose whether your measured open-loop magnitude is in decibels or linear ratio.
- Enter the magnitude at the phase crossover frequency, where phase equals -180 degrees.
- Enter the crossover frequency and select either hertz or radians per second.
- Set your desired minimum margin, proposed gain change, and uncertainty allowance.
- Press the calculate button. Review the result block above the form, then export it as CSV or PDF if needed.
Frequently asked questions
1. What does gain margin tell me?
Gain margin shows how much loop gain can increase before the closed-loop system reaches instability. Larger positive margins usually indicate greater tolerance to model error, component drift, and tuning changes.
2. Why is the phase crossover frequency important?
Gain margin is evaluated at the frequency where the loop phase equals -180 degrees. At that point, extra gain can push the loop to the stability boundary, so the magnitude there matters directly.
3. Can I enter magnitude as a linear ratio?
Yes. Select the linear ratio mode when your Bode data or simulation provides absolute magnitude instead of decibels. The calculator converts it automatically and reports both linear and decibel results.
4. What happens if gain margin is negative?
A negative value means the magnitude at phase crossover is already above unity. That indicates the loop is unstable or extremely close to instability under the measured condition.
5. Why include uncertainty allowance?
Measurements, modeling assumptions, and plant variation can reduce real stability reserve. The uncertainty allowance subtracts a chosen buffer from the nominal margin, giving a more conservative decision value.
6. What does proposed gain change mean?
It represents a planned percentage increase or decrease in controller gain. The tool estimates how that change alters the available gain margin before you apply the adjustment to your loop.
7. What is a reasonable target gain margin?
Many practical control designs aim for several decibels of positive reserve, often around 6 dB or more. The best target depends on plant uncertainty, response speed, noise sensitivity, and operating risk.
8. Does this replace full stability analysis?
No. Gain margin is useful, but it should be reviewed alongside phase margin, bandwidth, time-domain response, nonlinear effects, delays, and operating constraints before final design decisions.