CALCULATORS / CONTROL SYSTEMS AND DYNAMIC RESPONSE

Stability margins from crossover measurements calculator

Margins from supplied measured crossover gain/phase; does not find crossovers.

controls-stability-margins.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	phaseMargindeg	gainMargin	gainMarginDb
	45	2	6.0206
	72	2	6.0206

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

phase margin target45.00 deg✓ passes

BASELINE INPUTS

phaseAtGainCrossover-135 deggainAtPhaseCrossover0.5

CALCULATED

phaseMargin45 deg

gainMargin2

gainMarginDb6.0206

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Gain and phase margins
# Scope: Margins from supplied measured crossover gain/phase; does not find crossovers.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

phaseAtGainCrossover = -135 deg
gainAtPhaseCrossover = 0.5

phaseMargin := 180 deg+phaseAtGainCrossover [deg]
gainMargin := 1/gainAtPhaseCrossover
gainMarginDb := 20*log10(gainMargin)

check phase margin target: phaseMargin >= 30 deg

scenario alternative: phaseAtGainCrossover = -108 deg

Calculated from your source · not saved

Baseline · Baseline

phase margin target45.00 deg ✓ passes

alternative · alternative

phase margin target72.00 deg ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

phase margin: phaseMargin = 180 deg+phaseAtGainCrossover [deg]
gain margin: gainMargin = 1/gainAtPhaseCrossover
gain margin db: gainMarginDb = 20*log10(gainMargin)

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

phase at gain crossover: -135 deg
gain at phase crossover: 0.5

Calculated

phase margin: 45 deg
gain margin: 2
gain margin db: 6.0206

Assumptions and limits

Margins from supplied measured crossover gain/phase; does not find crossovers.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Gain and phase margins. Inputs: open-loop transfer function; delays. Outputs: crossover frequencies; gain/phase margins. Model scope: Declared linear or low-order nonlinear plant models. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: open-loop transfer function, delays
Outputs: crossover frequencies, gain/phase margins
Modes: calculate, compare, sweep
Drawing: Response and stability plots

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS