Comparison

Bode Plot vs Nyquist Plot

Both Bode and Nyquist plots display how an open-loop system behaves across frequency, but they do it differently — Bode separates magnitude and phase on log-frequency axes, while Nyquist wraps the entire frequency response into a single polar curve. A control engineer checking a simple stable plant reaches for Bode; one dealing with a non-minimum phase system or an unstable plant opens a Nyquist plot because Bode cannot handle RHP open-loop poles directly.

EEE, ECE

Side-by-side comparison

ParameterBode PlotNyquist Plot
Plot typeTwo separate plots: |G(jω)| in dB vs log ω, ∠G(jω) vs log ωSingle polar plot: Im vs Re of G(jω) for ω from −∞ to +∞
Frequency axisLogarithmic (decades)No explicit frequency axis; frequency is implicit
Stability criterionGM > 0 dB and PM > 0° (only for open-loop stable plants)Nyquist criterion: Z = N + P (works for unstable plants too)
Handles unstable open-loop plant?No (Bode stability criterion invalid)Yes — counts encirclements of −1+j0
Gain margin read fromMagnitude plot at ωpcDistance from origin to −1 point crossing on real axis
Phase margin read fromPhase plot at ωgcAngle from negative real axis to phasor at |G|=1
Ease of constructionEasy — asymptotic straight-line approximationsHarder — requires full complex computation
Useful forLoop shaping, compensator design, quick stability checkRigorous stability of complex/non-minimum phase systems

Key differences

Bode plots are drawn using asymptotic straight-line approximations: each pole contributes −20 dB/decade and −45°/decade at the break frequency; each zero does the opposite. The Bode stability criterion (GM > 0 dB, PM > 0°) is valid only when the open-loop system is stable — use it for 90% of textbook problems. Nyquist plots apply the argument principle: the number of clockwise encirclements N of the −1+j0 point equals Z − P, where Z is closed-loop RHP zeros and P is open-loop RHP poles. For a stable closed-loop system, N must equal −P (counterclockwise encirclements cancel open-loop RHP poles).

When to use Bode Plot

Use a Bode plot when the open-loop plant is stable and you need to shape the loop — designing a lead compensator or checking gain and phase margin on an op-amp feedback network is fastest with Bode.

When to use Nyquist Plot

Use a Nyquist plot when the open-loop transfer function has right-half-plane poles or when the Bode criterion would give an incorrect result — analysing a conditionally stable system or a plant with an integrator that has been inverted requires the full Nyquist criterion.

Recommendation

For routine university exams, choose Bode — it is faster, graphically straightforward, and tested in most questions. Reserve Nyquist for questions that explicitly mention unstable open-loop poles, encirclements, or the Nyquist criterion.

Exam tip: GATE asks you to count encirclements of −1+j0 in a Nyquist plot and apply Z = N + P to determine closed-loop stability — practise with both clockwise (unstable) and counterclockwise (stabilising) encirclement examples.

Interview tip: Interviewers at embedded control and automotive companies expect you to state clearly when Bode stability criterion fails — specifically, when the open-loop system has poles in the right-half s-plane, and to name the Nyquist criterion as the correct alternative.

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