Side-by-side comparison
| Parameter | Bode Plot | Nyquist Plot |
|---|---|---|
| Plot type | Two separate plots: |G(jω)| in dB vs log ω, ∠G(jω) vs log ω | Single polar plot: Im vs Re of G(jω) for ω from −∞ to +∞ |
| Frequency axis | Logarithmic (decades) | No explicit frequency axis; frequency is implicit |
| Stability criterion | GM > 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 from | Magnitude plot at ωpc | Distance from origin to −1 point crossing on real axis |
| Phase margin read from | Phase plot at ωgc | Angle from negative real axis to phasor at |G|=1 |
| Ease of construction | Easy — asymptotic straight-line approximations | Harder — requires full complex computation |
| Useful for | Loop shaping, compensator design, quick stability check | Rigorous 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.