Two different ways of visualizing the same thing — how a control system responds across every frequency, and how close that response is to becoming unstable.
Both Bode and Nyquist plots answer the same underlying question — how does a control system respond across every possible input frequency, and how close is that response to instability? They present the answer differently: a Bode plot shows magnitude and phase as two separate graphs against frequency; a Nyquist plot combines both into a single curve on the complex plane, with the point (-1, 0) marking the threshold of instability. Adjust the corner frequency and open-loop gain above to see how both representations shift together.
A Bode plot has two parts sharing the same frequency axis: the magnitude plot shows how much a system amplifies or attenuates a signal at each frequency (in decibels), and the phase plot shows how much the output signal is delayed relative to the input at that same frequency. Reading them together tells you not just how a system responds, but how quickly that response degrades as frequency increases — the corner frequency is where the response starts rolling off, a critical design parameter for filters and control-loop bandwidth.
The Nyquist plot takes the same open-loop frequency response and plots it as a single curve in the complex plane, parameterized by frequency. Its distinguishing value is the Nyquist stability criterion: whether the plotted curve encircles the critical point (-1, 0) tells you directly whether the closed-loop system will be stable, without needing to solve the closed-loop characteristic equation explicitly. This makes it especially useful for systems where the open-loop response is known (from measurement or simulation) but an explicit transfer function isn't easily available.
Gain margin (how much the gain could increase before the system becomes unstable) and phase margin (how much additional phase lag could be tolerated before instability) are the two standard measures of "how close to unstable" a control loop is — both readable directly from a Bode plot at specific frequencies (where phase crosses -180° for gain margin, where magnitude crosses 0 dB for phase margin). A design with too little margin is fragile — small changes in the real system (component tolerances, temperature effects) can push it into instability; too much margin often means a sluggish, overly conservative response.
Decibels (a logarithmic scale) compress a very wide range of gain values into a readable plot, and — critically — they turn multiplication of transfer function terms into addition, since log(a×b) = log(a) + log(b). This makes Bode plots of complex systems (built from multiple simpler stages) easy to construct by simply adding each stage's individual Bode plot.
The point (-1, 0) on the complex plane represents the specific gain and phase combination (gain of 1, phase of exactly 180°) that would make the closed-loop system's denominator equal zero — the mathematical signature of instability. The Nyquist stability criterion checks whether the open-loop frequency response curve encircles this point to determine closed-loop stability.
Neither is strictly better — they show the same underlying information differently. Bode plots are generally easier to sketch by hand and to read gain/phase margin values directly off, which is why they're more commonly used for everyday controller design and tuning. Nyquist plots are more rigorous for stability analysis of certain system types (especially those with right-half-plane poles) where the Bode-based margin readings can be misleading.
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