How it works
Magnitude plot: each factor contributes a slope change at its corner frequency. A gain K contributes 20 log K dB (horizontal line). A pole at ω_c contributes a −20 dB/decade slope break at ω = ω_c; a zero contributes +20 dB/decade. An integrator 1/s contributes −20 dB/decade across all frequencies. Phase plot: each first-order pole contributes −45° at its corner frequency, ranging from 0° (one decade below) to −90° (one decade above). The actual magnitude error at the corner frequency is ±3 dB for a first-order factor.
Key points to remember
Gain margin (GM) = −20 log|G(jω_pc)| in dB, where ω_pc is the phase crossover frequency (where phase = −180°). Phase margin (PM) = 180° + ∠G(jω_gc), where ω_gc is the gain crossover frequency (where |G| = 0 dB). For a stable system, GM > 0 dB and PM > 0°. Typically PM of 30°–60° is desired; below 30° the transient response is highly oscillatory. A second-order system with ζ = 0.5 gives PM ≈ 52°. The Bode gain formula for Type 1 system: the −20 dB/decade line extended to ω = 1 gives 20 log K_v.
Exam tip
Every Anna University paper asks you to draw the Bode magnitude and phase plots for a given G(jω) and find gain and phase margins — tabulate the corner frequencies and slope contributions before drawing, because a missed corner frequency ruins the entire plot.