Frequency Domain Analysis
While time-domain simulations show how a system responds to specific inputs, frequency-domain analysis reveals the complete input-output behavior at all frequencies simultaneously. A Bode plot decomposes this into two intuitive graphs: how much the system amplifies each frequency (magnitude) and how much it delays each frequency (phase). Together, they fully characterize a linear time-invariant system.
Reading the Bode Plot
The magnitude plot shows gain in decibels versus log frequency. A flat region means constant amplification, a -20 dB/decade slope indicates a single pole, and -40 dB/decade indicates a double pole or two cascaded poles. Resonance peaks reveal underdamped natural frequencies. The phase plot shows the cumulative phase shift — each pole contributes up to -90° of lag, distributed over two decades centered at the pole frequency.
Stability from Frequency Response
The Bode stability criterion states that a feedback system is stable if the open-loop gain is less than 0 dB when the phase reaches -180°. The gain margin quantifies how far below 0 dB the gain is at the phase crossover, while the phase margin measures how far above -180° the phase is at the gain crossover. Typical design targets are GM > 6 dB and PM > 30°–60° for robust performance.
Design with Bode Plots
Engineers use Bode plots to design compensators — lead networks that add phase at the crossover frequency to increase phase margin, and lag networks that reduce gain at high frequencies to increase gain margin. The graphical nature of Bode plots makes iterative design intuitive: reshape the magnitude and phase curves by adding poles, zeros, and gain until the stability margins and bandwidth meet specifications.