Search results
Results from the WOW.Com Content Network
The following Python code can also be used to calculate and plot the root locus of the closed-loop transfer function using the Python Control Systems Library [14] and Matplotlib [15]. import control as ct import matplotlib.pyplot as plt # Define the transfer function sys = ct .
These bear his name, Bode gain plot and Bode phase plot. "Bode" is often pronounced as which is a Dutch pronunciation, closer to English / ˈ b oʊ d ə / BOH-d. [2] [3] Bode was faced with the problem of designing stable amplifiers with feedback for use in telephone networks.
Bode plot illustrating phase margin. In electronic amplifiers, the phase margin (PM) is the difference between the phase lag φ (< 0) and -180°, for an amplifier's output signal (relative to its input) at zero dB gain - i.e. unity gain, or that the output signal has the same amplitude as the input.
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f 0 dB = βA 0 × f 1. Next, the choice of pole ratio τ 1 /τ 2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode ...
Tools include the root locus, the Nyquist stability criterion, the Bode plot, the gain margin and phase margin. More advanced tools include Bode integrals to assess performance limitations and trade-offs, and describing functions to analyze nonlinearities in the frequency domain.
The Bode plot of a transimpedance amplifier that has a compensation capacitor in the feedback path is shown in Fig. 5, where the compensated feedback factor plotted as a reciprocal, 1/β, starts to roll off before f i, reducing the slope at the intercept. The loop gain is still unity, but the total phase shift is not a full 360°.
A simple example of this is a pure time delay of time T, which has amplitude 1 at any frequency regardless of T, but has a phase dependent on T (specifically, phase = 2π × T × frequency). There is, however, a unique amplitude-vs-phase relation in the special case of a minimum phase system, [ 9 ] sometimes called the Bode gain–phase relation .
Hendrik Wade Bode (/ ˈ b oʊ d i / BOH-dee, Dutch:; [1] December 24, 1905 – June 21, 1982) [1] was an American engineer, researcher, inventor, author and scientist, of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.