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Figure 1B: Low-pass filter (1st-order, one-pole) Bode magnitude plot (top) and Bode phase plot (bottom). The red data curve is approximated by the straight black line. In electrical engineering and control theory, a Bode plot (/ ˈ b oʊ d i / BOH-dee) is a graph of the frequency response of a system.
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let L be the loop transfer function and S be the sensitivity function .
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.
The great circle g (green) lies in a plane through the sphere's center O (black). The perpendicular line a (purple) through the center is called the axis of g, and its two intersections with the sphere, P and P ' (red), are the poles of g. Any great circle s (blue) through the poles is secondary to g. A great circle divides the sphere in two ...
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A generalization of the Smith chart to a three dimensional sphere, based on the extended complex plane (Riemann sphere) and inversive geometry, was proposed by Muller, et al in 2011. [ 26 ] The chart unifies the passive and active circuit design on little and big circles on the surface of a unit sphere, using a stereographic conformal map of ...
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
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