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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.
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
The way in which the radius can be used to specify the angle of rotation is not straightforward. It can be related to circles of latitude in a sphere with a defined north pole and is explained as follows: Beginning at the north pole of a sphere in three-dimensional space, we specify the point at the north pole to represent the identity rotation.
For a rational and continuous-time system, the condition for stability is that the region of convergence (ROC) of the Laplace transform includes the imaginary axis.When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the "largest pole", or the pole that has the greatest real part of any pole in the system.
The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot). Evans also invented in 1948 an analog computer to compute root loci, called a "Spirule" (after "spiral" and "slide rule"); it found wide use before the advent of digital computers.
The homothety scales the image by a factor of 2 (a ratio of a diameter to a radius of the sphere), hence the values X and Y produced by this projection are exactly twice those produced by the equatorial projection described in the preceding section. For example, this projection sends the equator to the circle of radius 2 centered at the origin.
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In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. In cartesian coordinates therefore the circle would pass through the points (+1,0) and (−1,0) on the x -axis and the points (0,+1) and (0,−1) on the y -axis.