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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.
A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel. By convention, the poles of the system are indicated in the plot by an X while the zeros are indicated by a circle or O.
The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode gain plot for the two-pole amplifier in the range of frequencies up to the second pole position. The assumption behind Figure 5 is that the frequency f 0 dB lies between the lowest pole at f 1 = 1/(2πτ 1) and the second pole at f 2 = 1/(2πτ 2). As indicated in ...
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For example, a polynomial of degree n has a pole of degree n at infinity. The complex plane extended by a point at infinity is called the Riemann sphere . If f is a function that is meromorphic on the whole Riemann sphere, then it has a finite number of zeros and poles, and the sum of the orders of its poles equals the sum of the orders of its ...
The final step depends on the geometry of the waveguide. The easiest geometry to solve is the rectangular waveguide. In that case, the remainder of the Laplacian can be evaluated to its characteristic equation by considering solutions of the form ψ ( x , y , z , t ) = ψ 0 e i ( ω t − k z z − k x x − k y y ) . {\displaystyle \psi (x,y,z ...
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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.