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It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
Still image of a movie of increasing magnification on 0.001643721971153 − 0.822467633298876i Still image of an animation of increasing magnification. There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software.
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 ...
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 ...
# set terminal svg enhanced size 875 1250 fname "Times" fsize 25 set terminal postscript enhanced portrait dashed lw 1 "Helvetica" 14 set output "bode.ps" # ugly part of something G(w,n) = 0 * w * n + 100000 # 1 / (sqrt(1 + w**(2*n))) dB(x) = 0 + x + 100000 # 20 * log10(abs(x)) P(w) = w * 0 + 200 # -atan(w)*180/pi # Gridlines set grid # Set x axis to logarithmic scale set logscale x 10 set ...
We may graphically solve for as the intersection of two curves in the (,) plane: {= + = For fixed ,,, the second curve is a fixed hyperbola in the first quadrant. The first curve is a parabola with shape y = 9 16 β 2 ( z 2 ) 2 {\textstyle y={\tfrac {9}{16}}\beta ^{2}(z^{2})^{2}} , and apex at location ( 4 3 β ( ω 2 − α ) , δ 2 ω 2 ...
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The code is kind of kludgy, but makes a good output. Generated in gnuplot with the script below (save as butterworth_bode_plot.plt and then open in gnuplot). Then it was postprocessed with Inkscape. See Wikipedia graph-making tips. Many orders on one plot: Image:Butterworth orders.png