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Figures 2-5 further illustrate construction of Bode plots. This example with both a pole and a zero shows how to use superposition. To begin, the components are presented separately. Figure 2 shows the Bode magnitude plot for a zero and a low-pass pole, and compares the two with the Bode straight line plots.
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 ...
Bode magnitude plot for the voltages across the elements of an RLC series circuit. Natural frequency ω 0 = 1 rad/s, damping ratio ζ = 0.4. Sinusoidal steady state is represented by letting s = jω, where j is the imaginary unit. Taking the magnitude of the above equation with this substitution:
Linearity and time-invariance are important because they are the only types of systems that can be easily solved using conventional analog signal processing methods. Once a system becomes non-linear or non-time-invariant, it becomes a non-linear differential equations problem, and there are very few of those that can actually be solved.
It is sometimes taken to be the point in the filter response where a transition band and passband meet, for example, as defined by a half-power point (a frequency for which the output of the circuit is approximately −3.01 dB of the nominal passband value). Alternatively, a stopband corner frequency may be specified as a point where a ...
The achievable H ∞ norm of the closed loop system is mainly given through the matrix D 11 (when the system P is given in the form (A, B 1, B 2, C 1, C 2, D 11, D 12, D 22, D 21)). There are several ways to come to an H ∞ controller: A Youla-Kucera parametrization of the closed loop often leads to very high-order controller.
This page was last edited on 19 July 2005, at 14:41 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
# 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 ...