1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
|
\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2, thick]
\tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
\tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
\begin{scope}[xscale=0.9, yscale=1.8]
\draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$};
\draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
\begin{scope}[xshift=0cm]
\clip(-4.5,-1.25) rectangle (4.5,1.25);
\fill[yellow!30] (0,0) rectangle (1, 0.5);
\foreach \i in {-2,...,1} {
\foreach \j in {-2,...,1} {
\begin{scope}[xshift=\i*4cm, yshift=\j*1cm]
\draw[->, thick, orange!50] (0, 0) -- (0,0.5);
\draw[->, thick, darkgreen!50] (1, 0) -- (0,0);
\draw[->, thick, cyan!50] (2, 0) -- (1,0);
\draw[->, thick, blue!50] (2,0.5) -- (2, 0);
\draw[->, thick, purple!50] (1, 0.5) -- (2,0.5);
\draw[->, thick, red!50] (0, 0.5) -- (1,0.5);
\draw[->, thick, orange!50] (0,1) -- (0,0.5);
\draw[->, thick, blue!50] (2,0.5) -- (2, 1);
\draw[->, thick, purple!50] (3, 0.5) -- (2,0.5);
\draw[->, thick, red!50] (4, 0.5) -- (3,0.5);
\draw[->, thick, cyan!50] (2, 0) -- (3,0);
\draw[->, thick, darkgreen!50] (3, 0) -- (4,0);
\end{scope}
}
}
\draw[ultra thick, ->, orange] (0, 0) -- (0,0.5);
\draw[ultra thick, ->, darkgreen] (1, 0) -- (0,0);
\draw[ultra thick, ->, cyan] (2, 0) -- (1,0);
\draw[ultra thick, ->, blue] (2,0.5) -- (2, 0);
\draw[ultra thick, ->, purple] (1, 0.5) -- (2,0.5);
\draw[ultra thick, ->, red] (0, 0.5) -- (1,0.5);
\foreach \i in {-2,...,1} {
\foreach \j in {-2,...,1} {
\begin{scope}[xshift=\i*4cm, yshift=\j*1cm]
\node[zero] at ( 1, 0) {};
\node[zero] at ( 3, 0) {};
\node[pole] at ( 1,0.5) {};
\node[pole] at ( 3,0.5) {};
\end{scope}
}
}
\end{scope}
\draw[gray] ( 1,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north west] {\small $K$};
\draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=south east]{\small $jK^\prime$};
\end{scope}
\node[zero] at (4,3) (n) {};
\node[anchor=west] at (n.east) {Nullstelle};
\node[pole, below=0.25cm of n] (n) {};
\node[anchor=west] at (n.east) {Polstelle};
\begin{scope}[yshift=-4cm, xscale=0.75]
\draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$};
\draw[ultra thick, ->, purple] (-5, 0) -- (-3, 0);
\draw[ultra thick, ->, blue] (-3, 0) -- (-2, 0);
\draw[ultra thick, ->, cyan] (-2, 0) -- (0, 0);
\draw[ultra thick, ->, darkgreen] (0, 0) -- (2, 0);
\draw[ultra thick, ->, orange] (2, 0) -- (3, 0);
\draw[ultra thick, ->, red] (3, 0) -- (5, 0);
\node[anchor=south] at (-5,0) {$-\infty$};
\node[anchor=south] at (-3,0) {$-1/k$};
\node[anchor=south] at (-2,0) {$-1$};
\node[anchor=south] at (0,0) {$0$};
\node[anchor=south] at (2,0) {$1$};
\node[anchor=south] at (3,0) {$1/k$};
\node[anchor=south] at (5,0) {$\infty$};
\end{scope}
\end{tikzpicture}
|
