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# 36. bode

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## 36.1 Functions and Variables for bode

Function: bode_gain (H, range, … plot_opts …)

Function to draw Bode gain plots. To use this function write first `load(bode)`. See also `bode_phase`.

Examples:

Examples (1 through 7 from http://www.swarthmore.edu/NatSci/echeeve1/Ref/Bode/BodeHow.html, 8 from Ron Crummett):

```(%i1) load("bode")\$
(%i2) H1 (s) := 100 * (1 + s) / ((s + 10) * (s + 100))\$
(%i3) bode_gain (H1 (s), [w, 1/1000, 1000])\$
```

```(%i4) H2 (s) := 1 / (1 + s/omega0)\$
(%i5) bode_gain (H2 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i6) H3 (s) := 1 / (1 + s/omega0)^2\$
(%i7) bode_gain (H3 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i8) H4 (s) := 1 + s/omega0\$
(%i9) bode_gain (H4 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i10) H5 (s) := 1/s\$
(%i11) bode_gain (H5 (s), [w, 1/1000, 1000])\$
```

```(%i12) H6 (s) := 1/((s/omega0)^2 + 2 * zeta * (s/omega0) + 1)\$
(%i13) bode_gain (H6 (s), [w, 1/1000, 1000]),
omega0 = 10, zeta = 1/10\$
```

```(%i14) H7 (s) := (s/omega0)^2 + 2 * zeta * (s/omega0) + 1\$
(%i15) bode_gain (H7 (s), [w, 1/1000, 1000]),
omega0 = 10, zeta = 1/10\$
```

```(%i16) H8 (s) := 0.5 / (0.0001 * s^3 + 0.002 * s^2 + 0.01 * s)\$
(%i17) bode_gain (H8 (s), [w, 1/1000, 1000])\$
```

Function: bode_phase (H, range, … plot_opts …)

Function to draw Bode phase plots. To use this function write first `load(bode)`. See also `bode_gain`.

Examples:

Examples (1 through 7 from http://www.swarthmore.edu/NatSci/echeeve1/Ref/Bode/BodeHow.html, 8 from Ron Crummett):

```(%i1) load("bode")\$
(%i2) H1 (s) := 100 * (1 + s) / ((s + 10) * (s + 100))\$
(%i3) bode_phase (H1 (s), [w, 1/1000, 1000])\$
```

```(%i4) H2 (s) := 1 / (1 + s/omega0)\$
(%i5) bode_phase (H2 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i6) H3 (s) := 1 / (1 + s/omega0)^2\$
(%i7) bode_phase (H3 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i8) H4 (s) := 1 + s/omega0\$
(%i9) bode_phase (H4 (s), [w, 1/1000, 1000]), omega0 = 10\$
```

```(%i10) H5 (s) := 1/s\$
(%i11) bode_phase (H5 (s), [w, 1/1000, 1000])\$
```

```(%i12) H6 (s) := 1/((s/omega0)^2 + 2 * zeta * (s/omega0) + 1)\$
(%i13) bode_phase (H6 (s), [w, 1/1000, 1000]),
omega0 = 10, zeta = 1/10\$
```

```(%i14) H7 (s) := (s/omega0)^2 + 2 * zeta * (s/omega0) + 1\$
(%i15) bode_phase (H7 (s), [w, 1/1000, 1000]),
omega0 = 10, zeta = 1/10\$
```

```(%i16) H8 (s) := 0.5 / (0.0001 * s^3 + 0.002 * s^2 + 0.01 * s)\$
(%i17) bode_phase (H8 (s), [w, 1/1000, 1000])\$
```

```(%i18) block ([bode_phase_unwrap : true],
bode_phase (H8 (s), [w, 1/1000, 1000]));
```

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