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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])$

../figures/bodegain1

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

../figures/bodegain2

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

../figures/bodegain3

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

../figures/bodegain4

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

../figures/bodegain5

(%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$

../figures/bodegain6

(%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$

../figures/bodegain7

(%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])$

../figures/bodegain8

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])$

../figures/bodephase1

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

../figures/bodephase2

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

../figures/bodephase3

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

../figures/bodephase4

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

../figures/bodephase5

(%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$

../figures/bodephase6

(%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$

../figures/bodephase7

(%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])$

../figures/bodephase8

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

../figures/bodephase9


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