File:Butterworth filter bode plot de.svg
![File:Butterworth filter bode plot de.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Butterworth_filter_bode_plot_de.svg/800px-Butterworth_filter_bode_plot_de.svg.png?20150406095834)
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Summary
[edit]DescriptionButterworth filter bode plot de.svg |
Deutsch: Das Bodediagramm eines Butterworthfilters mit logarithmischen Achsen und verschiedenen Beschriftungen. Die Kennfrequenz ist aus 1 rad/s normiert. Die Verstärkung ist im Passband auf 0dB normiert. Die Phase ist wie üblich in Grad angegeben.
Die Datei wurde mit gnuplot erstellt. (Übersetzung aus dem englischsprachigen Wikipedia) |
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Source |
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Author | Alejo2083 |
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Generated in gnuplot with the following script (save as butterworth_bode_plot.plt and then open in gnuplot):
set samples 2001
set terminal svg enhanced size 1250 875 fname "Times" fsize 25 background rgb 'white'
set output "butterworth bode plot.svg"
# Butterworth amplitude response and decibel calculation. n is the order, which is just 1 in this image.
G(w,n) = 1 / (sqrt(1 + w**(2*n)))
dB(x) = 20 * log10(abs(x))
# Phase is for first order
P(w) = -atan(w)*180/pi
# Gridlines
set grid
# Set x axis to logarithmic scale
set logscale x 10
# No need for a key
set nokey #0.1,-25
# Frequency response's line plotting style
set style line 1 lt 1 lw 2
# Asymptote lines and slope lines are the same "arrow" style
set style line 3 lt 3 lw 1
set style arrow 3 nohead ls 3
# -3 dB arrow style
set style line 4 lt 4 lw 1
set style arrow 4 head filled size screen 0.02,15,45 ls 4
# Separator between passband and stopband line style
set style line 2 lt 2 lw 1
set style arrow 2 nohead ls 2
set multiplot
# Magnitude response
# =============================================
set size 1,0.5
set origin 0,0.5
# Set range of x and y axes
set xrange [0.001:1000]
set yrange [-60:10]
# Create x-axis tic marks once per decade (every multiple of 10)
set xtics 10
#set ytics 10
# No need for two sets of numbers
set format x ""
# Use 10 x-axis minor divisions per major division
set mxtics 10
# Axis labels
set ylabel "Verstaerkung (dB)"
# Draw asymptote lines
set arrow 1 from 1,0 to 1000,-60 as 3
set arrow 2 from .001,0 to 1,0 as 3
# -3 dB arrow
set arrow 4 from 2,3 to 1,0 as 4
# "Kennfrequenz" label uses same coordinates as the function
set label 3 "Kennfrequenz" at 2,4 l
# "-3 dB" label
set arrow 5 from 0.5,-6 to 1,-3 as 4
set label 4 "-3.01 dB" at 0.5,-7 r
# Draw a separator between passband and stopband and label them
set arrow 3 from 1,-60 to 1,10 as 2
# Label coordinates are relative to the graph window, not to the function, centered at the 1/4 and 3/4 width points
set label 1 "Passband" at graph 0.25, graph 0.1 c
set label 2 "Stopband" at graph 0.75, graph 0.1 c
# Draw slope lines and label
set arrow 6 from 100,-20 to 12,-20 as 3
set arrow 7 from 100,-20 to 100,-39 as 3
set label 5 "Abfall: -20 dB/Dekade" at 100,-15 c
plot dB(G(x,1)) ls 1 title "1st-order response"
#Phase response
# =============================================
set size 1,0.5
set origin 0,0
# Set range of x and y axes
set yrange [-105:15]
# Create y-axis tic marks every 15 degrees
set ytics 30
# Regular numbers
set format x "% g"
# Axis labels
set ylabel "Phase (Grad)"
set xlabel "Kreisfrequenz (rad/s)"
# Draw asymptote lines
set arrow 1 from 0.1,0 to 10,-90 as 3
set arrow 2 from 0.001,0 to 0.1,0 as 3
set arrow 10 from 10,-90 to 1000,-90 as 3
# -3 dB arrow
unset arrow 4 #from 2,3 to 1,0 as 4
# "Kennfrequenz" label uses same coordinates as the function
unset label 3 #"Cutoff frequency" at 2,4 l
# "-3 dB" label
unset arrow 5 #from 0.5,-6 to 1,-3 as 4
unset label 4 #"-3.01 dB" at 0.5,-7 r
# Draw a separator between passband and stopband and label them
set arrow 3 from 1,-105 to 1,15 as 2
# Label coordinates are relative to the graph window, not to the function, centered at the 1/4 and 3/4 width points
set label 1 "Passband" at graph 0.25, graph 0.5 c
set label 2 "Stopband" at graph 0.75, graph 0.5 c
# Draw slope lines and label
unset arrow 6 #from 100,-20 to 12,-20 as 3
unset arrow 7 #from 100,-20 to 100,-39 as 3
unset label 5 #"Slope: -20 dB/decade" at 100,-18 c
plot P(x) ls 1 title "Phaseantwort"
unset multiplot
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:58, 6 April 2015 | ![]() | 1,250 × 875 (81 KB) | Chris828 (talk | contribs) | User created page with UploadWizard |
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File usage on Commons
The following 9 pages use this file:
- File:Butterworth filter bode plot-IT.svg
- File:Butterworth filter bode plot.png
- File:Butterworth filter bode plot.svg
- File:Butterworth filter bode plot de.svg
- File:Butterworth filter bode plot ru.png
- File:Butterworth filter bode plot ru.svg
- File:Butterworth filter bode plot sv.svg
- File:Butterworth filter bodediagram.png
- Template:Other versions/Butterworth filter bode plot
File usage on other wikis
The following other wikis use this file:
- Usage on de.wikipedia.org
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Short title | Gnuplot |
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Image title | Produced by GNUPLOT 4.6 patchlevel 4 |
Width | 1250 |
Height | 875 |