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# Archivo:Butterworth filter bode plot.png

## Resumen

 Descripción English: The Bode plot of a Butterworth filter with logarithmic axes and various labels. Cutoff frequency is normalized to 1 rad/s. Gain is normalized to 0 dB in the passband. Phase is in degrees because that's typical.The code is kind of kludgy, but makes a good output.See Wikipedia graph-making tips. Generated in gnuplot with the script below (save as butterworth_bode_plot.plt and then open in gnuplot). Then I opened the butterworth_bode_plot.ps file in a text editor to edit the line colors and linestyles, as per this description. This avoids needing to open in proprietary software, and really isn't that difficult (especially if you don't know the commands in the proprietary software either). ;-) Identify the lines easily by their color (the arrow is currently magenta and I want it to be black. Ah, there is the entry with 1 0 1, red + blue = magenta) or by using the gnuplot linestyle−1. (For instance, gnuplot's linestyle 3 corresponds to the ps file's /LT2.) Then you can edit the colors and dashes by hand. I changed the original: ```/LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def ``` into this: ```/LT0 { PL [] 0 0 1 DL } def /LT1 { PL [4 dl 2 dl] 0.5 0.5 0.5 DL } def /LT2 { PL [6 dl 3 dl] 0.3 0.3 1 DL } def /LT3 { PL [] 0 0 0 DL } def ``` /LT4–/LT8 I left unchanged. (I don't know what they're used for anyway.) /LTw, /LTb, and /LTa are for the grid lines and such. To convert the PostScript file to PNG: Open it in the GIMP (make sure you have ghostscript installed! - Windows instructions) Enter 500 under Resolution (it doesn't say "DPI" but I think that's what it means) Uncheck Try bounding box (since the bounding box cuts off the edge, unfortunately. You can try with the bounding box first.) Enter large values for Width and Height Check Color Check Strong anti-aliasing for both graphics and text Crop off extra whitespace (Shift+C if you can't find it in the toolbox) Possibly need to rotate it: Click Image → Transform → Rotate 90 degrees clockwise Filters → Blur → Gaussian blur at 2.0 px (No need to blur if you use strong anti-aliasing during conversion. I see no significant difference between end results.) Image → Scale Image... Width and Height at 25% Cubic interpolation You can view at normal size if you want by pressing 1, Ctrl+E Save as Butterworth filter bode plot.png  Este PNG gráfico fue creado con Gnuplot. Many orders on one plot: File:Butterworth orders.png Fecha 8 de octubre de 2005 (fecha de carga) Fuente Trabajo propio Autor Omegatron gnuplot source ```set samples 2001 set terminal postscript enhanced landscape color lw 2 "Times-Roman" 20 set output "butterworth bode plot.ps" # 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) = -pi/2-atan(1.2*w)-atan(0.09*w) # 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 "Gain (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 # "Cutoff frequency" label uses same coordinates as the function set label 3 "Cutoff frequency" 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 "Slope: -20 dB/decade" 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 (degrees)" set xlabel "Angular frequency (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 # "Cutoff frequency" 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 "Phase response" unset multiplot ```
File:Butterworth filter bode plot.svg es una versión vectorial de este archivo. Debería usarse esa versión en lugar de esta imagen rasterizada, cuando sea mejor.

File:Butterworth filter bode plot.png → File:Butterworth filter bode plot.svg

## Licencia

Yo, titular de los derechos de autor de esta obra, la publico en los términos de las siguientes licencias:
 Este archivo se encuentra bajo la licencia Creative Commons de Atribución/Compartir-Igual 3.0 Unported, 2.5 Genérica, 2.0 Genérica y 1.0 Genérica. Eres libre: de compartir – de copiar, distribuir y transmitir el trabajo de remezclar – de adaptar el trabajo Bajo las siguientes condiciones: atribución – Debes otorgar el crédito correspondiente, proporcionar un enlace a la licencia e indicar si realizaste algún cambio. Puedes hacerlo de cualquier manera razonable pero no de manera que sugiera que el licenciante te respalda a ti o al uso que hagas del trabajo. compartir igual – En caso de mezclar, transformar o modificar este trabajo, deberás distribuir el trabajo resultante bajo la misma licencia o una compatible como el original.
 Se autoriza la copia, distribución y modificación de este documento bajo los términos de la licencia de documentación libre GNU, versión 1.2 o cualquier otra que posteriormente publique la Fundación para el Software Libre; sin secciones invariables, textos de portada, ni textos de contraportada. Se incluye una copia de la dicha licencia en la sección titulada Licencia de Documentación Libre GNU.
Puedes usar la licencia que prefieras.

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