Image:Linkwitz vs Butterworth.png

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Linkwitz_vs_Butterworth.png‎ (800 × 600 pixels, file size: 43 KB, MIME type: image/png)

[edit] Summary

Comparison of the magitude response of the summed Butterworth and Linkwitz-Riley crossover filters. The Butterworth crossovers have a +3dB peak at the crossover frequency, whereas the L-R filters have a flat summed output.

[edit] How the image was created

The original image was derived from Image:Butterworth_filter_bode_plot.png It was created in gnuplot with the following script:

set terminal svg fname "Times" fsize 24 size 800 600
#set terminal png transparent font times 18
set output "linkwitz_vs_butterworth.svg"
set samples 1000

# Magnitude plot of Butterworth filter
G(w,n) = 1 / (sqrt(1 + w**(2*n)))

# Magnitude plot of highpass Butterworth filter
H(w,n) = 1 / (sqrt(1 + 1/w**(2*n)))

# convert to decibel scale
dB(x) = 20 * log10(abs(x))

# put legend
set key 0.1, -12

# add grid
set grid

set logscale x 10

# Set range of x and y axes
set xrange [0.01:100]
set yrange [-60:10]

# Create 10 x tick marks per decade
set xtics 10
set ytics 10

set xlabel "Angular frequency (rad/s)"
set ylabel "Gain (dB)

set style line 3 lt -1 lw 1
set arrow 3 ls 3 head filled size screen 0.02,15,45
set arrow 3 from 2,5 to 1,3
set label 3 "+3dB" at 2,5

#unset label 4
#unset arrow 4
 
# Draw LR crossovers
plot \
  0 notitle w line 1, \
  dB(G(x,1))*2 title "LR2" w line 1, dB(H(x,1))*2 notitle w line 1,\
  dB(G(x,2)) title "Butterworth" w line 3, dB(H(x,2)) notitle w line 3, \
  dB(G(x,2)+H(x,2)) notitle w line 3 \

[edit] Licensing

I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. Subject to disclaimers.

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