Image:Linkwitz vs Butterworth.png
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Linkwitz_vs_Butterworth.png (800 × 600 pixel, 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.
File history
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- (del) (cur) 08:00, 12 May 2006 . . Rohitbd (Talk | contribs) . . 800×600 (43,604 bytes) (Resized back to 800 x 600)
- (del) (rev) 07:58, 12 May 2006 . . Rohitbd (Talk | contribs) . . 800×602 (43,626 bytes) (Indicated -3dB & -6dB summing at crossover.)
- (del) (rev) 13:08, 7 May 2006 . . Scoofy (Talk | contribs) . . 800×600 (37,287 bytes) (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.)
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