set samples 1001
 set terminal svg enhanced size 800 600 background rgb 'white'
 set output "butterworth_orders.svg"

 G(w,n) = 1 / (sqrt(1 + w**(2*n)))

 dB(x) = 20 * log10(abs(x))

 set grid linestyle 1 lt 1 lc rgb "#808080"

 # Set x axis to logarithmic scale
 set logscale x 10

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

 # Create 10 x tick marks per decade
 set xtics 10

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

 # Put legend in bottom left corner
 set key at 0.1,-45

 # Plot five orders of the filter
 plot \
     dB(G(x,1)) title "1st order", \
     dB(G(x,2)) title "2nd order", \
     dB(G(x,3)) title "3rd order", \
     dB(G(x,4)) title "4th order", \
     dB(G(x,5)) title "5th order"