set terminal svg enhanced size 1250 875 fname "Times" fsize 25 set output "Butterworth_filter_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 "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