G(w,n) := 1/sqrt(1+w**(2*n));
H(w,n) := 1/sqrt(1+1/w**(2*n));
dB(x)  := 20*log(x)/log(10);
load(draw);
draw2d( terminal=svg,logx=true,
        grid=true,user_preamble="set mxtics; set mytics;set key 100,-5",
        xtics_axis=false,ytics_axis=false,ip_grid=[100,100],
        color=black,xlabel="Angular frequency (rad/sec)",ylabel="Gain (dB)",
        xaxis_type=solid,yaxis_type=solid,line_width=1.5,yrange=[-50,10],
        axis_bottom=true,axis_top=false,axis_right=false,axis_left=true,
        key="LR2",color=red,explicit(dB(G(w,1))*2,w,0.01,100),
        key="",color=red,explicit(dB(H(w,1))*2,w,0.01,100),
        key="Butterworth",color=blue,explicit(dB(G(w,2)),w,0.01,100),
        key="",color=blue,explicit(dB(H(w,2)),w,0.01,100),
        key="Butterworth sum",color=magenta,explicit(dB(H(w,2)+G(w,2)),w,0.01,100),
        key="LR2 sum",color=cyan,explicit(dB(H(w,2)**2+G(w,2)**2),w,0.01,100),
        color=black,line_width=1,line_type=dots,
        key="",parametric(t,3,t,0.5,1.5),parametric(t,-3,t,0.5,1.5),parametric(t,-6,t,0.5,1.5),
        label_alignment=right,label(["+3dB",0.4,3]),label(["-3dB",0.4,-3]),label(["-6dB",0.4,-6])
        );