(*simple illustration of low pss filter. Nasser M. Abbasi, oct 13, 2015*)
Manipulate[
Module[{tf,w,p},
tf=h[k,e,s];
p=BodePlot[tf,{0.1,range},
PlotLayout->"List",
ImageSize->400,
GridLines->Automatic,
GridLinesStyle->LightGray,
ImageMargins->40,FrameLabel->{{{"magnitude (db)",None},{"ω (rad/sec)","H(s) Magnitude plot"}},{{"phase(deg)",None},{"Frequency (rad/sec)",None}}},
PlotRange->{{{0.1,range},Automatic},{{0.1,100},Automatic}},
BaseStyle->14];
Text@Grid[{
{Style[Row[{"H(s)=\!\(\*FractionBox[\(\(1\)\(\\ \)\), SuperscriptBox[\((\(\(1\)\(+\)\) ∈ \\ s)\), \(k\)]]\) = ",tf}],16]},
{
p[[1]]
(*
LogPlot[1/(1+e^2*w^2)^(k/2),{w,0.1,range},PlotRange->All,ImageSize->300,Frame->True,FrameLabel->{{"|H(s)|",None},{"ω","Low pass filter"}},ImageMargins->10,GridLines->Automatic,GridLinesStyle->LightGray,Epilog->{Dashed,Line[{{1/e,0},{1/e,1/2^(k/2)}}],Line[{{1/e,1/2^(k/2)},{0,1/2^(k/2)}}]}]
*)
}
},Alignment->Center,Frame->All,FrameStyle->LightGray,Spacings->{1,2}
]
],
{{k,4,"k"},1,20,1,Appearance->"Labeled"},
{{e,.1,"ϵ"},0.01,1,.01,Appearance->"Labeled"},
{{range,1000,"max ω"},1,1000,1,Appearance->"Labeled"},
TrackedSymbols:>{k,e,range},
Initialization:>
{
h[k_,e_,s_]:=1/(1+e*s)^k;
}
]