# Getting asymptotic lines in a electronic filter design plot

I've the following code:

LogLinearPlot[
20 Log10[(5/
Sqrt[2])*(1/(\[Sqrt]((8 f \[Pi] 56000 (5.601443110900379*^-8) \
- 8 (1.6672176431702952*^-7) f^3 \[Pi]^3 56000^3 \
(5.601443110900379*^-8)^2)^2 + (1 -
8 f^2 \[Pi]^2 56000^2 (5.601443110900379*^-8) \
((1.6672176431702952*^-7) + (5.601443110900379*^-8)))^2)))], {f,
0.01, 1000}]


It is a logarithmic plot of a electronic filter.

Now, I want to get some asymptotic lines in my plot. So at the beginning of the plot my code produces a straight line at $20\log_{10}(5/\sqrt{2})$ and further it dies asymptotic off to $-\infty$ but I want to have a dotted asymptotic line to give that in the plot.

Something like this:

The red line I got in my function and I want the blue lines that asymptoticly give my values in the plot.

func[f_] :=
20 Log10[(5/
Sqrt[2])*(1/(\[Sqrt]((8 f \[Pi] 56000 (5.601443110900379*^-8) \
- 8 (1.6672176431702952*^-7) f^3 \[Pi]^3 56000^3 \
(5.601443110900379*^-8)^2)^2 + (1 -
8 f^2 \[Pi]^2 56000^2 (5.601443110900379*^-8) \
((1.6672176431702952*^-7) + (5.601443110900379*^-8)))^2)))]


Finding the asymptotic lines:

Horizontal asymptote:

a1=Limit[func[x], x -> 0]


10.9691

Oblique asymptote:

m = Limit[func[x]/Log[x], x -> \[Infinity]]
q = Limit[func[x] - m*Log[x], x -> \[Infinity]]


-26.0577

103.815

Plot:

Show[LogLinearPlot[func[x], {x, 0.01, 10000}
, PlotStyle -> Red
, Frame -> True
, GridLines -> Automatic
, Axes -> True
, AxesOrigin -> {1, 0}
]
,
Plot[a1, {x, 0.01, 10000}
, PlotStyle -> {Blue, Dotted}]
,
Plot[m*x + q, {x, 0.01, 10000}
, PlotStyle -> {Blue, Dotted}
]
]


• How can I make the blue lines dotted? – asd Jun 8 '18 at 13:50
• With the option "Dotted" in PlotStyle: see edit in my answer – Fraccalo Jun 8 '18 at 13:53