Date: Feb 3, 2013 2:49 AM
Author: Themis Matsoukas
Subject: Re: Labelling each curve and changing grid in ParametricPlot

Here is one way to label the curves:

plot[\[Tau]_, \[CapitalOmega]_] :=
Module[{arg, abs}, {arg, abs} =
Through[{Arg,
Abs}[(1 + I*2*\[CapitalOmega])/(1 +
I*2*\[Tau]*\[CapitalOmega])]];
{arg/Degree, 20*Log10[abs]}]

\[Tau]list = {7, 8, 9, 10, 11, 12, 13, 14, 15};

txtlist =
Table[plot[\[Tau], \[CapitalOmega]], {\[Tau], \[Tau]list}] /. \
\[CapitalOmega] -> -0.52;

Show[ParametricPlot[
Table[plot[\[Tau], \[CapitalOmega]], {\[Tau], \[Tau]list}], {\
\[CapitalOmega], -0.5, -0.01}, AspectRatio -> 1,
GridLines -> Automatic, GridLinesStyle -> Dashed,
ImageSize -> Large],
Graphics[Table[
Text[\[Tau]list[[ii]], txtlist[[ii]]], {ii,
1, \[Tau]list // Length}]]]

I am not sure what exactly you want to do with the grid but you can specify your own regular or irregular grid using the option GridLines. See the examples in documentation.

Themis