How do I calculate effective dielectric constant for a coplanar waveguide (CPW) and other related structure including antennas? Can you give me some reference.
Typically, waveguides are analyzed as an eigen-value problem. This means their cross section is analyzed and all the possible modes that could exist in the waveguide are calculated. Pictures of the modes are obtained from the eigen-vectors. The effective refractive index neff is obtained through the eigen-values as you will see in the Lectures. Each mode has its own neff. The effective permittivity is simply the effective refractive index squared, neff^2.
For the effective dielectric constant of CPW, you may refer to the classic book - Brian C. Wadell's Transmission Line Design Handbook (Artech House, 1991).
For the effective dielectric constant of antennas, you may find the following book interesting - Microstrip and printed antennas: new trends, techniques, and applications from Debatosh Guha, Yahia M.M. Antar (Wiley, 2011). In particular, Chap 2 (Computer Aided Design of Microstrip Antennas) of this book discusses the performance of multiple novel microstrip antennas heavily based on the effective dielectric constant.
If you do not want to use softwares such as MicroWave Office, you could use the coplanar mapping techniques to estimate the effective dielectric constants surrounding your coplanar geometry. There is a very useful text book on this topic, which covers many different CPW and microstrip configurations, where analytical conformal mapping expressions are presented:
N. S. Rainee, Coplanar Waveguide Circuits, Components, and Systems,