A lossy dielectric medium is one which an EM wave as it propagates losses power owing to imperfect dielectric,that is a lossy dielectric is an imperfect conductor that is a partially conducting medium .
where as a lossless dielectric is a perfect dielectric,then wave equations for conductors are also holds good here
Equation (1) is called helm holtz equation and is called propagation constant.
Since is a complex quantity it can be expressed as
– is attenuation constant measured in Nepers/meter.
-is phase constant measured in radians/meter.
by equating real and imaginary parts separately
by substituting value in the equation (2)
the roots of the above quadratic expression are