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

i.e,

then

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

and

by substituting value in the equation (2)

let

the roots of the above quadratic expression are

similarly,