Hi colleague,

I have a twisted question. There are two ways to define the complex dielectric permittivity.

First one using e(jwt) Fourier Transform where we get:

e(w)=e(w)'-je''(w)

Second, using the e(-jwt) Fourier Transform where:

e(w)=e(w)'+je''(w)

The first one is mostly used in engineering and the later one in physics.

Does the sign comes from e''(w)? Or from the definition of Fourier Transform to get causality.

I mean if we have a dielectric for example which is defined as:

e(w)=1-j0.2 in the engineering convention for example. In the physics convention the same dielectric is e(w)=1+j0.2 or is the same e(w)=1-j0.2

I see in other contributions that the dielectric loss tangent is defined as:

tanD=e''(w)/e'(w) in engineering and tanD=-e''(w)/e'(w). This loss tangent has a physical meaning and both must be the same. This is why I thought that e''(w)_engineering = -e''(w)_physic

However, If this is true we have at the end the same e(w) and when we transform it to the time domain using the correspondent exponential we will get different phases differences.

I mean if I assume e''(w)_engineering=-e''(w)_physic 

At the end I will have e(w)_engineering=e(w)'-je''(w)_engineering and e(w)_physic=e(w)=e(w)'+je''(w)_physic=e(w)'-je''(w)_engineering.

So at the end we get the same. With the previous example e(w)=1-j0.2

And if we apply the inverse fourier transform using en physic and engineering

integral(e(w)*e(jwt))

integral(e(w)*e(-jwt))

We do not get the same in the time domain.