Dielectric loss reveals a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle δ or the corresponding loss tangent tan δ. Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart. We take the ratio of two quantities, so we have to define in term of Tan. As I can guess, in Control system, we define our second order output response in terms of Tan in final expression.

Thanks

I agree with Smrity Dwivedi , in electromagnetic we define the dielectric loss in terms of Tan

Imagine the dielectric property as a complex number, and you want to plot it in Z-plane to see both real and imaginary parts together (e.g. smith chart).

The angle that you see from the center of the plane to your dielectric value will represent the loss tangent. You also need to consider the effect of frequency.

When electric and magnetic fields are harmonic then the time derivative operation in the equations (e.g. Maxwell's equations) can be replaced by a multiplication by jw.  The result of this in the equations is two terms that multiply the electric field in dielectrics, One is epsilon, the real dielectric constant, or permittivity, and the other is -j/w times the (hopefully small) conductivity.  These two are 90 degrees out of phase.  They can be added together to give something that is interpreted as the complex dielectric constant.  The ratio of the imaginary part (missing out the minus sign) to the real part is the tangent of the angle between the complex number and the real axis.  This angle is the loss angle, the tangent is called the loss tangent.  This use of a complex dielectric constant is only valid when the fields are harmonic, i.e. when a frequency is defined.

The permittivity of dielectric is in general complex and is given by :

ε =ε ′ − jε ′′

when you draw this on x-y plane and find Tangent of the angle between the Real and Imaginary part. You will end up with the result:

tanδ = ε ′′/ε ′

i.e: the ratio of the Imaginary part to the real part of the permittivity is found to be another quantity (Loss Tangent) which is used to express the losses in a Dielectric Material.

also see the topic Complex Permittivity on wikipedia.

https://en.wikipedia.org/wiki/Permittivity