AC power loss in lossy dielectric (capacitor) with DC-bias field

[Ohm113]

TL;DR Summary

In a lossy dielectric with constant eps and tanD, does the energy loss increase with dc-bias while keeping the ac voltage and frequency constant?

Hi there,

if a dielectric (capacitor) is described with a constant permittivit eps (or C) and loss-tangent DF, how much energy ist lost when charging the capacitor by 1V?

For example: C=1, DF=0.1.
When charging from 0 to 1V, the lost energy (in J) is ...?
When charging from 1V to 2V, the lost energy (in J) is?

Since DF is the fraction of dissipation to stored energy, I would say the lost energy for the 1->2 transition is 3x that of the 0->1 transition. However, if a ESR equivalent resitance is calculated using ESR=DF*omega*C and that is used in a circuit simulator, the energy loss is the same for both transitions. However, the ESR approach might only be possible for pure AC signals without bias and also with a constant sinus shape. Looking forward for your discussions!

Thanks, Ohm

 

[berkeman]

Welcome to PF.

Summary:: In a lossy dielectric with constant eps and tanD,

Sorry, what is "eps"?

 

[dlgoff]

Welcome to PF.
Sorry, what is "eps"?

I did a google search on "dielectric constant eps" and this is what I found, for what it's worth:

Eps=x Specifies the static (or zero-frequency) dielectric constant of the solvent. EpsInf=x Specifies the dynamic (or optical) dielectric constant of the solvent. For SMD calculations, it should be set to the square of the solvent's refractive index at 293 K.

 

[Baluncore]

Summary:: In a lossy dielectric with constant eps and tanD, does the energy loss increase with dc-bias while keeping the ac voltage and frequency constant?

It seems to me that this question is over-constrained, by focus on the dielectric.

It is not the dielectric loss that is important in tanD.
It is loss in the ESR of the thin foil conductors.

It is the changing capacitor voltage that generates heat in the ESR.
The DC zero or bias voltage is not important.

How can the DC bias be changed while having a zero AC component?
Surely that must be an AC voltage change.

 

[The Electrician]

It seems to me that this question is over-constrained, by focus on the dielectric.

It is not the dielectric loss that is important in tanD.
It is loss in the ESR of the thin foil conductors.

Figure 4 in this Murata document: https://article.murata.com/en-us/article/impedance-esr-frequency-characteristics-in-capacitors

shows that dielectric loss is responsible for a substantial part of the loss at frequencies below the self resonant frequency: