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

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Discussion Overview

The discussion revolves around energy loss in a capacitor with a lossy dielectric when subjected to a DC-bias field while charging. Participants explore the implications of the dielectric's permittivity and loss tangent on energy dissipation during charging transitions, particularly comparing the energy lost when charging from 0 to 1V versus from 1V to 2V.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant queries the energy lost when charging a capacitor with a given capacitance and loss tangent, suggesting that the energy loss for the 1V to 2V transition should be three times that of the 0V to 1V transition based on the loss tangent's definition.
  • Another participant introduces the concept of equivalent series resistance (ESR) and questions whether the ESR approach is valid for circuits with DC bias and constant AC signals.
  • Some participants express confusion regarding the term "eps" and its relevance to the discussion, with one providing a definition related to dielectric constants.
  • A later reply suggests that the focus on dielectric loss may be misplaced, arguing that the energy loss is more significantly influenced by the ESR of the conductors rather than the dielectric properties.
  • One participant references a document that illustrates the relationship between dielectric loss and frequency, indicating that dielectric loss can be substantial at lower frequencies.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the primary factors contributing to energy loss in the capacitor, with some emphasizing the role of the dielectric properties while others highlight the importance of ESR in the conductors. The discussion remains unresolved with competing views on the significance of each factor.

Contextual Notes

There are limitations in the assumptions made regarding the behavior of the dielectric and the ESR, particularly in the context of AC signals with DC bias. The discussion does not resolve the mathematical implications of these assumptions.

Ohm113
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TL;DR
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
 
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Welcome to PF.

Ohm113 said:
Summary:: In a lossy dielectric with constant eps and tanD,

Sorry, what is "eps"?
 
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berkeman said:
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.
 
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Ohm113 said:
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.
 
Baluncore said:
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:

ESR Chart.png
 
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