Calculating the Dielectric Strength of multiple materials

[SpiderPig]

If I had two different materials between two oppositely charged plates, would the total dielectric strength just be an average of both dielectric constants with respect to each of their thicknesses? Or is it more complicated than that?

Material A is in full contact with one plate and material B is in full contact with the other plate.

 

[Baluncore]

It is more complicated.
Imagine the layers of dielectric are separated by equipotentials of foil.
Each layer of dielectric is then a single capacitor, one of several capacitors in series.
Work out the values of the capacitance for each layer, based on Er, area and d.
Each will have the same charge, so you can work out the voltage applied to each.
C = Q / V; V = Q / C.
Now you can work out which dielectric layer will limit the voltage of the series stack.

 

[Gavran]

If I had two different materials between two oppositely charged plates, would the total dielectric strength just be an average of both dielectric constants with respect to each of their thicknesses?

The question in the original post should be changed because a dielectric constant is not the same as dielectric strength.
The dielectric strength of an insulating material is its ability to act as an insulator.
The dielectric constant of an insulating material is its ability to store electrical energy.

 

[Baluncore]

The dielectric constant of an insulating material is its ability to store electrical energy

When capacitors are connected in series, the relative voltage dropped by each capacitor, is inversely proportional to that capacitance.

The dielectric constant, Er, determines the capacitance, so it also determines the proportion of the voltage dropped by that layer of dielectric.

 

[Baluncore]

Here is some code for multiple layers of dielectric

' several layers of dielectric

Type layer
    d As Double     ' layer thickness in metre
    er As Double    ' relative permittivity
    vpm As Double   ' dielectric strength, V/m
    c As Double     ' capacitance of this layer
    vbd As Double   ' breakdown voltage of this layer
    qx As Double    ' maximium charge on layer
End Type

Dim As Integer i, n = 3    ' number of layers
Dim layer( 1 To n ) As layer

' initialise
Dim As Double area = 0.01   ' area of dielectric
' for each layer    d        er    vpm   c vbd qx
layer( 1 ) = Type( 0.001 ,    2,   5e6,  0, 0, 0 )
layer( 2 ) = Type( 0.0015,    5,   1e5,  0, 0, 0 )
layer( 3 ) = Type( 0.0001,   22,   5e5,  0, 0, 0 )

Const As Double Eo = 8.8541878128e-12   ' Farad / metre
Dim As Double elast = 0     ' elastance = 1 / capacitance
Dim As Double d_total = 0   ' total thickness
Dim As Double q_min = 1e30  ' minimum breakdown charge

' compute each layer, sum and select
For i = 1 To 3
    With layer( i )
        ' compute for this layer
        .c = Eo * .er * area / .d   ' capacitance
        .vbd = .d * .vpm            ' breakdown voltage
        .qx = .c * .vbd             ' limiting Q, from C = Q / V
        ' gather for later
        If Q_min > .qx Then Q_min = .qx ' find lowest charge limit
        elast += 1 / .c             ' sum the elastance
        d_total += .d               ' sum of thickness
    End With
Next i

' final combined
Dim As Double c_total = 1 / elast
Dim As Double v_total = 0
For i = 1 To n
    v_total += Q_min / layer( i ).c
Next i

Print " Series capacitance ="; c_total; " farad "
Print " Breakdown voltage  ="; v_total; " volts "
Print
Print " Average dielectric strength ="; v_total / d_total; " V/m"
Print " Average dielectric constant ="; d_total * c_total / ( Eo * area )
Print

 

[Gavran]

When capacitors are connected in series, the relative voltage dropped by each capacitor, is inversely proportional to that capacitance.

$V = V_1 + V_2 = \frac{Q}{C_1} + \frac{Q}{C_2}$ (*)

The dielectric constant, Er, determines the capacitance, so it also determines the proportion of the voltage dropped by that layer of dielectric.

(*) $= Q\frac{d_1}{\varepsilon_{r1}\varepsilon_0A} + Q\frac{d_2}{\varepsilon_{r2}\varepsilon_0A}$

 

[berkeman]

The question in the original post should be changed because a dielectric constant is not the same as dielectric strength.
The dielectric strength of an insulating material is its ability to act as an insulator.
The dielectric constant of an insulating material is its ability to store electrical energy.

Yeah, the OP question is confusing, since it mixes two different phenomena.

@SpiderPig -- Can you clarify whether you meant dielectric constant $\epsilon$ or dielectric breakdown strength? The latter phenomena is more complicated than the former. Thanks.

 

[SpiderPig]

Yes it is confusing now that I'm reading it again! I'll edit it once I figure out where the edit button is...

I'd actually like to know both the dielectric strength & dielectric constant.

 

[Baluncore]

The "edit" button is at the bottom left of your posts, next to the "report" button.

 

[SpiderPig]

I see it on post #8 of mine but it's not on post #1... I'll investigate, thanks.

 

[berkeman]

I'll edit it once I figure out where the edit button is...

Please don't edit old posts to try to fix things up -- it makes for a very confusing thread. Instead, just post any corrections in a new reply. Thanks.

I'd actually like to know both the dielectric strength & dielectric constant.

An important subtlety with dielectric strength (the ability not to arc through at high electric field strengths across the insulator) is that there are typically pinholes and imperfections in the insulator that serve as starting points for the arc-throughs. That is why high voltage insulation is often done in layers, so that the pinholes and imperfections don't line up, which helps to raise the dielectric strength value of the overall double-insulation.

 

[berkeman]

I see it on post #8 of mine but it's not on post #1... I'll investigate, thanks.

There is a timeout for most users to edit their posts. I think it's 24 hours, but I'm not sure. Again, it is best just to add a new reply with any corrections/updates. If you do edit a previous post to fix a mistake or something, please use strikethrough to show the wrong info and maybe bold to highlight the new info you've added. At least that way your change will be visible and obvious. Thanks.

 

[SpiderPig]

An important subtlety with dielectric strength (the ability not to arc through at high electric field strengths across the insulator) is that there are typically pinholes and imperfections in the insulator that serve as starting points for the arc-throughs. That is why high voltage insulation is often done in layers, so that the pinholes and imperfections don't line up, which helps to raise the dielectric strength value of the overall double-insulation.

That's a good point, I never thought about that.

 

[Baluncore]

That is why high voltage insulation is often done in layers, ...

Sometimes, electrically floating layers of metal foil or chrome, are used to define the equipotentials between the layers of insulation. That makes a stack of leaky capacitors, which is designed to share the total voltage, evenly across all layers. The equipotentials prevents failures by deep electrical treeing.
https://en.wikipedia.org/wiki/Electrical_treeing

With AC, the capacitance between the foil layers, equalises the voltage drop between equipotentials.

With DC, it is the controlled leakage between the layers, that forms a potential divider.