coupling capacitance and actual capacitance

Hi,

There are two scenario, which has higher coupling capacitance and higher actual capacitance between A and B ? and why ?

a> Metal A and Metal B

b> Metal A, Metal C and Metal B

Spacing between Metal A and Metal B in both cases is same.

Please help

i would seem that scenario <b> will have a higher capacitance, since A-C and B-C distance is smaller. However, this also leads to two higher-value cap's connected in series.

Now if your middle plate C has non-zero thickness, then even with the series connection, option <b> will have an overall higher capacitance. Some quick formula manipulation shows it to be true.

About the difference between 'coupling cap' and 'actual cap' I'm not sure what it means.

Yes, b) version will have higher coupling cap if Metal C is floating.

rameshiloveu said:

Hi,

There are two scenario, which has higher coupling capacitance and higher actual capacitance between A and B ? and why ?

a> Metal A and Metal B

b> Metal A, Metal C and Metal B

Spacing between Metal A and Metal B in both cases is same.

Please help

Click to expand...

When additional conductors (metals) are brought into the system, the total capacitance of A is increased (if coupling capacitance between A and that additional metal C is non-zero - otherwise capacitance of A stays the same). The same holds true for conductor B.

Now, the change of the coupling capacitance between A and B depends on whether conductor C is floating or grounded.
If it is floating, capacitance between A and B is increased (or stays constant).
If C is grounded (or held at another fixed potential) - coupling capacitance between A and B is decreased. (the reason is that a part of the original coupling capacitance between A and B will now be redirected to C).

Max
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As already said there are two possibilities:

1. Thickness of C is zero (negligible)
2. Thickness of C is not negligible

These are shown in the following picture:


In both case 1 and 2, the distance between A and B is d=d1+d2, then using the formula of the parallel plates capacitor we have:

Cab=ε•[A/(d1+d2)]

CASE 1 (Thickness of C negligible):

C1=Cac=ε•(A/d1), C2=Ccb=ε•(A/d2)

since they are in series Cacb1=C1•C2/(C1+C2)=ε•[A/(d1+d2)]

This means the value is the same as Cab, without the metal C in between

CASE 2 (Thickness of C NOT negligible):

The thickness of C is 2•Δ, then the distances AC and CB are d1-Δ and d2-Δ; in this case:

C1=ε•[A/(d1-Δ)], C2=ε•[A/(d2-Δ)]

again, C1 and C2 are in series Cacb2=ε•[A/(d1+d2-2•Δ)]

this means, in this case the capacitance is higher with respect to that without the metal C in between. You can see it is equivalente to a capacitor having distance between plates A and B = d1+d2-2•Δ (with no metal C inserted)
This fact is quite intuitive; in the thickness of C, no charge can be stored since it is a conductor.

I don't understand the problem of C floating or grounded (or held to any other potential). There is no difference between the two cases since the two plates A and B are completely floating, then no current can flows to any other point.

albbg said:

I don't understand the problem of C floating or grounded (or held to any other potential). There is no difference between the two cases since the two plates A and B are completely floating, then no current can flows to any other point.

Click to expand...

This is completely wrong.

What happens with a conductor when other conductor potentials or charges are changed - whether it is held at a fixed potential (i.e. the charge can flow in or out form that conductor), or it keeps a constant charge (meaning that its potential is not fixed - i.e. this conductor is said to be "floating") - has a significant effect on capacitances of other conductors.

albbg said:

..I don't understand the problem of C floating or grounded (or held to any other potential). There is no difference between the two cases since the two plates A and B are completely floating, then no current can flows to any other point.

Click to expand...

The difference is illustrated here:

How can flows current through GND if A' and B' are floating with respect to it ? There is no path. If there is then the circuit is different from the one proposed.

albbg said:

How can flows current through GND if A' and B' are floating with respect to it ? There is no path. If there is then the circuit is different from the one proposed.

Click to expand...

You're right... small correction required.

If the plate C is infinite in size, then my 2nd diagram is correct - NO coupling between A' and B'.

However if C is finite, and especially if C size is smaller than A and/ or B, then there will be coupling between A' and B'.
So the diagram should look like ---



where C5 is the direct capacitance between A' and B' which bypasses the center plate.

The correction you made allows to calculate the capacitance in case the size of C is smaller than A and B. If the size of the three metals is the same (we consider no fringe effect is present) the situation is that described in my post #5.
However, in any case, the GND connection doesn't play any role.

The ciruit is the following:



As you can see there is only one mesh ! Applying KCL, there is no way to make the current circulating through GND (it's a floating node with respect to both A and B). Remember that the current is I=dQ/dt, then if the current cannot circulate the charge cannot be injected to (or removed from) the plates.
To have the current circulating in GND you need at least two nodes connected to GND.

albbg said:

....
However, in any case, the GND connection doesn't play any role.
.....

Click to expand...

This seems a bit counter-intuitive. I think the trouble is how you are applying the input signal. We are thinking of applying it between A' and GND, and then looking at the output between B' and GND.

albbg said:

The correction you made allows to calculate the capacitance in case the size of C is smaller than A and B. If the size of the three metals is the same (we consider no fringe effect is present) the situation is that described in my post #5.
However, in any case, the GND connection doesn't play any role.

The ciruit is the following:

View attachment 96480

As you can see there is only one mesh ! Applying KCL, there is no way to make the current circulating through GND (it's a floating node with respect to both A and B). Remember that the current is I=dQ/dt, then if the current cannot circulate the charge cannot be injected to (or removed from) the plates.
To have the current circulating in GND you need at least two nodes connected to GND.

Click to expand...

We cant say there is no current in the center plate as proposed equivalent they just work like a series with a parallel capacitor....
Your scheme just considers a balanced voltage source with only these two capacitors assume may be the center plate is not in exact center or add a capacitor in any side you could see the current to the ground........

Venkadesh_M said:

We cant say there is no current in the center plate as proposed equivalent they just work like a series with a parallel capacitor....
Your scheme just considers a balanced voltage source with only these two capacitors assume may be the center plate is not in exact center or add a capacitor in any side you could see the current to the ground........

Click to expand...

No there is any current from central plate to ground. Ground is just a convention, I can call it as I want, there is no special meaning of GND. A single node can't draw any current. To have the current circulating I need a forward and a return path.

@kripracharya: you propose a circuit different from the origina onel. To measure a capacitance (as well as any impedance) I've to give it a difference of potential to its terminals, then measure the current drawn and take Z=V/I

albbg said:

No there is any current from central plate to ground. Ground is just a convention, I can call it as I want, there is no special meaning of GND. A single node can't draw any current. To have the current circulating I need a forward and a return path.

Click to expand...

You are saying there is no connection between ground and voltage source...

Then your voltage source's positive and negative mentions what??? (I believe everything is proportional to gnd!!)

Venkadesh_M said:

(I believe everything is proportional to gnd!!)

Click to expand...

Why ? I can put GND to node A and connect the central plate to a node that I'll call GND2. There is no connection between GND and GND2. Nothing changes.
GND is just a convention to say with respect to which node I want to measure my difference of potential.

If I place the GND at node C I'll have Vca (from GND to a) and Vbc (from b to GND), then at the plates A, B I'll have Vbc-Vca=Vba
If I place the GND at node A I'll direcly have Vba

But is only matter of measurement reference.

Can i take you are saying there wont be any current flow through a resistor connected between (#10) V1's positive to gnd???

Venkadesh_M said:

Can i take you are saying there wont be any current flow through a resistor connected between (#10) V1's positive to gnd???

Click to expand...

If you mean to replace one of the capacitor or put in parallel or in series a resistor to one of the capactitors, then yes it is: no current will flows to GND. Doesn't matter the component.
If the current will flow through GND, where the electrons go, in your opinion ? If you have a generator the flows from + to - (is a convention because physically they flows from - to +)

Ok It is a AC source then where is the + an - comes from??

- - - Updated - - -

You are talking about the source which has no links with the ground, I am talking about source linked with ground.....

- - - Updated - - -

Every circuit is some where linked with ground that why we are able to address the voltage with respect to ground, (thats why we are calling it as ground), If the gnd potential links with a circuit at any point surely it will make the current flow through the capacitors... (you cant refer voltage of any point without marking some place as ground)

AC or DC doesn't make difference. In DC sources the elctron always moves the same direction while in AC the reverse the direction as functin of time. This mean AC generators have + and - flipped with time.

GND (Ground) is just a label. The name is coming from the fact that at the origin it was a point fixed physically to the ground (the soil); now that is called "earth" . You can put it where you want: each of the nodes of the circuit is OK.

Each point in the space stays at a defined potential we cannot measure; what we can measure is the difference of potential between two point (the voltage). So I can refer my measurement to the node of the circuit I prefer.
For instance many cars have the ground referred to the negative pole of the battery, while other manufacturers prefer to refers to the positive pole. The circuit is in principle the same (of course there are difference manufacturer by manufacturer) but the reference is different. In the first case the body of the car is placed at -V, while in the second is placed at +V.

that is a common concept, you are saying that there is no part of the circuit is linked with the ground and no current flow in the capacitors.... yeah that was common if there is no external connection surely there will be no current but the point is already ground, you know so there is already a connection with some part of the circuit with the ground pin now you are making a new connection (grounding the center plate of capacitor) so surely it will make changes in potential...

If you are saying already that terminal is open then that is not a ground before that...