Problem in finding capacitance

I know that it's a complex impedance, but you can find equivalent circuit which can be either series RC or parallel one.

But you didn't yet tell a reason, why one of both representations should be preferred.

Click to expand...

In fact, it doesn't make any difference for me to choose which one of them. But, in both circuits (parallel or series) the value of capacitance would be a function of conductivity, as I told the reason before.
Let's make it clear, as I understood, you say that in equivalent circuit, the value of capacitance is merely a function of permittivity, and resistance is also merely a function of resistivity. is it what you say?
I think both capacitance and resistance values are functions of both permittivity and resistivity. In other words, capacitance value is a function of ε(ω) and σ(ω), same as resistance value.

But, in both circuits (parallel or series) the value of capacitance would be a function of conductivity, as I told the reason before.

Click to expand...

I don't agree for the parallel case, and i didn't hear a reason for. The calculations you referred to have been related to a series circuit in my understanding.

The calculations you referred to have been related to a series circuit in my understanding.

Click to expand...

As I told before, you can convert series circuit to the parallel one just with applying just tiny changes. As depicted in this link, and it's clear,
Capacitor - Wikipedia, the free encyclopedia
the only change is using Xc in parallel circuit instead of C.
Who can you justify that in series equivalent circuit, capacitance value is a function of conductivity, but in the parallel one, it is independent?

---------- Post added at 21:46 ---------- Previous post was at 20:46 ----------

KerimF said:

Just an idea, if we have a loop formed by an ideal capacitor C and its two electrodes are connected by an ideal conductor. The equivalent capacitor around the loop is C which means that the part of the loop formed by the conductor has a capcitance = ∞ . This is a starting to point for saying that a capacitance value is a function of conductivity :wink:

Click to expand...

It's not a good reason! the capacitance is infinite because its permittivity is infinite. Here is the question, if a material's permittivity and resistivity were, let's say, 10 and 5S/m, respectively, the capacitance value can be defined using only 10 or using both values of 10 and 5S/m?

the only change is using Xc in parallel circuit instead of C

Click to expand...

It's not the only change, the resistance value is different as well. This point is unfortunately confused in the said Wikipedia article by using the same formula sign Rc for the resistance in both circuits. This article also doesn't calculate anything. Strictly spoken, Xc is nothing but the formula sign for the reactance of a capacitor. But to calculate a parallel circuit, you have to refer to the admittance sum Y = G + jB, while Z = R + jX applies for a series circuit.

So I think, you should better try to understand the problem from text book literature. For the time being, I keep my opinion, that the two relations in post #11 can be used to calculate the parallel circuit representation of a block of lossy dielectric material.

One way to see this is to consider the granular conductivity (not perfectly homogenous) as forming tiny electrodes (in parallel and in series). So the end component could be modelled by a matrix of elementary R's and C's, from which one can deduce that a practical model may consist of four equivalent elements only in three branches:

Cs and Rs
Cp
Rp

I wish I had a real composite component as of the original post to check its impedance versus frequency and find out how close these 4 values can describe its behavior in a real circuit. Only then it will be the time to study it in depth matematically. :???:

Kerim

One way to see this is to consider the granular conductivity (not perfectly homogenous) as forming tiny electrodes (in parallel and in series). So the end component could be modelled by a matrix of elementary R's and C's, from which one can deduce that a practical model may consist of four equivalent elements only in three branches:

Cs and Rs
Cp
Rp

Click to expand...

What make's you think that four element are needed to model the device? A homogenous block specified by a frequency independent σ and ε can be represented by exactly two elements.

To model a lossy capacitor with arbitrary frequency characteristic, you'll need a large number of RC elements in the equivalent circuit. Real capacitors with frequency dependent loss tangent can be usually modelled by a ladder of RC series elements with stepped time constants. But the original question wasn't asking for a model of this kind.

In my opinion, the discussion suffers from the fact, that many of the quoted articles, including those referred by the original poster, aren't exactly related to the given problem.

I have the impression that 'Monady' already has an answer (on his own) for his question and he tries to find out if this problem was already studied in depth by some others.

Personally, if it were a real problem to me I would certainly find a practical formula for such combination so I think it is the same for 'Monady'.

For instance, when I had a real problem to prove to my teachers that DSB-SC 'should', logically speaking, be easier to demodulate than SSB-SC (since the former takes twice the bandwidth), only then I was able to discover the 4th simple method... defying the knowledge of all great professors in communications. ;-)

Thank you guys for helping me through this problem. I think problem is solved to me, FvM was right about parallel equivalent circuit. Take a look at this link:
Microsystem design - Google Books

Though the things mentioned in the above link is a little bit different frm the things described in the link below:
Molecular electronics: from ... - Google Books

I appreciate the clear presentation in Molecular electronics. It seems to me like an excellent handbook of applied physics for engineers. Thanks for pointing to this literature.