Dear Pratibha,

Capacitance and parallel conductance depends on the dimension of the dielectric slab between the capacitor plates. However, the calculated values of dielectric constant and dielectric loss should not depend on the geometry of the dielectric material provided no barrier capacitance is effective at the contacts or inside the dielectric. Frequency may affect dielectric constant and loss if dielectric dispersion occurs in that frequency range.

With my limited knowledge,

Here the dimension means thickness and area, though this will not effect your loss ideally, but in practice as you increase the area of contact the probability for getting contact effect will come in to picture because i) your contact may not be uniform, and ii) new grains which comes in to contact may not be uniform.

similarly if you change the thickness, different grains with different sizes i.e., different interfacial capacitances will come in picture.

Again to understand whether contac between material and elctrode is effecting or iterface between grains is effecting we should go for impedance spectroscopy analysis at low frequency

Dear Pratibha...

As per I know, Dielectric loss does not depends on the dimension of plate....Dielectric loss is the dissipation of energy through the movement of charges in an alternating electromagnetic field as polarization switches direction...It depends on frequency, temperature, electric field, sintering temperature etc...but not on plate dimension....

When electric field is applied, polarization occurs in the dielectric material which reduces the electric field between the capacitor plates. If a.c field is applied, as long as polarization follow the field, dielectric loss does not occur. However, when polarization does not follow a.c. field, dielectric loss occurs. Capacitance depends on the dimensions of the plates but dielectric constant and loss does not depend on the geometry of capacitor.

Actually Dr. A. Kumar has very briefly, but very precisely answered your question.

I may like to give a practical picture, for further understanding.

Try to picturize the electrical equivalent of a capacitor, imagine the following:

A capacitor is always represented as a C in parallel with R.

a) For an ideal capacitor with very low dielectric loss, R will be high (infinity) , and in case it is a lossy capacitor R will low.

If R is low, or gets short circuited, you no longer have a capacitance, or in other words the capacitor is gone bad, or short circuited.

b) Now It is hard to find an ideal capacitor with R being infinity.

    R will always have a some finite value (maybe high or low).

c) All practical capacitors will have some finite value for R. It depends on the resolution and accuracy of the capacitance bridge that you are using for measuring the dielectric loss factor (tan delta).

d) Capacitance value will depend upon the dielectric constant, and dimensions of the capacitor.

e) Resistance value (or alternately the conductance) value will depend on the insulating material in your capacitor. Its leakage characteristics. These properties can vary with temperature, and frequency.

Now if you increase the dimensions of your capacitor, then any spatial inhomogeneities can also influence the value R. 

(I mean you take an insulator make a small capacitor with small dimensions, you may get a certain value of dielectric loss. Now take the same insulator material, and make a large capacitor, with large dimensions, now spatial homogeneity and uniformity of the insulator can vary over large dimensions.  This depends on how the insulator material is being prepared (film, foil, bulk) and what are the variations in its properties (spatial, and internal defect related properties though its thickness), and other dimensions. These can cause a variation in the dielectric properties.(especially the dielectric loss), and can be a function of frequency.

K. Sreenivas

As a generic question, we have a negative answer: the dielectric loss is not a function of the geometric factor of the dielectric cell (let's call it Fg which is equal to d/A for the parallel-plate capacitor case, where d is distance between plates and A is the surface area of a plate). The rationale is justified no matter the interpretation of dielectric loss, as follows.

First, it is well known that epsilon''=E_im (imaginary part of the material permittivity) is associated with the dielectric loss. E_im=Er_im * Eo, where Er_im is the relative E_im. Since Eo is a constant, we want to analyze Er_im which is derived as the sigma_eff / omega, where sigma_eff is the effective conductivity (it takes into account both ohmic and dielectric losses) and omega is the angular frequency. Sigma_eff is associated with the inverse of the resistivity of the material which can change with frequency but is not generally described/tabulated as a function of the dimensions of the dielectric cell (Fg), Hence, a priori, E_im is not a function of Fg. 

A second classic way to describe dielectric loss (DL) is the "DL per unit volume" (power loss), say W_v = Power_loss / volume = V^2 * G / (A*d) for a parallel-plate capacitor, where V is the magnitude of the applied voltage and G is the conductance of the material. G = w *Eo * Er_im / d. Hence, W_v = V^2 * (omega*Eo*Er_im/d) / (A*d).   We know that the magnitude of the electric field E is defined for this scenario as V/d. Therefore, W_v = omega * E^2 * Eo * E_im. As we can see, Fg (or part of it) does not show up here: W_v, a prori, is not a function of Fg.

The third, and most usual, definition of DL is given as DF or loss tangent. If we model the dielectric cell with the material as a parallel RC circuit, DF = 1/ (omega*Rp*Cp). If we model the system as a series RC circuit, DF = (omega*R_s*Cs). So the question we want to answer is if R*C is a function of any geometric factor (Fg). Interesting: R*C is the relaxation time and this product is given as R*C = (resistivity * d / A) * (Eo*Er_real*A/d) = resistivity*Eo*Er_real. The terms A and d disappear: hence DF is not a function of Fg.

Can we conclude the discussion? No, and this is the case for at least for 2 reasons. First, we had not considered the effects of a larger or smaller cell on the dynamic of the sample, even without any external excitation. For instance, I work with soil analysis and depending on the water content level, it is possible that percolation effects occur and we can perceive this phenomenon as a parallel Rp which changes its value with Fg and this change is not compensated by the changes of Cp. In other words, the previous third analysis is invalidated!!

The second main reason why the geometric factor Fg of a dielectric cell can impact the dielectric measurements in a non-predictable way is associated with the fringing and associated effects. The clue in this case is given at the second previous analysis. Note that we considered that magnitude of the electric field E=V/d. This is the case only when the E lines are perfectly parallel to each other. In a non-homogeneous material, this may not be the case. Moreover, depending on the frequency and values for A and d, the E lines at the boundaries of the dielectric cell will have a shape very different form the E lines at the center. Therefore, we can have a situation that the dielectric cell geometry is interfering with the results!! Even worse, in many cases, with a fixed geometry Fg, this value still changes with frequency. That is why some papers show the spectra of Fg: if this one is stable, it means that the instrumentation is potentially not impact the analysis of the material.

I omitted from this discussion the impact of the electrode interfaces at low frequency (e.g.,

Hello All,

I am trying to design an equivalent circuit of my coil resonator. Which is resonating around 3.6GHz. As we know the coil resonator have parasitic capacitance and resistance i.e. resistance in series with inductor and capacitor is in parallel. But I want to remove this capacitor by the physical capacitor. I tried some of the structure like ideal parallel plate capacitor model in series with coil model but it's not working. So, can anyone suggest me how we can find the total equivalent circuit ( coil and capacitor model), It will be helpful for me.