There is a huge difference between complete and incomplete definition especially when explaining an equation.
For instance, we might define displacement as the product of velocity and times (s = v*t). However, this definition is incomplete. It is only true if the velocity of the subject that we are considering is constant during time t. If the velocity of the subject is varying, displacement is the integration of velocity with respect to time ( s = Integration (v) dt). Thus, different definition will lead us to different answer.
Most of us may define capacitance as C = (Xo*Xr*A)/d where Xo is the permittivity of free space, Xr is the relative permittivity of the material filling between the electrodes, A is the area of the capacitor electrode and d is the distance between the two electrodes. Is this definition complete? No, it is not.
First, the definition of the A is very obscure. What if the area between the two electrodes are not the same? For instance, if the bottom electrode is larger than the top electrode, how do we define A? We should define A as the area of the overlapping electrodes.
Probably most of us are not aware that by defining C = (Xo*Xr*A)/d, we already made an assumption and this assumption is very important. We assumed that the contribution due to parasitic capacitances are negligible. Parasitic capacitances exist due to contribution of fringes, backs of electrodes and connecting wires. If we have a capacitor of several hundred femto Farads ( ie 200fF = 200 x 10^-15), we cannot use the above equation because the parasitic capacitance may be the same order or greater in magnitude with the capacitor itself. Thus, complete definition should include this assumption.
Kelvin proposed a solution for this by introducing a 3rd electrode, the guard ring. The guard ring encloses one of the electrode while the other electrode is enlarged in its sideways. Thus, the guarded electrode will look like an island and surrounded with a guard ring.
There are two rules that need to be obeyed to eliminate the parasitic capacitances using this technique. First, the guard ring must be connected to the ground and the gap between the island electrode and the guard ring must be very small compared to d. Very small here means the gap must be at least 1/10 of d.
When the capacitor is connected to voltage supply, V, the potential of island electrode will be V. For simplicity, let assume the potential of the other electrode is zero. At the same time, the potential of the guard ring is also 0 because it is connected to the ground. Since the gap between the island electrode and the guard ring is very small compared with the other electrode, the parasitic capacitances tend to connect with the guard ring. Thus, during charge and discharge of the capacitor, we won't measure the current contribution due to the parasitic components. This will eventually lead to better measurement.
However, if the gap between the island electrode and the guard ring is comparable with d, the stray capacitances will still tend to connect with the other electrode thus, parasitic capacitances will not be eliminated totally.
If Kelvin guard ring is implemented and both of the rules are obeyed, only then we can determine the capacitance with high level of accuracy with equation C = (Xo*Xr*A)/d. If not, high level of accuracy can only be achieved if further analytical calculations are implemented to produce another equation which take care of the parasitic components.
For instance, we might define displacement as the product of velocity and times (s = v*t). However, this definition is incomplete. It is only true if the velocity of the subject that we are considering is constant during time t. If the velocity of the subject is varying, displacement is the integration of velocity with respect to time ( s = Integration (v) dt). Thus, different definition will lead us to different answer.
Most of us may define capacitance as C = (Xo*Xr*A)/d where Xo is the permittivity of free space, Xr is the relative permittivity of the material filling between the electrodes, A is the area of the capacitor electrode and d is the distance between the two electrodes. Is this definition complete? No, it is not.
First, the definition of the A is very obscure. What if the area between the two electrodes are not the same? For instance, if the bottom electrode is larger than the top electrode, how do we define A? We should define A as the area of the overlapping electrodes.
Probably most of us are not aware that by defining C = (Xo*Xr*A)/d, we already made an assumption and this assumption is very important. We assumed that the contribution due to parasitic capacitances are negligible. Parasitic capacitances exist due to contribution of fringes, backs of electrodes and connecting wires. If we have a capacitor of several hundred femto Farads ( ie 200fF = 200 x 10^-15), we cannot use the above equation because the parasitic capacitance may be the same order or greater in magnitude with the capacitor itself. Thus, complete definition should include this assumption.
Kelvin proposed a solution for this by introducing a 3rd electrode, the guard ring. The guard ring encloses one of the electrode while the other electrode is enlarged in its sideways. Thus, the guarded electrode will look like an island and surrounded with a guard ring.
There are two rules that need to be obeyed to eliminate the parasitic capacitances using this technique. First, the guard ring must be connected to the ground and the gap between the island electrode and the guard ring must be very small compared to d. Very small here means the gap must be at least 1/10 of d.
When the capacitor is connected to voltage supply, V, the potential of island electrode will be V. For simplicity, let assume the potential of the other electrode is zero. At the same time, the potential of the guard ring is also 0 because it is connected to the ground. Since the gap between the island electrode and the guard ring is very small compared with the other electrode, the parasitic capacitances tend to connect with the guard ring. Thus, during charge and discharge of the capacitor, we won't measure the current contribution due to the parasitic components. This will eventually lead to better measurement.
However, if the gap between the island electrode and the guard ring is comparable with d, the stray capacitances will still tend to connect with the other electrode thus, parasitic capacitances will not be eliminated totally.
If Kelvin guard ring is implemented and both of the rules are obeyed, only then we can determine the capacitance with high level of accuracy with equation C = (Xo*Xr*A)/d. If not, high level of accuracy can only be achieved if further analytical calculations are implemented to produce another equation which take care of the parasitic components.
In conclusion, defining equation accurately is very important as different definition leads us to different result. Accurate definition can only be achieved if one understand the root of the equation and all assumptions made during the process of producing the equation.
6 comments:
man..very scientific but interesting to share.
before this i never know that the capacitance equation that i use everyday is only true if the parasitic capacitances are negligible compared to the capacitance of the capacitor. none of my lecturer mentioned that. thank God i came across this when doing some research.
man, i cant understand la...
i put some pictures later. i think it may help
whoah! professori...so complex loh...hhhmmm...heard that sheffield was snowing last nite...
owh, i didn't know that. probably the outskirt areas were snowing. certainly not the city centre.
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