Sunday, 2 March 2014

Capacitors

Capacitor is an energy storage element, which stores energy in the form of electrical energy. Capacitance is measured in 'Farad'.
      Simplest capacitor is a parallel plate capacitor. Two conductive plates each having area of 'A' and are separated by a distance’d’, arranged parallel acts as a parallel plate capacitor. The capacitance C offered by this structure is given by 
 
Where ℰ is given by permittivity of dielectric between plates. If air is the dielectric then ℰ=ℰ0. If any other dielectric material is used then ℰ=ℰ0ℰr.
If V is the potential difference applied across parallel plate capacitor C, then charge Q stored in the capacitor is given by
Q=CV
The energy E stored in a parallel plate capacitor is  
Capacitor won't allow sudden changes in voltage.
Symbols:
Voltage across the capacitor
 Current through capacitor
 
So if the voltage across the capacitor is changed suddenly in 0 time, then ideally current through capacitor is infinite. (since dt =0)
Impedance offered by the capacitor 'C' is  

 where ω=2πf, f=frequency
As the frequency 'f' increases the impedance offered by the capacitor reduces. So high frequency AC signals simply pass through capacitor. Since DC signal has '0' frequency, impedance offered by capacitor to DC signal is infinity. So DC will be blocked by capacitor.
In ideal capacitor current leads thee voltage by 90 degrees.
Transient response of a capacitor:
 

In the above circuit pulsed voltage source is used across capacitor. Pulse duration is 1ms, and rise time and fall time are 1ns. So this makes voltage across capacitor to change suddenly. Using Ic ammeter, we are measuring current through capacitor. Below figure shows the simulation results.
 
You can observe, the current through capacitor is abnormally high. So capacitor won’t allow sudden change in voltage and acts as short circuit. That’s the reason why current through it increased abnormally high.   
Capacitor equivalent circuit:
'C' is the ideal capacitance

Rd, Cd represents dielectric absorption properties

RL is the leakage resistance

ESR is the equivalent series resistance of the device. This is due to electrode resistance, lead resistance etc.

ESL is the equivalent series inductance of the capacitor. This is also due to inductance of electrode and lead inductance.


Capacitor parameters:

Working DC voltage: This is the maximum peak DC voltage that can be applied across a capacitor continuously.

Reverse Voltage and polarity: Reverse voltage means applying negative voltage to positive pin. All capacitors having polarity, will get damaged if a reverse voltage is applied across it.

DC Leakage current: This is the current, which flows through a capacitor, when voltage is applied across it. (After one to five minute charging period is over)

Equivalent series resistor: ESR is the high frequency parameter. It represents capacitor ohmic resistance. As temperature increases ESR reduces.

AC Power dissipation: Maximum power dissipation depends on case size (package size) of the capacitor.
 
Dissipation factor/Loss tangent: Any ideal capacitor will have 90 degree phase difference between applied voltage and current. I.e. Current leads the voltage by 90 degrees. But because of ESR of capacitor, this phase difference will change. You can see this from the below figure, V practical is having less phase difference than V ideal. 

So the 'V' will have two components VR and VC. VR is in phase with the current I, which will dissipate power . tanδ is called loss tangent (or) dissipation factor.

Reciprocal of loss tangent is called quality factor.

Dissipation factor is measured at 120Hz, up to 1Vrms max and up to 2V DC max. at 25oC. Dissipation factor increases with temperature.  This is a useful measurement of resistive component of capacitor at low frequencies
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