The Capacitor and It's Uses

What is a capacitor and what is it used for?This picture shows capacitors ranging from 10 picofarads to 3300 microfarads.  Ceramic, film, and electrolytic capacitors types are shown.

A capacitor is two terminal device that has the ability to store an electrical charge. It is most commonly used to block instantaneous changes in voltage between two nodes of a circuit, but other fields may use it in other ways such as to hold the charge for the ignition of an engine. Such ignitions are called CDI for Capacitive Discharge Ignition. We will be focusing on the electronics application here. The capacitor's ability to block instantaneous changes in voltage makes them particularly useful for power or signal conditioning to filter out unwanted frequency content.

 

Units used for capacitance

The unit of measurement for capacitance is the farad. Remember from from our Electrical Theory tutorial that the unit of measure for an electrical charge is the coulomb. One farad is equal to the number of coulombs per volt of potential placed across the capacitor.

Capacitance in farads equals charge in coulombs divided by potential in volts.

In practice one farad is much more capacitance that we will need in most electronics.  We will more often be measuring capacitance in picofarads (pF), nanofarads (nF), or microfarads (μF).

 

1 pF = 0.000000000001 F

1 nF = 0.000000001 F

1 μF = 0.000001 F

 

How do capacitors work?

Remember from our Electrical Theory tutorial that electrical charge is created by having more or less electrons than protons in an atom and that current is the flow of of free electrons. A capacitor does not allow those electrons to flow through it, but it has parallel plates for storing them when a voltage is applied across the capacitor. The plates are separated by an insulator, also known as a dielectric, that prevents the actual flow of current between the plates.

 

At rest, there is no charge on the plates of the capacitor, but when a voltage is applied across the two terminal of the capacitor, the electrons flow into the plate on the negative side and flow out of the plate on the positive side to form negatively charged ions on the negative side of the capacitor and positively charged ions on the positive side of the capacitor. When voltage is first applied, there is little impedance (another word for resistance usually associated with transient conditions) for electrons flowing into and out of these plates and the change in voltage across the capacitor is rapid.  As the negatively charged plate fills up with electrons and the positively charged plate empties, the impedance to flow of electrons increases and the rate of change in voltage across the capacitor is reduced.

 

To use an analogy, imagine a conference room at the end of a long hallway is the negative side of a capacitor and a crowd of people represent free electrons. When people first start to enter the empty room, they can file in quickly, but as the room fills up, the rate at which people can enter the room slows as people have to jostle around for space.

 

Capacitor transient behaviors

The time it takes for the capacitor to charge from zero charge to the applied voltage or the time it takes to return to zero charge from the applied voltage level is called the "transient period". This transient period can be calculated, but first you must calculate what is known as the "time constant", represented by the Greek letter tau.

The time constant of a capacitor is represented by the Greek letter tau and is equal to resistance times capacitance.

 

Once the time constant is calculated, the voltage across the the capacitor at any point during this transient condition can be easily calculated per the equations to the right. Notice the charging profile is the inverse of the discharging profile. If you work out these equations you will find that the transient period is always equal to approximately five time constants. Therefore, if we want to just find out the length of the transient period, we can forgo using the charge time or discharge time formula, and just multiply the time constant by 5.

The voltage across a capacitor during its transient can be calculatd once the time constant it know.  The transient period is 5 time constants.

The transient behavior of a simple resistor-capacitor (RC) circuit is shown below. The circuit is shown to the left and the voltage measured at three points is displayed to the right. Oscilloscope-XSC1 shows the voltage source signal (V1) as a square wave with a 0.5 ms on-time, and a 1 ms period. This means it is a 1 kHz ( 1 cycle / 0.001 s = 1000 Hz) signal square wave with a 50% duty cycle. This signal provides adequate time for the RC circuit to return to a steady state value between each change in the signal so that we can demonstrate the formulas above. Oscilloscope-XSC2 shows the voltage across R1 and the voltage across C1. All three signals are synchronized in the time domain. We can calculate the time constant  as R * C = 3000 Ω * 0.00000002 F = 0.00006 seconds or 60 μs (microseconds). Remember the transient period is equal to approximately five time constants. 5 * 60 μs = 300 μs. Notice that each division in the time axis of the oscilloscope plots below represents 200 μs.  So 300 μs would be equal to 1.5 division. You can see that is precisely how long the voltage across the both the capacitor and the resistor in the circuit takes to reach a steady state condition after a change in voltage level.

 

Some other observations that can be made from the circuit simulation below are:

 

The transient period of a resistor capacitor circuit is equal to five time constants.  KVL is obeyed throughout the transient.

 

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