Basic knowledge about capacitors

To put it simply, a capacitors is a component which can store energy and release stored energy when necessary. Due to the fact that the energy stored (charge) is less than a battery, a capacitor can only provide current for a short time when releasing energy (discharge), but it can repeat charging and discharging cycles.

Capacitance (C) can become bigger, when permittivity of dielectric (Ɛ) is bigger, or surface of electrode (S) is bigger, or insulator (d) is thinner.

Structure:

1. Terminal
2. Electrode
3. Insulator (dielectric)
4. Terminal

Let’s have a look at the voltage and current of a capacitor, which is being discharged after charging with DC power supply via resistors.

In a schematic, if we switch on charging side, there will be peak current of V0/R1 flowing through, and capacitor current will become lower while voltage Vc becomes higher.

Charging will complete when Vc = Vo and current will become zero.

Then if we switch on discharging side there will be peak current of V0/R2 flowing through, and capacitor current will become lower while voltage Vc becomes lower. Discharging will complete when Vc = 0 and current will become zero.

What we need to understand here is, that the volume of capacitor current is depending on the amount of capacitor voltage change.

Also, current of V0/R is flowing when switch is on, and when R = 0, theoretically there will be unlimited current flowing and charging discharging will complete in an instant. But in reality, influenced by the internal resistance (ESR) of capacitor, wiring resistance and reactance, there will be no unlimited current.

However, capacitor has much less resistance compared with battery, so it may possibly realize instantaneous charging and discharging.

Let’s have a look at the voltage and current of a capacitor, which is applied with AC power supply.

In example 1, we mentioned that the magnitude of the current flowing through the capacitor follows the magnitude of the change in the voltage of the capacitor, and this is the same for AC waveforms.

1. When the voltage rises from 0 V, the current flows greatly but as the voltage rising speed slows down the current decreases and when the voltage becomes maximum (zero voltage change) the current becomes zero.
2. When the voltage begins to fall from the maximum value, a negative current begins to flow, and at the point where the voltage becomes zero (the change in voltage is the maximum), the current becomes maximum.
3. and 4. area work in the same way as above.

Looking at the waveform of voltage and current, if the voltage waveform is a sinusoidal wave, the current waveform is also a sinusoidal wave, and the current waveform is shifted by 1/4 cycle before the voltage waveform (the phase of the current is 90 degrees ahead).

In addition, it can be seen that large current flows when the voltage change is large, in other words, the larger the high frequency voltage change has, the larger the current flows.

The flowing current (effective value) at this time is indicated by the following equation:

Ic = 2πf * C * Vc

• Ic:  Capacitor current (Arms)
• π: Pi (3.14)
• f: Frequency (Hz)
• C: Capacitance (F)
• Vc: Power supply voltage (Vrms)

Discharge circuit

Discharge circuit is a circuit that operates the connected load by discharging the charge stored in the capacitor. Since a capacitor can instantaneously discharge large current, it is used as a camera strobe or backup power supply for emergency.
In the circuit example, when the switch is connected to the power supply side, the capacitor is charged and charging stops when charge accumulates to the power supply voltage.
When the switch is connected to the load (bulb) side, the capacitor starts discharging and the bulb lights up.

Smoothing circuit
The smoothing circuit is a circuit that smooths pulsating flow after rectifying alternating current and converts it into direct current.
A typical example is a power supply circuit. The capacitor makes the voltage wave (ripple, pulsating flow) which is rectified by the diode bridge rectified (full-wave rectified in the circuit example) AC input voltage more flatter.

Decoupling circuit
As its name implies, the decoupling circuit is a circuit that uses a capacitor to isolate signal coupling.
In this example, by placing a capacitor as shown in the figure, on the signal path including the AC component with high frequency (noise) in the basic AC, only the noise component with high frequency passes through the capacitor and becomes separated, and noises are not transmitted after this.

Coupling circuit
The coupling circuit is a circuit in which only AC component passes but no DC component passes.
It is used when you want to eliminate the influence of direct current component (also called DC cut etc.) in the amplifier circuit etc. of the audio signal.

An ideal capacitor is only the capacitance component, but an actual capacitor contains resistance component and inductance component. These parasitic components have a great influence on the performance of the capacitor. The simplified equivalent circuit of a capacitor is shown in this figure.

1. Capacitance (C)
2. Insulation resistance (IR)
3. Equivalent series resistance (ESR) or loss tangent (tanδ)
4. Equivalent series inductance (ESL)

From the formulas above, we can see the following.

In the low frequency area, the impedance is almost determined by capacitance (C).
The impedance is determined by ESR at the self-resonant frequency (frequency coming from 2πf L = 1 / (2πf C)).
In the high frequency area, the impedance is almost determined by ESL.
This is shown in the graph on the right side. 

The impedance Z of the capacitor decreases with the capacitance (C) up to the self-resonant frequency, but at self-resonant frequency the influence of C and ESL becomes zero and becomes ESR only, after that it becomes inductive (ESL) in high frequency area.

When using a capacitor in its main application of noise absorption (decoupling), the noise absorption effect is determined by impedance, therefore it is necessary to select parts according to the following points.

The noise frequency and the self-resonant frequency of the capacitor are close.
The ESR is small. 
In case of high frequency noise, ESL is small.

Ceramic capacitors

Ceramic capacitors are capacitors that use ceramics with a high dielectric constant for the dielectric and have the following features:

• Nonpolar
• Excellent high-frequency characteristics (low ESR)
• High heat resistance
• Long lifetime

Originally it was a high-voltage / low-capacitance single-plate capacitor. However, its use range has expanded greatly, after the appearance of multilayer ceramic capacitors which have small size and large capacitance due to the thin-film layered structure, as well as the appearance of temperature compensation which overcomes its temperature characteristic (big change ratio of capacitance due to temperature), and it became the most widely used capacitor among capacitor world. For temperature compensation, the shape is larger than the conventional high dielectric constant type and it is difficult to increase the capacitance, so it is used depending on the application.

However, ceramic capacitors have also disadvantage of DC bias characteristics (big change ratio of capacitance due to applied voltage), Piezoelectric effect (unusual noise due to vibration at high frequency), and cracking due to temperature /mechanical shock. Those points shall be checked when using it.

Film capacitors

Film capacitors are capacitors using plastic film for dielectric and have the following features:

• Nonpolar
• Excellent high-frequency characteristics (low ESR)
• Excellent temperature characteristics (Change rate of capacitance by temperature is small)
• Long lifetime

Compared to ceramic capacitors, film capacitors have low heat resistance; but they have excellent temperature characteristics and possible high precision of capacitance, and additionally no DC bias characteristics, squeal noise, or problem of cracking due to temperature / mechanical shocks. Therefore, they are capacitors with higher performance compared with ceramic capacitors, however, they have disadvantages such as large size and high price. Therefore, they have been used in voltage / capacitance range that cannot be covered by ceramic capacitors, with high performance and high precision.
 

Aluminum electrolytic capacitors have a structure in which an aluminum oxide film, which becomes a dielectric, is formed on the surface of the aluminum foil of the anode, and electrolyte liquid (consisting of a solvent in which electrolyte is dissolved) is used as an electrolyte (cathode).

One feature of aluminum electrolytic capacitors is their large capacity, which is achieved by increasing the electrode surface area (S) through the etching of the aluminum foil surface to form irregularities and by forming ultra-thin (d) of oxide films at the Angstrom level.

However, their equivalent series resistance (ESR) is higher than that of ceramic and film capacitors.

Aluminum electrolytic capacitors are products with a limited life. The electrolyte liquid vaporizes depending on the temperature and gradually penetrates the sealing rubber. Consequently, the capacity decreases and ESR rises over time, eventually leading it to be in an open state (electrolyte liquid having dried up).

When estimating the life of aluminum electrolytic capacitors, the "10ºC 2-fold law" can usually be applied.

Electric double layer capacitors

A electric double layer capacitor is a special capacitor having an intermediate capacitance between an aluminum electrolytic capacitor and a secondary battery (battery), and its capacitance density is about 1,000 times or more of an aluminum electrolytic capacitor, about 1/10 of a secondary battery.

There is no dielectric like an electrolytic capacitor in an electric double layer capacitor. Instead, it uses the electric double layer that is formed at the interface between the electrode and the electrolyte as function of the dielectric. This is where the name “electric double layer capacitor” comes from.

Charge and discharge of electric double layer capacitors is based on the adsorption / desorption of ions on the electrode surface of activated carbon which is used for positive and negative electrodes. Changes of the double layer due to this charging / discharging are shown in following figure.

An electric double layer capacitor has the following features compared with a secondary battery.

• The number of charge / discharge cycles hardly affects the characteristic deterioration (maintenance free)
• Easy charging / discharging (dischargeable up to 0 V, energy level can be known with terminal voltage, has the following features, chargeable with both small and large current)
• Not subject to environmental regulations (collection, disposal, tariffs) like batteries

Therefore, it is used as a backup power supply, such as data protection of IC memory during power off.