In the previous tutorial, we learned about signal behavior and the function of a capacitor in a circuit. A capacitor stores electrical charge in the form of an electrostatic field in response to an applied voltage. It charges whenever the applied voltage increases (relative to the current voltage through the capacitor), allowing a charging current until the voltage across it is equal and opposite to the applied voltage. It discharges whenever the applied voltage decreases (relative to the current voltage through the capacitor), allowing a discharge current through it in the opposite direction until the voltage across it is equal and opposite to the applied voltage. The capacitor retains voltage when there is no change in voltage or when it is left open circuit. The capacitor allows current to pass only when the voltage across it changes. For constant DC voltages, it becomes an open circuit, not allowing current to pass through.

**Factors that determine the capacitance of a capacitor
** Any capacitor is basically two conducting plates separated by a dielectric medium. The following equation gives the capacitance of a capacitor:

C=ε*A/d

Where,

C = Capacitance of the capacitor

ε = Absolute permittivity of the dielectric medium

A = surface area (in meters ^{2} ) of conductive plates parallel to each other

d = distance between the conductive plates

The capacitance of a capacitor is proportional to the absolute permittivity of the dielectric material used and the effective surface area of the conducting plates (the surface area of the conducting plate is the smaller of the two). At the same time, it is inversely proportional to the distance between the conducting plates. The absolute permittivity of a dielectric medium is related to the absolute permittivity of free space by the following equation:

ε = ε _{0} * _{εR
} Where,

ε = Absolute permittivity of the dielectric material

ε _{0} = Absolute permittivity of free space or vacuum

ε _{R} = Relative permittivity of the dielectric medium (for free space or vacuum)

**Practical construction of a capacitor**

Any capacitor is designed to achieve a nominal capacitance while keeping the capacitor size as small as possible. Therefore, manufacturers try to achieve maximum capacitance in construction. The capacitance of a capacitor can be maximized in the following three ways:

1) Using a suitable dielectric medium – The absolute permittivity of dry air is approximately equal to that of free space. If the absolute permittivity of free space is taken as 1, that of dry air will be 1.0006. By using a dielectric material with higher absolute permittivity, the capacitance of a capacitor can be increased many times over. There are a variety of materials that are used as the dielectric medium in capacitors. Some of the commonly used dielectric materials are listed in the following table with their relative permittivity (dielectric constants):

By using a suitable dielectric material such as mica in place of dry air, the capacitance can be increased by 5 to 7 times.

2) Increased surface area – The more the surfaces of the conducting plates are parallel to each other, the greater the capacitance. One way to increase surface area is multiplate capacitors. In a multiplate capacitor, the conductive surfaces are designed as multiple conductive sheets connected to a common conductor. The two arrangements of conducting sheets are paired so that in one of the conductors, only one surface of the outer sheets remains in contact with the dielectric medium. In contrast, with the other conductor, both surfaces of the outer sheets remain in contact with the dielectric medium.

A nine-plate capacitor is shown in the image above. One of the terminals of the above capacitor has five plates, while the other terminal has four plates connected. The capacitor above has eight times the surface area, therefore eight times the capacitance. The following equation gives the capacitance of a multiplate capacitor:

C = ε * (n-1) *A/d

Where n is the number of plates in the multiplate capacitor and A is the surface area of each plate.

3) Reducing the distance between plates – Capacitance can be increased by minimizing the distance between plates. However, this aspect has practical limitations (such as leakage current).

**Types of capacitors
** Capacitors are classified by the dielectric material used in their construction. There are a variety of dielectric materials used in the construction of capacitors. Some of the common types of capacitors are below –

1) Paper

2) Mica

3) Plastic Film

4) Glass

5) Ceramics

6) Electrolyte

7) Semiconductor

8) Variable

**Polarized and non-polarized capacitors**

Although most capacitors can be connected in a circuit without considering the polarity of the voltage applied to them, electrolytic capacitors have a positive terminal and a negative terminal. The positive electrode of the electrolytic capacitor must only be connected to the positive terminal of a battery (direction of the current entering the capacitor) and the negative electrode to the negative terminal of a battery (direction of the current leaving the capacitor). Due to their fixed polarity in any circuit, electrolytic capacitors are called *Polarized Capacitors* . The other types of capacitors, which do not require a fixed polarity connection, are called *Non-Polarized Capacitors* . Polarized capacitors can only be used in DC applications.

**Main performance indicators of a capacitor**
Just like resistors or other electronic components, capacitors also have several electrical properties and some non-ideal characteristics. These properties and characteristics can be an important consideration when selecting the capacitor for a circuit. The same can be considered a key performance indicator of a capacitor. The KPIs associated with capacitors are as follows –

1) *Nominal Capacitance* – Nominal capacitance of a capacitor is the capacitance that should be offered by a capacitor. This is the most important property of a capacitor and is marked on its body along with the working voltage. The actual capacitance provided by the capacitor may not be the same as the nominal capacitance, as the capacitance changes with the frequency of the applied signal and the ambient temperature. The nominal capacitance of standard capacitors is expressed in Microfarad (10 ^{-6} F), Nanofarad (10 ^{-9} F) and Picofarad (10 ^{-12} F).

2) *Working Voltage* – The Working Voltage, or DC Working Voltage, is the maximum continuous voltage that a capacitor can operate without breaking or damaging. It is generally the DC voltage rating marked on the body of a capacitor along with its nominal capacitance. AC signals are generally specified RMS voltage levels. The peak voltage level of any AC signal is 1.414 times the RMS voltage. Therefore, when using a capacitor in an AC circuit, its working voltage is comparable to the peak voltage of the AC signal and not the RMS voltage. Selecting a capacitor with a working voltage at least 1.5 times or twice the specified voltage for a given circuit is always safe. The most common working voltages for standard capacitors are 6.3V, 10V, 16V, 25V, 30V, 35V, 40V, 50V, 63V, 100V, 160V, 200V, 250V , 400 V, 450 V, 500 V and 1000 V.

3 *) Forming voltage* – Forming voltage or test voltage is the maximum voltage that the capacitor can withstand. It can be found in the technical data sheet of the capacitor provided by the manufacturer. A capacitor should rarely be exposed to its test voltage.

4) *Tolerance* – Tolerance indicates the variation in the real capacitance of a capacitor in relation to its nominal capacitance. Typically, capacitors have a capacitance of 10% or 5%. Some capacitors can have a tolerance as low as 1%. Capacitor tolerances can vary between 20% and 80% depending on the intended application. Capacitor tolerance is expressed as a plus or minus value in Picofarad for low value capacitors. In contrast, it is expressed as a percentage change in capacitance for high value capacitors.

5) *Leakage current* – Leakage current is a small amount of current that leaks through the dielectric medium of the capacitor due to the strong electrostatic field on its plates. Leakage current is generally in nano amps. It is related to the dielectric constant (relative permittivity) of the dielectric medium used in the capacitor. The lower the dielectric constant, the greater the leakage current.

Leakage current counts towards the dissipation factor of a capacitor. Generally, the leakage current is very low, often indicated as insulation or leakage resistance in data sheets. It is modeled as a parallel resistance leaking current through the pure capacitor. In electrolytic capacitors, the leakage current is quite significant and is usually explicitly stated in their data sheets as “leakage current”.

Leakage current is an important indicator when a capacitor must be used to couple circuits or store charge. A capacitor that is to be used for charge coupling or storage must have minimum leakage current. The leakage current, however low it may be, is always sufficient to fully discharge the capacitor over time, without any voltage applied.

*6) Polarization* – It is always important to observe polarization in the case of electrolytic capacitors. The positive terminal of a polarized capacitor must always be connected to a positive connection and a negative terminal to a negative connection. The negative terminal of polarized capacitors is usually indicated by a black stripe, stripe, or arrows on one side of the capacitor. Connecting an electrolytic capacitor in reverse polarity will generate a reverse voltage, resulting in a large breakdown current that can permanently damage the capacitor.

7) *reverse voltage* – Reverse voltage is an indicator associated with polarized capacitors. It is the maximum voltage (or the sum of all DC and AC peak ripple voltages) in reverse polarity that the biased capacitor can withstand. Any voltage in reverse polarity other than the 'Reverse Voltage' of the polarized capacitor can damage it permanently.

8) *Ripple Current* – Ripple current is the maximum RMS value of AC current that the capacitor can withstand. It is generally indicated for a frequency of 120 Hz and a temperature of 85°C until otherwise specified. The ripple current through a capacitor increases with increasing frequency and decreasing ambient temperature.

9) *Temperature classification* – Capacitors generally have a working temperature range between -55°C to 125°C. The operating temperature range depends specifically on the capacitor type. Similarly, plastic capacitors have a low temperature range of -30°C to 70°C, and electrolytic capacitors have an operating temperature range of -40°C/-55°C to 85°C. Temperature changes affect the actual capacitance of the capacitor, cause current ripple through it, and can stress the capacitor, posing environmental challenges. For example, at temperatures as low as -10°C, the electrolytic gelatin in electrolytic capacitors begins to freeze. Similarly, other dielectric media also experience stress due to changes in ambient temperature.

10) *Temperature coefficient* – Like resistors, capacitors have positive or negative temperature coefficients. The temperature coefficient of capacitors is expressed in parts per million (PPM) per degree centigrade. The positive temperature coefficient is generally expressed by the letter P followed by a rating in PPM/°C, as P100 indicates a positive temperature coefficient equal to 100 PPM/°C. Likewise, the negative temperature coefficient is indicated by the letter 'N' followed by a classification in PPM/°C. Condensers can have a zero temperature coefficient for a range of temperatures, which is indicated by a temperature coefficient expressed by the letters 'NPO'.

In some circuits, where there should be a minimum tolerance for capacitance, capacitors with negative and positive temperature coefficients can be connected in series or parallel to cancel the effects of temperature on capacitance. Positive and negative temperature coefficient capacitors can also be connected to nullify the effect of temperature on other components in a circuit, such as resistors and inductors. When connecting capacitors with positive and negative temperature coefficients to cancel the effects of temperature, careful calculations must be made to find out the effective capacitance over a range of temperatures.

11) *Equivalent Series Resistance (ESR)* – The Equivalent Series Resistance (ESR) of a capacitor is the internal resistance of the capacitor due to the DC resistance of the plates, the effective resistance of the dielectric medium and the resistance at the contact of the dielectric and the plates conductors. This is the pure resistance offered by the capacitor, which causes energy loss by heating the capacitor during charging and discharging of the capacitor by an AC signal. The ESR of a capacitor is modeled as a resistance connected in series to the pure capacitance. ESR, like capacitance, depends on frequency and serves as a dynamic series resistance of the capacitor.

ESR is counted among the capacitor's operating losses. It is an important indicator because it determines the loss of electrical energy in the case of coupling capacitors and the maximum attenuation in the case of bypass and filter capacitors. The higher the ESR, the greater the RC constant (time required to charge or discharge) of the capacitor, as a capacitor with a higher ESR will offer more resistance to the charging or discharging current.

12) Dielectric Absorption – Dielectric absorption refers to the residual voltage left at the capacitor terminals after complete discharge. Generally, this voltage is not significant, but it can be a serious concern in the case of sampling capacitors used in analog-to-digital converter circuits.

13) Self-inductance – Self-inductance is the inductance induced in a capacitor at high frequencies. This inductance can influence the impedance of the capacitor at high frequencies and can determine which high frequency currents the capacitor will be able to bypass. The ESR, dissipation factor, dielectric absorption, and self-inductance are counted among the operating losses of a capacitor.

Capacitors need to be handled with care. High value capacitors (capacitance greater than 0.01 uF) used in high voltage circuits may have a residual or undischarged voltage that can cause a DC shock at the contact. Therefore, a high-value capacitor must be discharged by short-circuiting its terminals using a screwdriver while troubleshooting such circuits. In the next article we will discuss the different types of capacitors and their technical specifications.