Capacitors
- Micah Black
- Aden Chu
- Kevin Li
What are Capacitors?
Capacitors are passive two-terminal energy storage elements composed of two conductors separated by an insulating (dielectric) material. The most basic parallel-plate capacitor is a device consisting of two parallel conducting plates of area A separated by a distance d.
How do Capacitors Work?
Consider the basic circuit shown below consisting of a voltage source connected to a capacitor controlled by a switch.
When the switch closes, the voltage source becomes electrically connected to the capacitor. Naturally, electrons begin to flow from the negative terminal of the voltage source to the lower plate as shown below. Electrons residing above along the upper plate are then repulsed towards the positive terminal of the voltage source. As the electrons continue along this behaviour, the lower plate will be associated with an increasingly negative charge. Similarly, the upper plate will have an increasingly positive charge of the same magnitude.
The resulting effect of this phenomenon is the formation of a potential difference across the two plates. This is characterized by an electric field which stores electrical energy. It must also be noted that the voltage across capacitors may not change in a discontinuous fashion, that is, the function describing the voltage across a capacitor with respect to time is continuous. The current "across" capacitors however, can change instantaneously. In DC steady state, capacitors act ideally as open circuits.
Capacitor Theory
Charge on a Capacitor
For a fully charged capacitor in steady state, we have the following expression:
Here, we note:
Units of Capacitance
The unit of capacitance is farads (F).
A 1F capacitor stores 1C of charge with a 1V potential applied to it.
Capacitance of Two Parallel Plates
The capacitance of a parallel plate capacitor is:
Here, we note:
Capacitor Current
The current "across" a capacitor is given by:
Capacitor Voltage
The voltage across a capacitor is given by:
Note that t_0 is an initial time where the voltage across the capacitor is known, and tau is merely a variable of integration representing time.
Capacitor Power
The instantaneous power of a capacitor is given by:
Capacitor Energy
The energy of a capacitor is given by
where:
Capacitors in Parallel
The equivalent capacitance Ceq of n capacitors connected in parallel is given by:
Capacitors in Series
The equivalent capacitance Ceq of n capacitors connected in series is given by:
Specifications/Performance Metrics
Capacitance
The capacitance of a capacitor is its nominal/ideal capacitance value. It may be quoted at a particular frequency as capacitance may vary slightly with differing frequencies for some types of capacitors (typically seen for datasheets of electrolytic capacitors).
The standard unit of capacitance is the farad (F). Most capacitors have capacitance values well below 1F. Some supercapacitors have capacitances that are quite high, and are measured in terms of farads.
Tolerance
The tolerance value of a capacitor describes the extent to which the actual capacitance can vary from its specified nominal capacitance value. Tolerance is often expressed as a percentage, and may also be expressed as an actual value (i.e., 20pF+-1pF). In general, capacitors should be selected with an understanding of the given application’s sensitivity.
Tolerance values of ±5%/10%/20% are commonly used for coupling and decoupling applications. More sensitive applications may require the use of capacitors with tolerances of ±1% and ±2% or better. For example, ceramic capacitors used for coupling and decoupling applications are typically rated at ±5% and ±10%, or ±20%. Electrolytic capacitors often have a tolerance of -20% and +80%.
Voltage Rating (Maximum Voltage / Working Voltage)
The voltage rating of a capacitor is the maximum voltage that can be safely applied across it. Exceeding the maximum voltage can result in permanent damage to the capacitor. This specification is typically quoted for DC voltages. For AC applications, an RMS value is typically quoted. In general, capacitors should be selected with a sufficiently large safety margin from the maximum voltage rating.
Equivalent Series Resistance (ESR)
The equivalent series resistance of a capacitor is the impedance of the capacitor to alternating current and is particularly important to consider at high frequencies. This specification is the accumulation of the resistance of the dielectric material, the DC resistance of the terminal leads, the DC resistance of the connections to the dielectric, and the capacitor plate resistance. These resistances are all measured at a particular frequency.
Ripple Current
The ripple current of a capacitor refers to the maximum amount of current that can flow into it such that it does not cause a significant rise in temperature (due to ESR heat dissipation). High levels of ripple current can lead to noticeable levels of heat dissipation, which can diminish a capacitor’s lifespan.
This specification is important for circuits with high current flow (i.e., smoothing capacitors for power supply circuits).
Leakage Current
The leakage current of a capacitor refers to the amount of current that flows through its insulating barrier. Ideally, zero current should flow through the dielectric between the two plates of a capacitor. This phenomenon occurs because capacitors are not perfect insulators. Leakage current may also be quoted with voltage and temperature. It must be noted that leakage current increases with increasing temperature.
A previously charged capacitor will slowly lose its stored energy due to leakage. When a fully charged capacitor is continuously supplied, current will also leak and flow through it. Leakage current is typically quoted for large capacitors and when leakage is a significant factor.
Supercapacitors and aluminum electrolytic capacitors normally have values of leakage current quoted.
Leakage Resistance / Insulation Resistance
The leakage/insulation resistance is related to leakage current by Ohm’s law. Insulation resistance is typically quoted when very high values of resistance are encountered.
Ceramic capacitors or plastic film capacitors (where leakage current is insignificant), the values of resistance are typically quoted.
Leakage current and resistance can impact circuits in a variety of ways. High voltage circuits can experience large quantities of heat dissipation with even the smallest levels of leakage current. In general, leakage current can greatly impact high impedance circuits.
Types of Capacitors
Electrolytic Capacitor
An electrolytic capacitor is a type of polarized capacitor which uses an electrolyte as one of its conducting plates (electrodes) to achieve relatively large capacitances or high charge storage (an electrolyte is a liquid or gel that contains a high concentration of ions).
Electrolytic capacitors can be subcategorized into three families based on the material used to construct the dielectric:
Aluminum electrolytic capacitors
Tantalum electrolytic capacitors
Niobium electrolytic capacitor
Structure: Electrolytic capacitors are polarized as their internal structures are asymmetrical in nature. Typically, the anode (positive plate) is made of a metal which forms an insulating oxide layer that acts as the dielectric. The (true) cathode (negative plate) is made of a solid, liquid, or gel electrolyte which covers the surface of the dielectric oxide layer. The enlarged anode surface and thin dielectric oxide layer of electrolytic capacitors give them their large capacitances.
Important Considerations: Since electrolytic capacitors are polarized, the voltage at the anode (positive) must be higher than at the cathode (negative) at all times. Applying a reverse polarity voltage, or exceeding the maximum rated working voltage by even a small magnitude can destroy the dielectric, rendering the capacitor useless. It must also be noted that electrolytic capacitors typically have large tolerances. Capacitance drift (divergence from nominal capacitance) is prevalent among electrolytic capacitors.
Applications: Electrolytic capacitors are widely used for decoupling or noise filtering in power supplies and DC link circuits for variable-frequency drives, for coupling signals between amplifier stages, and for storing energy. In general, electrolytic capacitors are used for passing or bypassing low-frequency signals, and storing large amounts of energy.
Advantages:
Large capacitance or high charge storage
Low cost
Disadvantages:
Polarized nature may lead to assembly errors
Large leakage current
Short lifetime
Capacitance drift (divergence from nominal capacitance)
Mica Capacitor
Silver mica capacitors use mica as its dielectric material. These capacitors have great high-frequency properties due to their nature of having low resistive and inductive losses. These capacitors are also very stable over time.
Mica refers to a group of natural minerals which are very electrically, chemically, and mechanically stable. There are two types of mica capacitors: silver and clamped mica capacitors (clamped mica capacitors are now obsolete and will not be discussed).
Structure: Silver mica capacitors are composed of sandwiched sheets of mica coated with metal on both sides encased in epoxy for environmental protection. These capacitors are generally used when circuit design calls for stable and reliable capacitors of relatively small capacitance values. Additionally, they are low-loss capacitors, allowing them to be used at high frequencies.
Applications: To recall, mica capacitors have great stability and high-frequency properties as they yield low resistive and inductive losses. In general, mica capacitors are used for:
Power RF circuits (high stability is required)
High-frequency tuned circuits such as filters and oscillators
Pulsed applications such as snubbers
High power applications such as RF transmitters
High-voltage applications in general
Advantages:
High stability as their capacitance changes little over time
Low resistive and inductive losses (useful for high-frequency applications)
Disadvantages:
Less economical than ceramic capacitors which have similar properties at a fraction of the price of mica capacitors
Ceramic Capacitor
Ceramic capacitors use ceramic materials as their dielectric. They are the most frequently used capacitors in our modern industry. Ceramic capacitors are divided into four classes, two of which that are primarily considered:
Class 1: Used in relatively precise applications, offering high stability and low losses for resonant circuit applications. These capacitors are very accurate, and have nominal capacitance values which are relatively stable with respect to applied voltage, temperature, and frequency.
Class 2: Used for less sensitive applications, offering high volumetric efficiency for buffer, by-pass, and coupling applications
The two most common types of ceramic capacitors are the multi-layer ceramic capacitors and the ceramic disc capacitors.
Ceramic Disc Capacitors: Ceramic disc capacitors are created by coating a ceramic disc with silver contacts on both sides. Larger capacitances can be achieved by stacking multiple layers. Ceramic disc capacitors are typically through-hole components and are less size-efficient compared to MLCCs. These capacitors typically have capacitances that can range from 10pF to 100uF, with voltage ratings between 16V to 15kV.
Multi-layer Ceramic Capacitor (MLCC): MLCCs are created by accurately mixing finely ground granules of paraelectric and ferroelectric materials and alternatively layering the mix with metal contacts. The device is then brought to a high temperature to sinter the mixture, resulting in our typically desired ceramic material. MLCCs are highly size efficient, consist of 500 layers or more, and have a minimum layer thickness of approximately 0.5 microns.
Applications: Class 2 high-power capacitors are used in high voltage laser power supplies, power circuit breakers, induction furnaces etc. Small-form SMD capacitors are often used in PCBs and high-density applications use capacitors which are size comparable to a grain of sand. They are also used in DC-DC converters which operate at high-frequencies and emit high levels of electrical noise. Ceramic capacitors are used as general-purpose capacitors, used in a large variety of applications.
Advantages:
Size efficient
High stability as their capacitance changes little over time, or with differing applied voltage, temperature, and frequency
Low resistive and inductive losses
(Class 2) High capacitance per volume
Ceramic Dielectric Codes
The ceramic capacitor family consists of many different ceramic dielectrics.
Class 1 Ceramic Capacitor Dielectric
Ceramic capacitors which use Class 1 dielectrics offer the highest stability and low loss performance. These dielectrics provide accurate high tolerance capacitors with stable voltage and temperature coefficients. These capacitors are suitable for oscillators, filters, and etc.
Class 1 ceramic dielectrics are based on finely ground materials such as TiO2, with additives of Zn, Zr, Nb, Mg, Ta, Co, Sr. Many modern C0G (NP0) formulations contain Nd, Sm, and other rare earth oxides.
Class 1 Capacitor Codes:
The performance of a class 1 ceramic capacitor dielectric is defined by a three-character code.
The first character is a letter describing the significant figure of the change in capacitance over temperature in ppm/°C
The second character is numeric and provides the multiplier
The third character is a letter and gives the maximum error in ppm/°C
For example, type C0G (NP0) has 0 drift, with an error of approximately ±30ppm/°C. C0G is the most popular formulation of the EIA Class 1 ceramic materials.
C0G (NP0) ceramics offer one of the most stable capacitor dielectrics available. The change in capacitance with respect to temperature is 0±30ppm/°C. Capacitance drift of hysteresis is negligible at less than ±0.05% versus up to ±2& for films. The C0G (NP0) ceramic dielectric usually has a “Q” in excess of 1000 and shows little capacitance or “Q” changes with respect to frequency. The dielectric absorption is typically less than 0.6%, similar to that of mica, which has very low absorption.
Class 2 Ceramic Capacitor Dielectric
Ceramic capacitor class 2 dielectrics have a much higher level of permittivity than their class 1 counterparts. This gives them higher volumetric capacitance efficiency at the expense of accuracy and stability. These capacitors also exhibit a non-linear temperature coefficient and a capacitance that is slightly dependent on the applied voltage. These capacitors are therefore ideal for decoupling and coupling applications where exact capacitance is noncritical, but where space might be of concern.
Class 2 Capacitor Codes:
The performance of a class 2 ceramic capacitor dielectric is defined by a three-character code.
The first character is a letter describing the low-end operating temperature
The second character is numeric and describes the high-end operating temperature
The third character is a letter describing the capacitance change over the temperature range
Popular class 2 ceramic dielectrics include:
X7R, which has a temperature range of -55°C to 125°C, with a ΔC/C0 of ±15%
Y5V, which has a temperature range of -30°C to 85°C, with a ΔC/C0 of +22%/-82%
Z5U, which has a temperature range of +10°C to 85°C with a ΔC/C0 of +22%/-56%
MLCC Package Sizes
MLCCs are manufactured in standardized shapes and sizes for comparable handling. Standardization for MLCCs is dominated by American EIA standards, and so the dimensions of MLCC chips are provided in units of inches. For example, a rectangular chip with dimensions 0.06 inches length and 0.03 inches width is coded as “0603”.
It is important to note that packaging size can impact the performance of a capacitor. For example, smaller packages will generally have large parasitic inductances. Also note that larger package sizes typically correlate to greater working voltage ratings.
DC Bias Characteristic
The capacitance, especially of capacitors classified as high dielectric constants (B/X5R, R/X7R characteristic), may differ from the nominal value when a DC voltage is applied.
For example, as shown in the chart, the larger the DC voltage applied to the high dielectric constant capacitors, the more the effective capacitance is reduced.
The characteristic of change in capacitance with respect to the applied voltage is called the “DC bias characteristic).
In high dielectric constant capacitor type ceramic capacitors, mainly BaTiO3 (barium titanate) is used as a principal component of high dielectric.
BaTiO3 has a perovskite shaped crystal structure and above the Curie temperature, it becomes a cubic shape with Ba2+ ions present at the vertices, O2- ions present at face centers, and Ti4+ ions present in body centers.
At the Curie temperature (approximately 125°C) or more, BaTiO3 has a cubic crystal structure. Below the Curie temperature, and within an ambient temperature range, BaTiO3 has a tetragonal crystal structure.
Polarization occurs as a result of the unit shift of axially elongated Ti4+ ion crystals. This polarization occurs without the application of an external field or pressure, and is known as “spontaneous polarization”. A characteristic that has spontaneous polarization and a property to change the orientation of spontaneous polarization by an external electric field to reverse is called ferroelectricity.
The reversal of the spontaneous polarization per unit volume is equivalent to relative permittivity. Relative permittivity is observed as capacitance.
Without a DC voltage, spontaneous polarization can happen freely. When a DC voltage is externally applied, spontaneous polarization is tied to the direction of the electric field in the dielectric, inhibiting its ability to be independently reversed. Consequently, capacitance becomes lower than before by applying a DC bias.
In temperature compensation capacitors such as CH, C0G, etc., the capacitance does not change from applying DC voltages because paraelectric ceramics are used as their main materials.
Larger MLCCs experience less significant drops in capacitance with respect to DC bias voltage as supported by the figure below.
Generally, higher working voltage ratings for MLCCs do not necessarily improve DC bias characteristics. This is supported by the figure shown below.
In conclusion, when designing power systems, it is necessary to confirm the effective capacitance of all MLCCs used based on the DC bias characteristic provided by vendors to appropriately satisfy design requirements.
Inrush Current
Inrush current is the instantaneous high input current drawn by a power supply or electrical equipment at turn-on. This phenomenon arises due to the high initial currents required to charge capacitors, inductors, or transformers. Inrush current is also known as switch-on surge, or input surge current.
Inrush current is the maximum peak current experienced in the system. This unwanted spike in current can heat devices tremendously and even damage them. Oftentimes, high inrush current drops the source voltage and results in a brownout reset for microcontroller-based circuitry. In few cases, the amount of current supplied to the circuit exceeds the acceptable maximum voltage of the load circuit, causing permanent damage.
Inrush current protection circuits should be used when designing electronic circuits or PCBs. Active or passive devices may be used, and the choice depends on the frequency of the inrush current, performance, cost, and reliability.
Passive Device: NTC thermistor (Negative Temperature Coefficient): Works as an electric resistor whose resistance is very high at low-temperature values. The NTC thermistor connects to the power supply input line in series. It exhibits high value of resistance at ambient temperatures. When the device is turned on, the high resistance limits the inrush current to flow into the system. As the current flow continuously increases, the temperature of the thermistor rises which reduces the resistance significantly. Hence, the thermistor stabilizes the inrush current and allows the steady current to flow int the circuit. NTC thermistors are widely used for the current limiting purpose due to its simple design and low cost. This implementation has some drawbacks, which includes not being able to rely on the thermistor in extreme weather conditions.
Active Device: Costlier option and also increases the size of the system or circuit. This implementation consists of sensitive components which switch high incoming current. Some of the active devices are soft starts, voltage regulators, and DC/DC converters.
These protections are used to protect the electrical and mechanical system by limiting the instantaneous inrush current.
Applications of Capacitors
Decoupling (Bypass) Capacitors
Decoupling capacitors suppress high-frequency noise in power supply signals. They aid in removing voltage ripples (caused by electrical noise) that harm delicate ICs.
In a sense, decoupling capacitors act as very small, local power supplies for ICs. If the power supply temporarily drops in voltage, a decoupling capacitor can briefly supply power to the correct voltage (hence the term bypass capacitor, as they can temporarily act as a power source, bypassing the power supply).
Only high-frequency signals can run through the capacitor to ground. DC signals proceed along to their respective ICs as desired. The high frequencies bypass the IC by running through the capacitor to ground.
Decoupling capacitors connect between the power source and ground. Different valued and different types of capacitors may be used to bypass the power supply in order to filter out select frequencies of noise.
De-rating: It is important to ensure that selected capacitors in a circuit design have a much higher tolerance than the potentially highest voltage spike possible in the system.
Placement of Decoupling Capacitors: When placing decoupling capacitors, a good rule of thumb is to minimize the distance between the component’s voltage pin and the capacitor. For IC pins, this implies placing decoupling capacitors as close as possible to it. Note that this rule does not necessarily result in good decoupling. When designing a multilayer PCB, the capacitor can be placed below the component’s pad. On single-layer designs, these capacitors are placed near the pin and routed with a short trace.
Decoupling capacitors can be placed before ground plane connections. When using vias to connect to a power plane, connect the capacitor to the component pin, and then to the via to ensure that current flows through the plane.
In more precise terms, the inductance of the current loop between the capacitor and IC should be minimized. This is especially important for two-layer PCBs, where traces sometimes need to be routed on the ground layer. Hence, it is important to consider the return path of the current when routing traces on the ground layer.
Parallel Capacitors for Power Supply Filtering
To convert an AC signal into a clean DC signal, rectifiers are typically paired with capacitors connected in parallel. This process is called bridging a rectifier. A rectified signal may be adjusted with the use of these kinds of capacitors as shown:
This application makes use of the fact that the voltage across capacitors must be continuous with respect to time (in other words, capacitors naturally resist sudden changes in voltage). The filter capacitor charges up as the rectified voltage increases. When the increasing rectified voltage starts its rapid decline, the capacitor will discharge very slowly, supplying energy to the load. It is important to note that the capacitor should not fully discharge before the input rectified signal starts to increase again, recharging the capacitor.
Bulk Capacitor
Bulk capacitors are used to help supply a power rail with instantaneous power that exceeds the ability of the power supply feedback loop to react to. In other words, bulk capacitors accommodate for current changes that are too fast for voltage regulators to respond to.
For example, when a sudden change in current occurs in some load, a decoupling capacitor may prove useful initially in providing needed power. By then, bulk capacitors begin to notice the power rail drooping, and will consequently take over. The feedback loop in the regulator will start to respond at an altered timescale, and the droop found in the power rail will be gradually restored, recharging all the involved capacitors.
ESD Capacitors
ESD (electrostatic discharge) capacitors are capacitors placed directly at a connector in order to absorb ESD events there. ESD events often occur when a connection retaining a high voltage is disconnected or connected. In these cases, high potential may reside at the ends of the disconnected or connected wires. This may cause injury and damage components. ESD capacitors ensure that the voltages harbouring a given connector adjust smoothly when plugging or unplugging connections.
Simulation Tools
Murata SimSurfing Characteristics View
Murata SimSurfing Characteristics Viewer is a great tool used to provide accurate characteristics data in order to select appropriate electronic components for circuit design. Manufacturers do not typically produce comprehensive datasheets for individual components. This tool provides a ton of information regarding various characteristics for individual components, and in our case, capacitors. For example, Murata SimSurfing has graphs for characteristics versus frequency plots, and changes in capacitance with respect to various conditions. To learn more about this tool, see the provided link: About the SimSurfing characteristics viewer | Design Support Software SimSurfing | Murata Manufacturing Co., Ltd. .
KEMET Design Tools
KEMET provides various design tools which can be used to ensure proper electronic component selection. K-SIM is a parameter simulation tool used to analyze the performance of capacitors over frequency, temperature, ripple, and DC bias conditions. K-LEM is a calculator used to estimate the life of power film capacitors while considering voltage, temperature, and humidity. The KEMET Aluminum Electrolytic Capacitor Life Calculator can be used to calculate the life expectancy for a specific KEMET aluminum electrolytic capacitor. The Aging Calculator for Ceramics is a calculator for determining the life expectancy of ceramic capacitors. This tool requires parameters such as referee time, aging rate, capacitance, and tolerance code. For more information, see: KEMET – A YAGEO Company .
Sources:
https://learn.sparkfun.com/tutorials/capacitors/all
Different Types of Capacitors And Their Applications
https://eepower.com/capacitor-guide/types/electrolytic-capacitor/#
Mica Capacitor | Capacitor Types | Capacitor Guide
Ceramic Capacitor | Capacitor Types | Capacitor Guide
Understanding Ceramic Capacitors: MLCC, X7R, C0G, Y5V, NP0...
What is Inrush Current and How to Limit it?
when shuld i use bulk capacitor to filter noises?
https://forum.digikey.com/t/what-are-esd-capacitors/1019
https://www.tempoautomation.com/blog/the-most-effective-decoupling-capacitor-placement-guidelines/
Old Content
As with the other pages here, I’ll just link to pages that already explain this instead of writing everything out again - as the pages I have linked explain everything way better than I could.
Capacitor Basics and Applications:
https://learn.sparkfun.com/tutorials/capacitors/all
Relevant Capacitor Specifications:
https://www.electronics-notes.com/articles/electronic_components/capacitors/specifications-parameters.php
What is Derating and Why You Should Do It:
https://www.sparkfun.com/news/1271?_ga=2.206578323.1082779402.1582500194-225400905.1540517045
Basically, just allow a good safety margin of at least 2x for any applied voltages, and you should be fine.
Capacitor Theory:
Does current flow through a capacitor? - Electrons don’t but 'current' does
https://www.youtube.com/watch?v=ppWBwZS4e7A
Why use multiple capacitor values for decoupling?
https://www.youtube.com/watch?v=wwANKw36Mjw
Voltage and Ceramic Capacitors - capacitance changes with voltage
https://www.youtube.com/watch?v=2MQyQUkwmMk
Are Bypass Capacitors Needed?
https://www.youtube.com/watch?v=P8MpZGjwgR0
Bypass Capacitors Tutorial:
https://www.youtube.com/watch?v=BcJ6UdDx1vg
As well as any/all videos here:
https://www.youtube.com/user/EEVblog/search?query=capacitors