# A Tutorial on Capacitors

## Introduction

A capacitor is a passive electrical component comprised of two terminals. And together with inductors and resistors, they are the most basic components used inelectrical circuits. For a fact, it’s quite rare to come across a circuit that doesn’t have a capacitor.

Fig 1: Different types of capacitors
Source:
Eric Schrader from San Francisco, CA, United States, Capacitors (7189597135)CC BY-SA 2.0

In case you are wondering, capacitors are pretty special because they can store energy, just like an electric battery that’s fully charged. Caps, as we normally call them,have plenty of vital circuit applications. Some of their most fundamental applications in circuits are such as storage of energy, suppression of voltage spikes, and filtering of complex signals.

## Tutorial Breakdown

In today’s tutorial, we are going to take a closer look at everything related to capacitors including:

• How capacitors are made
• How capacitors work
• Capacitance units
• Types of capacitors
• How can you identify capacitors?
• How to combine capacitors in series and parallel
• Popular applications of capacitors

However, you should bear in mind that this tutorial builds on a couple of electronics concepts that should be at your fingertips for easier and faster understanding of what we’ll cover today. So,before you go ahead and dig into the details of this tutorial, you should spare a few minutes to read about the following concepts;

• What is Electricity?
• What is a Circuit?
• Voltage, Current, Resistance, and Ohm’s Law
• Distinguishing between Series and Parallel Circuits
• What is a Multimeter and how to use it
• Metric Prefixes

## Symbols and Units

### Circuit Symbols

A capacitor can be represented in a circuit schematic in two main ways, and they will always have two terminals that are connected to the circuit at large. A capacitor’s symbol is represented by two parallel lines that can either be flat or curved; they are close to each other,but they don’t come into contact – which is, in fact, an indication of how a capacitor is actually made. Here’s a quick look at the capacitor symbols, plus how they are incorporated in a basic electrical circuit.

Fig 2: Capacitor Symbols
Jwratner1 at English Wikipedia., Types of capacitorCC0 1.0

Notes:

• The capacitor symbol (#b above) that comes with the curved line is an indication of a polarized capacitor; and thus, it’s most likely an electrolytic capacitor. Read on in the sections that follow below.
• Every capacitor must be named; C1, C2, C3, and so on, plus a value that indicated the capacitor’s capacitance in farads – more on that in the next part of this tutorial!

### Units of Capacitance

Like resistors and inductors, capacitors aren’t produced equal. Every other capacitor comes built with a specific capacitance value.And this value is what will let you know the amount of charge that the capacitor can store; the higher the capacitance value, the more capacity it has to store charge.

The Faradis the standard capacitance unit and is abbreviated as F. You should, however, know that one Farad is a remarkably huge amount of capacitance, and even the thousandth equivalent (0.001F) of a Farad or rather, one millifarad (1mF) capacitor is a pretty large capacitor. Thus, you’ll typically come across capacitors rated in the picofarad (10-12)and microfarad (10-6) range. Check out the table below for a quick overview of capacitance units

 Prefix Name Abbreviation Weight Equivalent Farads Picofarad pF 10-12 0.000000000001 F Nanofarad nF 10-9 0.000000001 F Microfarad µF 10-6 0.000001 F Milifarad mF 10-3 0.001 F Kilofarad kF 103 1000 F

And, when you hit the Kilofarad range, you are now in a level of special caps referred to as ultra or super-capacitors.

## Capacitor Theory

### How Capacitorsare Made

A capacitors schematic symbol looks pretty similar to how it’s created. Essentially, a capacitor is built from two plates of metals plus an insulation material referred to as a dielectric. These plates of metal are closely placed together and to ensure that they don’t come into contact, the dielectric is put in between the plates.

Fig 3:A standard parallel capacitor sandwich- two conductive plates separated by an insulating dielectric
Source:
Parallel plate capacitor, public domain image fromWikimedia Commons

This dielectric can be built from any type of insulation material such as plastic, ceramic, rubber, glass, paper or any other material that can prevent current from flowing. The plates, on the other hand,are built from metals like silver, tantalum, aluminium, or any other good electrical conductors, and each of the plates is connected to a circuit’s terminal wire.

A capacitor’s capacitance, which is measured in Farads will rely on how the capacitor is built. The larger the capacitor, the higher the capacitance. Plates that have more surface area with their overlapping plates will have more capacitance, and on the flip side, an increase in the distance between the plates translated to reduced capacitance. In addition, the dielectric’s material also affects the number of Farads that a capacitor will have. With all that in mind, you can then calculate a capacitor’s capacitance using this equation;

Where:

• r= the relative permittivity (a constant whose value will depend on the material of the dielectric) of the dielectric.
• A = surface area of the overlapping plates
• d = the distance between the plates

### How Capacitors Work

The flow of electric charge is what creates an electriccurrent, and this current is what is harnessed by regular electrical components to create motion, light or any other functions. When the current flows into a cap, the electric charge ‘sticks’ on the plates because they won’t go past the dielectric which is an insulator.

Negatively charged particles (electrons) are then absorbed by one of the plates,and overall, it becomes negatively charged. This massive amount of negative charges on that plate then pushes positively charged particles (protons) to the other plate,and likewise, it becomes positively charged.

Fig 4: How a capacitor works.
Source:
Papa NovemberCapacitor schematic with dielectricCC BY-SA 3.0

And since opposite charges attract, the protons and electrons on each of the plates attract each other. However, thanks to the insulating dielectric that sits between the plates, the charges will stay stuck on the respective plate, at least until they get the chance to go elsewhere. Because these charges stay stationary, an electric field is created,and that is what results in potential energy and voltage. As a result, the cap can store electric energy, similar to the way chemical energy is stored in a battery.

### Charging and Discharging

A capacitor becomes charged when the merging of positive and negative charges occurs. And it’s able to retain this charge (electric field) because these, unlike charges, attract each other from either side of the dielectric, but they never come into contact.

Caps can, however, get to a point where the plates are completely full of charged such that no more charges can be accepted;any others that try joining are repelled. This is where the maximum charge that can be stored comes into play – and this value is indicated in farads to represent the capacitance.

To discharge the capacitor, the circuit should have a different path that allows the charges to get into contact. When the charges leave the capacitor, it becomes discharged.

Take an example of the circuit shown below; The battery induces an electric potential across the cap, leading to the build-up of equal but opposite charges on either plate, to a point where the capacitor is so full that more current is repelled to prevent it from flowing into the cap. With the LED arranged in series with the capacitor, a new path is provided for the current. Therefore, following the new path, the energy stored in the capacitor flows to light up the LED for a short while.

Fig 5: Simple GIF diagram demonstrating charging and discharging a capacitor to light an LED
Source:Learn.Sparkfun.Com :
https://cdn.sparkfun.com/assets/d/2/d/5/1/519a737ece395fe042000002.gif

### Calculation of Charge, Voltage and Current

The capacitance of a capacitor, i.e. the value of farads, is an indicator of the amount of chargethat can be stored by the cap. And the amount of charge that a capacitor stores at any given time relies on the voltage (potential difference)between the plates. This connection between the charge, capacitance and the voltage can be depicted by a simple, fundamental equation;

Where:

Q = charge stored in the capacitor

C = capacitance

V = voltage applied to the capacitor

A capacitors capacitance, in this case, is a known value, which is always a constant. Thus, to increase or reduce the capacitors charge, we can change the voltage. Increasing the voltage increase the charge and vice-versa.

Moreover, the above equation is an exceptional way of defining the value of a unit farad; A unit farad (F) is the capacity of storing unit energy (in coulombs) per each unit volt.

### Calculation of Current

Now, let’s take this charge/capacitance/voltage equation to the next step so that we can determine how the current is affected by voltage and capacitance since current is defined as the rate of flow of charge. In essence, the relationship between the voltage and current of a cap is that; the quantity of current flowing through a cap is dependent on how fast the voltage increases or decreases, and the capacitance of the capacitor. Thus, a rapidincrease in the voltage across a capintroduces a huge amount of positive current in the cap. And on the flip side, a slower voltage increase across the capacitor means that much less current will flow through it. And finally, in the case of steady and fixed voltage, current will not flow through the capacitor.

With that in mind, the math starts getting a little more complicated since calculus is now involved in bringing things into perspective. So, to calculate the flow of current through a cap, you will use the equation below;

Where:

is the rate of rise or fall in voltage over time.

Basically, what this equation means is that if the voltage is steady, dv (change in voltage) will be equal to zero, and thus the current will also be zero. And that is why a capacitor holding a steady DC voltage won’t allow current to flow through it.

## Types of Capacitors

There are many types of capacitors that you will come across every other day, and each of the types will have specific features and a few downsides that will make them more suitable for different applications. The type of capacitor is normally decided upon depending on factors such as;

• Size: This refers to both the capacitance and physical volume of the cap. They can either be super small or even be the largest component of the circuit. And as we’ve already talked about, the larger the capacitor, the higher the capacitance.
• Maximum Voltage:Every capacitor comes with an indication of the maximum voltage it can handle. If this maximum voltage is exceeded, the cap will get damaged.
• Leakage Current:Like most electrical components, caps also come with some flaws. Each of them often leaks a very small amount (nanoamps or much less) of current between the terminals via the dielectric. And this leakage current will gradually drain all the stored energy out of the capacitor.
• Tolerance: The capacitance rating of caps is never flawlessly precise. Every single capacitor will have a nominal rating for its capacitance, but this value could be varying from anywhere between ±1% and ±20%, depending on the type of capacitor.
• ESR (Equivalent Series Resistance): Still on the flaws, the conductivity of a caps’ terminals isn’t 100%. They usually have minimal resistance (< 0.01?) which while small, ends up being an issue when lots of current flows through the capacitor, leading to power loss and production of heat.

### 1.      Ceramic Capacitors

This is the most common capacitor that you’ll find out there, and as the name suggests, the dielectric is made from capacitors. These caps are typically small in both the size and their capacitance. It’s rare to come across a ceramic cap with a rating of more than 10µF. You will often find this type of surface mount cap in a ± 0603 (0.6mm x 0.3mm)package. Through-hole ceramic capacitors, on the other hand, will resemble a tiny bulb with two terminals that protrude.

Fig 6: Different types of Ceramic Capacitors
Source:
GlennCeramic capacitorsCC BY-SA 3.0

When compared to electrolytic capacitors which are equally as popular, ceramic caps tend to be the better option especially because of their lower leakage and ESR currents, even though their miniature value of capacitance may be limiting. Moreover, the ceramic caps are also the most affordable choice. They are exceptionally suitable for applications such as high-frequency coupling and decoupling.

### 2.      Tantalum and Aluminum Electrolytic Capacitors

Electrolytic caps are remarkable especially since they can hold lots of capacitance in a rather small physical volume.In case you are looking for a 1µF – 1mF capacitor, there’s a good chance that you’ll find the electrolytic type. Thanks to their rather high ratings of maximum voltage, they are particularly good for applications that require high voltages.

And among the electrolytic capacitors available today, the Aluminum type is the most common,and they typically resemble tiny tin cans,and both terminals extend from the bottom side.

Fig 7: Electrolytic Capacitors (Aluminum & Tantalum)
Source:
ElcapElectrolytic capacitors-P1090328CC0 1.0

You must, however, note that electrolytic capacitors are often polarized; each comes with an anode (+ve pin) and a cathode (-ve pin). When applying voltage to this type of capacitor, the anode should be placed to handlemore voltage compared to the cathode. To make sure of this, an electrolytic cap’s cathode is typically markedwith a negative symbol, “ – “and the case comes with a colored strip on the cathode side to differentiate it with the anode side. Furthermore, the anode’s terminal could also be a little longer than the cathode’s for easier identification. As a result, in case you apply the voltage in reverse, the electrolytic capacitor, it will fail right there with a popping sound and burst open- a clear indicator of permanent damage. After this happens, the cap will behave like a shorted circuit.

Unfortunately, electrolytic capacitors are also prone to leakages, and thus, they aren’t really a preferable choice for storage of energy; this is such a bummer especially since they have higher capacities and voltage ratings.

### 3.      Supercapacitors

Looking for a cap that’s specifically built for storage of energy? Your best option is the supercapacitor type. These are specially designed for the accommodation of high capacitance values in the farads range. They typically with diameters of about 1cm on the base.

However, even though they have the capacity to store large amounts of charge, supercapacitors aren’t capable of handling higher voltages. For instance, a supercapacitor with a 10F capacitance could only come with a maximum rating of 2.5 volts. Any higher will, therefore, lead to permanent damage. Usually, supercaps are arranged in series so that they can attainhigher ratings of voltage even though this reduces the total value of the capacitance.

Fig 8: One Farad 5.5V electrolytic supercapacitor
Source:

When it comes to the application of supercaps, they are best suited for the storage and release of energy, just like batteries which are their primary competitors. However, in as much as supercapacitors can't contain as much energy as a battery of a similar size, they have the advantage of being able to release that energy way quicker,and they tend to last longer than batteries.

### 4.      Other Types of Capacitors

Out there 80% of the caps you can get your hands on are the ceramic and electrolytic types, while only 2% are supercapacitors. Other than those, the film capacitor is another type that’s pretty popular, and it a remarkable choice for dealing with higher currents mainly because it has exceptionally low ESR losses.

On the other hand, there are many other less popular capacitors. For instance, a variable capacitor can make a suitable substitute for variable resistor since it can generate a range of capacitance values in a tuning circuit. PCBs or twisted wires are also able to produce capacitance (which could be undesired sometimes) for the reason that they are basically two conductors that are separated by an insulating material.

Of all the capacitor types, the Leyden Jars are the veterans – a jar of glass that’s fitted with conductors both on the inside and outside parts of the jar. And for anyone who feels like going back to the good old days, you can try using flux capacitors, which are an unusual combo of an inductor and a capacitor.

## Capacitors in Parallel and Series

Just like resistors, caps can also be arranged either in parallel or in series to achieve a combined capacitance value. However, you’ll be interested to know that when summing capacitors up, you’ll do the complete opposite of what you would do for resistors.

### a)      Capacitors in Parallel

When you place capacitors in parallel with each other, you get their total capacitance by basically summing up all the capacitance values; the same way you add up resistors when they are arranged in series.

Fig 9: Capacitors in Parallel
Source:
OmegatronCapacitors in parallelCC BY-SA 3.0

CTotal= C1 + C2 + …… Cn-1 + Cn

Thus, for instance, if you have three caps with capacitances of 5µF, 10µF, and 20µF arranged in parallel, their total capacitance will be 5 + 10 + 20 = 35µF.

### b)      Capacitors in Series

Similar to the way the total resistance is a hard nut to crack when the resistorsare arranged in parallel, capacitors also get painfully stubborn when they are in a series arrangement. The total capacitance value nof caps placed in series is the inversesum of the inverse capacitance value of each capacitor. i.e.

Fig 10: capacitors arranged in Series
Source:
OmegatronCapacitors in seriesCC BY-SA 3.0

1/CTotal= 1/C1 + 1/C2 + …… 1/Cn-1 + 1/Cn

And in case there are only two capacitors in the circuit arranged in series, you can make things easier by using the ‘product over sum’ formula to get the total capacitance.

Ctotal=C1C2/C1+C2

Furthermore, for two capacitors of equal value arranged in series, the total value of the capacitance is half of their sum. For instance, two 16F supercaps placed in series will generate a total capacitance value of 8F, which on the other hand will have the advantage of doubling their total voltage ratings from 3V to 6V for instance.

## Applications of Capacitors

There are lots of applications for this essential passive component. If you’ve been wondering how they are used, here’s a quick look at the most common applications;

### 1)      Bypass/Decoupling Capacitors

The majority of capacitors that you’ll find in circuits, particularly those that come in ICs (integrated circuits) are there for decoupling. Essentially, they are installed to work as suppressors of high-frequency noise from the signals of the power supply. In simpler terms, this type of caps, take small ripples of voltage out of the circuit’s voltage supply since or else, these voltage ripples could end up damaging the sensitive ICs.

Furthermore, they can function as tiny local power supplies to the integrated circuits, nearly the same way UPSs work for computers. In case there’s a voltage drop in the circuit’s power supply (this often happens for circuits whose load requirementscontinuouslychange),the decoupling cap will supply the power at the required voltage for a short while. It’s no wonder why these caps are also known as bypass capacitors; they can act as a temporary source of powerbecause they bypass the primary power supply of the circuit.

Bypass caps are typically connected between the source of power and ground. And sometimes, several caps with different values (or even different types) are used to bypass the supply of power since some cap values tend to be better at sifting out of specific frequencies of noise as compared to others.

Fig 11: An LM7805 5V linear voltage regulator with 2 decoupling capacitors
Source:
Dalva24LM7805 with Decoupling CapacitorCC BY-SA 4.0

Even though it appears as though this could end up shorting from the power source to the ground, you should remember that only signals with high frequency can pass through the cap down to the ground. And just as needed, the signal of the DC will be received by the IC. Additionally, the other reason why these types of capacitors are known as bypass caps is due to the fact that the high-frequency signals (in the range of KHz to MHz)pass through the cap to the ground instead of passing through the IC. In a nutshell, the high-frequency signals bypass the IC.

Bear in mind that when you are connecting the bypass caps, they must be placed as close to the IC as possible. Otherwise, the further you place them, the less effective they are going to be.

And to adhere to good engineering practices, make sure that every IC should be accompanied by a 0.1µF, 1µF or 10µF capacitor. This is a super affordable way of guaranteeing that the IC won’t be exposed to any huge spikes or dips from voltage fluctuation.

### 2)      Power Supply Filtering

While diode rectifiers are typically used for turning the wall voltage from AC to DC, they conversion can’t be as clean as needed without the addition of capacitors into the mix.

Fig 12: Half Wave rectification graph with diodes only
Source:
Cuddlyable3Wall wart opened, marked as public domain, more details on Wikimedia Commons

So, in such cases, a parallel capacitoris added to a bridge rectifier. And thus, the signal is converted from AC to an almost level direct current signal as indicated below;

Fig 13: Rectification graph after introduction ofa capacitor in the circuit
Source:Original: Xapxivos. Edit: Tabby, Reservoircapidealised, marked as public domain, via
Wikimedia Commons

On the same note, caps are known to be exceptionally stubborn components in a circuit since they are always trying to counteract abrupt voltage changes – which of course is a good thing in this case. As the rectified voltage rises, the filtering cap charges up,and once this rectified voltage passing through the cap starts falling rapidly, the cap starts gradually discharging its stored energy to supply the load. And before the cap is discharged fully, the rise in the input rectified signal occurs once again, to start recharging the capacitor. As long as the power supply is being used, this process repeats itself over and over again in each passing second.

Fig 14: AC to DC Power Supply Filtering Schematic
Source:
JaunJimenez at English WikipediaACtoDCpowersupplyCC BY 3.0

Tear down any AC to DC power supply,and for sure, you will come across one or more massive cap. Take a look at this simpleAC wall adapterdismantled, do you see anything familiar from today’s discussion?The capacitor isclearly visible!

Fig 15:A common AC adapter teared down to unveil a simple, unregulated linear DC supply circuit: four diodes in a bridge rectifier, a transformer, and an electrolytic cap that smoothens the waveform
Source:
Cuddlyable3Wall wart opened, from Wikimedia Commons

### 3)      Storage and Supply of Energy

As you already know by now, caps are pretty nifty sources of storing and supplying energy. And as we’ve already talked about they function much like batteries in a circuit, the only drawback being that their energy density is much lower than what we get from chemical batteries of equal size. However, that gap has been narrowing pretty fast,and we expect the caps to catch up in the coming years.

Environmentally, caps are way better than batteries since their lifespan is way longer compared to that of batteries and better yet, they deliver their stored energy exceptionally quicker than batteries do. As a result, they are remarkable choices for usage in instances where high but short powers bursts are needed. For instance, the flash of your camera could draw its power from a cap which may have been charged by a battery!

### 4)      Filtering of Signals

Caps can block out DC or low-frequency signals and simultaneously allow passage of higher frequencies. Think of them as the bouncer of a high frequency only VIP club!

Such an application is super effective for the processing of signals for instance in radio receivers to help in tuning out frequencies that aren’t wanted.

The other excellent instance where caps are used to filter signals is in passive crossover circuits that you can find in speakers. This circuit’s work is to split one audio signal, and thanks to a capacitor arranged in series, low frequencies will be blocked out so that the remaining parts of the signals with high frequencies can pass to the tweeter of the speaker. For passing lower frequency signals,on the other hand, the subwoofer circuit shunts the high-frequency signals to the ground through a capacitor that’s placed in a parallel arrangement with the circuit.

## De-Rating

Above anything else, when you use capacitors, make sure that you design your circuits to use caps with a higher tolerance rating than the highest possible potential spike of voltage in the arrangement. At this juncture, you already know what will happen in case you don’t de-rate the caps and their maximum voltage is exceeded, right?

Fig 16: Exploded Electrolytic Capacitor after catastrophic failure
Source:
Frizb99Exploded Electrolytic CapacitorCC BY-SA 3.0

Capacitor Characteristics