Capacitors

The electronics world is ruled by the MOS (Metal Oxide Semiconductor) technology. That is tiny pieces of silicon (or germanium), thin layers of metal (aluminum or copper) and even thinner layers of metal oxide (aluminum oxide or copper oxide). The silicon is enhanced with impurities which form semiconductor electrical paths using induced electrical fields. Metal layers create electrically conductive paths inside tiny little chips. The oxide layers act as insulators, and they are also needed to form . . . capacitors!

Capacitors are used generously in electronics, and they have many (AC) functions. I will present them according to the following structure:
1. Types of capacitors
2. Useful formulas
3. Equivalent series and parallel capacitors
4. Growth and Decay in RC circuits
5. Filtering capacitors

Types of capacitors

Capacitors work based on the induced electrostatic effect. Note this word "effect". In physics, the word effect means something that can be measured, studied, and analyzed, but its origin is a mystery. Things are this way.

We use electricity extensively for about 150 years, and we all feel comfortable with it--in fact it is a necessity. Electrical phenomena are processes that happen at atomic level, and we have very little knowledge about the atom. Even more, due to the physical-mathematical model we currently use, there is little hope to further discover anything more. For example, electric effects today are said they are "totally" and "perfectly" described by the laws and theorems we already have.

That is a great limitation. Physics has lost its experimental character, and it has become a branch of mathematics. Of course, we need mathematics to formulate and postulate physical laws and theorems, but mathematics is just a tool helping physics, not vice-versa. The latest "findings", the "electro-magnetic unified theorems" exemplify perfectly well my words: people use physics to building nice, interesting, theoretical mathematical problems which are not going to take us anywhere.

Mathematics is just a tool, and it has to remain that way; it is the mean, not the purpose. It is possible mathematics is used today as it is due to gross ignorance, or as a sort of "propaganda", in order to mask, the truth and reality. Physics without mathematics is a set of concepts, and of unexplained phenomena. For example, we work with electrical current, and we are able to control it perfectly well. However, electrical current doesn't flow like water as some authors try to indoctrinate us; electrical current is an atomic process, and it comes with few additional troublesome effects, among which induced electrostatics is one of the strangest.

Somehow, all research in electrostatics is highly secret, for quite some time. It has been proven that electrostatic fields influence the gravity vector: they are capable to increase and to decrease it! Please believe me: we are going to hear about many revolutionary discoveries in "electricity" in the coming years, despite the fact it is "totally and perfectly" explained! Well!

Now, in electronics we control induced electrostatics with capacitors. On our PCB boards, capacitors are used:
1. to filter EMI (induced Elector-Magnetic Interference);
2. to control the amount of reactance or inductance in AC circuits;
3. to build RC timing circuits;
4. to control the "slew-rate" (the ramp) of electrical pulses;
5. to build resonant circuits;
6. to build frequency filtering circuits;
7. to build the analog-to-decimal circuits;
8. to achieve coupling inductance;
9. to build SMPS (Switched-Mode Power Supply) power-pumps;
10. to store energy;
11. many more.

The most general classification groups capacitors as being:
1. fixed capacitors
2. variable capacitors

Considering the mode they are connected to electrical circuits, capacitors are:
1. through hole
2. surface mount
3. big capacitors, or batteries of capacitors having specially designed mechanical fixtures and connectors

A capacitor is two metallic plates positioned at a certain distance, and having a dielectric material in between. The nature of the dielectric influences capacitors' general construction. The following types of capacitors are the most common:
1. ceramic
2. mica
3. paraffin solid or with paper
4. polyethylene
5. Tantalum (metal and oxide)
6. electrolytic (ammonia)
7. air (vacuum)
8. glass
9. porcelain
10. oil (transformer oil)

Variable capacitors come in few types:
1. RF variable capacitors
2. trimmers
3. banks of capacitors

NOTE
Although they are used a lot in DC circuits, please note that capacitors are AC circuit elements. There are no instances of pure DC circuits; all of them have (at least, some) AC characteristics.

USEFUL FORMULAS

In order to work with capacitors we need few mathematical formulas (as tools) close at hand. Here they are:

Formula	Description
C [F] = Q [C] / U [V]	Capacitance
K = C / Co (relative value; no unit)	K = Dielectric constant C = Capacitance of the capacitor with actual dielectric Co = Capacitance of the vacuum dielectric capacitor
C [C] = (ε * A) / d	C = Capacitance of the parallel plates type capacitor ε = dielectric permittivity A = Area of one plate d = distance between plates
ε [C2/N*m2] = εo * K	ε = dielectric permittivity εo = 8.85 * 10-12 [C2/N*m2] = permittivity of vacuum
Z [Ω] = U [V] / I [A]	Ohm's Law in AC circuits (details in Design Notes 1)
Z [Ω] = √[R2 + (XL - Xc)2]	Impedance (details in Design Notes 1)
Xc [Ω] = 1 / (2 * ∏ * f * C)	Capacitive Reactance
1 [pF] = 10-12 [F]	Pico Farad
1 [nF] = 10-9  [F]	Nano Farad
1 [uF] = 10-6  [F]	Micro Farad

NOTE
In case you are unfamiliar, the notations within square brackets represent the unit. For example, Xc [Ω] means capacitive reactance (Xc), and the symbol ([Ω]) means "the measurement unit" and it tells us Xc is measured in ohms. That is important because we could have instances when the measurement unit is mili-ohms or kilo-ohms, and the formulas have to be scaled appropriately. That is the reason the measurement unit needs to be added explicitly within square brackets.

EQUIVALENT SERIES AND PARALLEL CAPACITORS

The equivalent of series resistors is calculated with: 1/CT = Σ 1/Ci 
The equivalent of parallel resistors is calculated with: CT = Σ Ci 

Calculation examples for three capacitors:

	Fig 1: The equivalent capacitance of 3 capacitors in series 1/CT = 1/C1+1/C2+1/C3 CT = C1*C2*C3 / (C2*C3 + C1*C3 +C1*C2) CT = 24 / (12+8+6) = 24 / 26 = 0.923 uF CT is smaller than the smallest serial capacitor
	Fig 2: The equivalent capacitance of 3 parallel capacitors CT = C1+C2+C3 CT = 2uF+3uF+4uF = 9uF CT is greater than the greatest parallel capacitor

GROWTH AND DECAY IN RC CIRCUITS

A capacitor in series with a resistor forms a timing circuit, and this (AC) function is used intensely in electronics.

The time constant T is:    T [s] = R [Ω] * C [F]

In order to charge the capacitor to full capacity, however, it takes 5 time constants (R*C) calculated with the above formula. The "decay curve" behaves perfectly similar to the "growth" one illustrated further down, having only an inverse second derivate (the curve holds water).

Fig 3: RC Growth

FILTERING CAPACITORS

This (AC) topic is presented in Filter Design.