Capacitors

__Index__

Symbol

Definition

The Coulomb

The Farad

Identification

Capacitors in Parallel

Capacitors in Series

Dielectric Constants

Dialectric Strength

Q or Quality Factor

Dissipation Factor

Ripple Current

Dielectric Absorption

ESL

ESR

Formulas

__Symbol__

Dielectric Electrolytic

__Definition__

A capacitor (also known as a condenser) acts as a store for electrical charge. It contains a pair of metal plates separated
by a thin sheet of insulating material (the dielectric).

The dielectric can be made of glass, ceramic, Tantalum oxide, or plastics such as
polyethylene or polycarbonate. Even air can be used as the dielectric.

If you look at a catalog of electronic components you'll find an enormous variety
of sizes and types of capacitor. However, for most purposes we can divide capacitors
into two basic types:- dielectric and electrolytic.

Left to themselves the plates are electrically neutral - the number of positive
holes in each exactly equals the number of negative electrons. However, if we
apply an external voltage we can drag electrons off one plate and push them on to the
other. When the capacitor holds some energy in the form of extra electrons on one
plate and protons on the other we say that the capacitor is charged.

__The Coulomb__

The amount of charge in a capacitor is measured in coulombs (Q).

The coulomb is a unit of electrical charge and equals the quantity of electricity
transported in one second by one ampere.

Coulomb's Law implies that the mechanical force between two charged bodies is
directly proportional to the charges and inversely proportional to the squares
of the distance separating them.

__The Farad__

Capacitance (C) is the amount of charge per volt of potential that a
capacitor holds. (C =Q/V where Q = coulombs (the unit of charge) and V =
Volts)

__Capacitance is measured in Farads,__ but most often a small fraction of a Farad
thus:

- micro-farads uF millionths (10
^{-6}) Farads - nano-farads nF (10
^{-9}) Farads - pico-farads pF (10
^{-12}) Farads (or 'puffs' by most engineer's)

The energy stored in a capacitor is *E* = *CV*^{2}/*2*
*E* is in Joules.

Thus, the average power in watts is *P _{av}* =

The maximum voltage rating and its capacitance determine the amount of energy
a capacitor holds. The voltage rating increases with increasing dielectric
strength and the thickness of the dielectric. The capacitance increases with the
area of the plates and decreases with the thickness of the dielectric.

Thus, the capacitance of a capacitor (*C*) is related to the plate area
(*A*), plate separation distance (*d*) and permittivity (ε) of the
dielectric by the following equation:

*C = *ε*A/d *Here* A *and* d *are based on meters as the
unit and ε is in coulombs squared per Newton-meters squared notice the force
unit involved - it explains why capacitor microphonics (remember the good old
condenser microphone?) and a mechanical failure mode of capacitors).

__Identification__

Large capacitor have the value printed plainly on them, such as 10uF (Ten micro Farads) but smaller
types often have just 2 or three numbers on them?

First, most will have three numbers, but sometimes there are just two numbers. These are read as Pico-Farads.
An example: 47 printed on a small disk can be assumed to be 47 pico-Farads.

Now, what about the three numbers? It is somewhat similar to the resistor code. The first two are the
1st and 2nd significant digits and the third is a multiplier code. Most of the time the last digit tells
you how many zeros to write after the first two digits, but the standard (EIA standard RS-198) has a couple
of alternatives that you probably will never see. But just to be complete here it is in a table.
What these numbers don't tell us is the ESR rating of a capacitor.

Table 1 Digit multipliers | |
---|---|

Third digit | Multiplier (this times the first two digits gives you the value in Pico-Farads) |

0 | 1 |

1 | 10 |

2 | 100 |

3 | 1,000 |

4 | 10,000 |

5 | 100,000 |

6 not used | |

7 not used | |

8 | .01 |

9 | .1 |

Now for an example: A capacitor marked 104 is 10 with 4 more zeros or
100,000pF which is otherwise referred to as a .1 uF capacitor.

You will sometimes see a tolerance code given by a single letter written on
the capacitor.

So a 103J is a 10,000 pF with +/-5% tolerance

Table 2 Letter tolerance code | |
---|---|

Letter symbol | Tolerance of capacitor |

B | +/- 0.10% |

C | +/- 0.25% |

D | +/- 0.5% |

E | +/- 0.5% |

F | +/- 1% |

G | +/- 2% |

H | +/- 3% |

J | +/- 5% |

K | +/- 10% |

M | +/- 20% |

N | +/- 0.05% |

P | +100% ,-0% |

Z | +80%, -20% |

There is also sometimes a *letter-number-letter *(like Z5U) code that gives
you even more information.

Table 3 shows how to read these codes. A 224 Z5U would be a 220,000 pF (or .22
uF) cap with a low temperature rating of -10 deg C a high temperature rating of
+85 Deg C and a tolerance of +22%,-56%.

Table 3 Dielectric codes | |||||
---|---|---|---|---|---|

First symbol (a letter) |
Low temperature requirement | Second symbol (a number) |
High Temperature requirement | Third Symbol (a letter) |
MAX. Capacitance change over temperature |

Z | +10 deg. C | 2 | +45 deg. C | A | +1.0% |

Y | -30 deg. C | 4 | +65 deg. C | B | +/- 1.5% |

X | -55 deg. C | 5 | +85 deg. C | C | +/- 2.2% |

6 | +105 deg. C | D | +/- 3.3% | ||

7 | +125 deg. C | E | +/- 4.7% | ||

F | +/- 7.5% | ||||

P | +/- 10.0% | ||||

R | +/- 15.0% | ||||

S | +/- 22.0% | ||||

T | +22%, -33% | ||||

U | +22%, -56% | ||||

V | +22%, -82% |

With the above information you should be able to identify most of the capacitors that you are ever likely to come across. There are other codes used for capacitor identification, but they are either not seen on modern capacitors or are for use on military spec capacitors and as such they tend not to be seen in the commercial environment.

__Capacitors in Parallel__

Capacitors connected in parallel, which is the most desirable, have
their capacitance added together, which is just the opposite of parallel
resistors. It is an excellent way of increasing the total storage capacity of an
electric charge:**C _{total} = C_{1} + C_{2} + C_{3}**

Keep in mind that only the total capacitance changes,

__Capacitors in Series__

Again, just the opposite way of calculating resistors. Multiple
capacitors connected in series with each other will have the total capacitance
lower than the lowest single value capacitor in that circuit. Not the preferred
method but acceptable.

For a regular two capacitor series combo
use this simple formula:

__Dielectric Constants__

Dielectric constant (*k*) gets it's value by comparison of the charge
holding ability of a vacuum where *k* = 1. Thus, *k* is the ratio of
the capacitance with a volume of dielectric compared to that of a vacuum
dielectric.

K = ε_{d}/ε_{0 }Where ε_{d} is the permittivity of
the dielectric and ε_{0} is the permittivity of free space

Air has nearly the same dielectric value as a vacuum with *k* = 1.0001.
Teflon, a very good insulator, has a value of *k *=2 while the plastics
range in the low 2s to low 3s. Mica gets us a *k *=6. Aluminum oxide is 7,
Tantalum's *k* is 11 and the Ceramics range from 35 to over 6,000.

Dielectric constants vary with temperature, voltage, and frequency making
capacitors messy devices to characterize. Whole books have been written about
choosing the correct dielectric for an application, balancing the desires of
temperature range, Temperature stability, size, cost, reliability, dielectric
absorption, voltage coefficients, current handling capacity (ESR).

__Dielectric strength__

Dielectric strength is a property of the dielectric that is usually expressed
in volts per centimeter (V/cm). If we exceed the
dielectric strength, an electric arc will 'flash over and often weld the plates
of a capacitor together creating a short circuit.

__Q or Quality Factor__

The *Q* of a capacitor is important in tuned circuits because they are
more damped and have a broader tuning point as the *Q* goes down.*
*

*Q* = 1/*RX _{C}* where

*Q* is proportional to the inverse of the amount of energy dissipated in
the capacitor. Thus, ESR rating of a capacitor is inversely related to its
quality.

__Dissipation Factor__

The inverse of Q is the dissipation factor (δ). Thus, δ =
ESR/*X _{C}* and the higher the ESR the more losses in the capacitor
and the more power we dissipate. If too much energy is dissipated in the
capacitor, it heats up to the point that values change (causing drift in
operation) or failure of the capacitor.

__Ripple Current Rating__

The ripple current is sometimes rated for a capacitor in RMS current.
Remembering that P = I^{2}R where R in this case is ESR it is plain to
see that this is a power dispassion rating.

__Dielectric Absorption__

This is the phenomenon where after a capacitor has been charged for some
time, and then discharged, some stored charge will migrate out of the dielectric
over time, thus changing the voltage value of the capacitor. This is extremely
important in sample and hold circuit applications. The typical method of
observing Dielectric Absorption is to charge up a cap to some known DC voltage
for a given time, then discharge the capacitor through a 2 ohm resistor for one
second, then watch the voltage on a high-input-impedance voltmeter. The ratio of
recovered voltage (expressed in percent) is the usual term for Dielectric
absorption.

The charge absorption effect is caused by a trapped space charge in the
dielectric and is dependent on the geometry and leakage of the dielectric
material.

__ESL__

ESL (Equivalent Series Inductance) is pretty much caused by the inductance of
the electrodes and leads. The ESL of a capacitor sets the limiting factor of how
well (or fast) a capacitor can de-couple noise off a power buss.

The ESL of a capacitor also sets the resonate-point of a capacitor. Because
the inductance appears in series with the capacitor, they form a tank
circuit.

__ESR__

The ESR rating of a capacitor is a rating of quality. A theoretically perfect
capacitor would be loss less and have an ESR of zero. It would have no in-phase
AC resistance. We live in the real world and all capacitors have some amount of
ESR..

ESR is the sum of in-phase AC resistance. It includes resistance of the
dielectric, plate material, electrolytic solution, and terminal leads at a
*particular frequency*. ESR acts like a resistor in series with a capacitor
(thus the name Equivalent Series Resistance). This resistor can cause circuits
to fail that look just fine on paper and is often the failure mode of
capacitors.

To charge the dielectric material current needs to flow down the leads,
through the lead plate junction, through the plates themselves - and even
through the dielectric material. The dielectric losses can be thought of as
friction of aligning dipoles and thus appear as an increase (or a reduction of
the rate of decrease -- this increase is what makes the resistance vs freq line
to go flat.) of measured ESR as frequency increases.

As the dielectric thickness increases so does the ESR. As the plate area
increases, the ESR will go down if the plate thickness remains the same.

To test a Capacitors ESR requires something other than a standard capacitor meter.
While a capacitor value meter is a handy device, it will not detect capacitor failure
modes that raise the ESR. As the years go by, more and more designs rely on low ESR
capacitors to function properly. ESR failed caps can present circuit symptoms that are
difficult to diagnose.

__Formulas at a glance__

For the more scientific among you!!!

Where *k* = dielectric constant, *A* = area, *t* = thickness
of the dielectric,* Q* = coulombs the unit of charge, and *V* =
Volts*
*

Where* A *(area) and* d *(thickness) use meters as the unit and ε
is in coulombs (squared per Newton-meters squared), ε_{d} is the
permittivity of the dielectric, and ε_{0} is the permittivity of free
space

Where energy *E* (in joules) stored in a capacitor is given by

Thus, the average power in watts where *t *= time in seconds.

**T**ime**D**omain**R**efletometry (**TDR**) formulas- Characteristic Impedance of cable formulas
- Discontinuance of transmission characteristic impedance

*Z _{a}* = characteristic impedance through which the incident wave
travels first and

Where Z_{0} is the characteristic impedance: