Capacitors in Parallel
Capacitors in Series
Q or Quality Factor
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 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.
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:
The energy stored in a capacitor is E = CV2/2 E is in Joules.
Thus, the average power in watts is Pav = CV2/2t where t = time in seconds.
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 = εA/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).
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)
|6 not used|
|7 not used|
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|
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|
|Low temperature requirement||Second symbol
|High Temperature requirement||Third Symbol
|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%|
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:
Ctotal = C1 + C2 + C3
Keep in mind that only the total capacitance changes, not the supplied voltage. Every single capacitor will see the same voltage, no matter what. Be careful not to exceed the specified voltage on the capacitors when combining them all with different voltage ratings, or they may explode. Example: say you have three capacitors with voltages of 16V, 25V, and 50V. The voltage must not exceed the lowest voltage, in this case the 16V one. As a matter of fact, and a rule-of-thumb, always choose a capacitor which is twice the supplied input voltage. Example: If the input voltage is 12V you would select a 24V type (in real life 25V).
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 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 = εd/ε0 Where εd is the permittivity of the dielectric and ε0 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 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/RXC where XC is the capacitive reactance (XC = 2πFC) and R is the soon to be defined term of ESR.
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.
The inverse of Q is the dissipation factor (δ). Thus, δ = ESR/XC 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 = I2R where R in this case is ESR it is plain to see that this is a power dispassion rating.
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 (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.
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), εd is the permittivity of the dielectric, and ε0 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.
Za = characteristic impedance through which the incident wave travels first and Zb is the characteristic impedance through which the incident wave travels next. Vr is the reflected wave amplitude, Vi is the incident wave amplitude, and Vt is the transmitted wave amplitude.
Where Z0 is the characteristic impedance:
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