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Factors affecting capacitance


There are three basic factors of capacitor construction determining the amount of capacitance created. These factors all ictate capacitance by affecting how much electric field flux (relative difference of electrons between plates) will develop for a given amount of electric field force (voltage between the two plates):

PLATE AREA: All other factors being equal, greater plate area gives greater capacitance; less plate area gives less capacitance.

Explanation: Larger plate area results in more field flux (charge collected on the plates) for a given field force (voltage across the plates).

PLATE SPACING: All other factors being equal, further plate spacing gives less capacitance; closer plate spacing gives greater capacitance.

Explanation: Closer spacing results in a greater field force (voltage across the capacitor divided by the distance between the plates), which results in a greater field flux (charge collected on the plates) for any given voltage applied across the plates.

DIELECTRIC MATERIAL: All other factors being equal, greater permittivity of the dielectric gives greater capacitance; less permittivity of the dielectric gives less capacitance.

Explanation: Although its complicated to explain, some materials offer less opposition to field flux for a given amount of field force. Materials with a greater permittivity allow for more field flux (offer less opposition), and thus a greater collected charge, for any given amount of field force (applied voltage).

“Relative” permittivity means the permittivity of a material, relative to that of a pure vacuum. The greater the number, the greater the permittivity of the material. Glass, for instance, with a relative permittivity of 7, has seven times the permittivity of a pure vacuum, and consequently will allow for the establishment of an electric field flux seven times stronger than that of a vacuum, all other factors being equal.

The following is a table listing the relative permittivities (also known as the “dielectric constant”) of various common substances:

Material Relative permittivity (dielectric constant)
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Vacuum ————————- 1.0000
Air —————————- 1.0006
PTFE, FEP (“Teflon”) ———– 2.0
Polypropylene —————— 2.20 to 2.28
ABS resin ———————- 2.4 to 3.2
Polystyrene ——————– 2.45 to 4.0
Waxed paper ——————– 2.5
Transformer oil —————- 2.5 to 4
Hard Rubber ——————– 2.5 to 4.80
Wood (Oak) ——————— 3.3
Silicones ———————- 3.4 to 4.3
Bakelite ———————– 3.5 to 6.0
Quartz, fused —————— 3.8
Wood (Maple) ——————- 4.4
Glass ————————– 4.9 to 7.5
Castor oil ——————— 5.0
Wood (Birch) ——————- 5.2
Mica, muscovite —————- 5.0 to 8.7
Glass-bonded mica ————– 6.3 to 9.3
Porcelain, Steatite ———— 6.5
Alumina ———————— 8.0 to 10.0
Distilled water —————- 80.0
Barium-strontium-titanite —— 7500

An approximation of capacitance for any pair of separated conductors can be found with this formula:

A capacitor can be made variable rather than fixed in value by varying any of the physical factors determining capacitance. One relatively easy factor to vary in capacitor construction is that of plate area, or more properly, the amount of plate overlap.

The following photograph shows an example of a variable capacitor using a set of interleaved metal plates and an air gap as the dielectric material:

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As the shaft is rotated, the degree to which the sets of plates overlap each other will vary, changing the effective area of the plates between which a concentrated electric fied can be established. This particular capacitor has a capacitance in the picofarad range, and finds use in radio circuitry.

Series and parallel capacitors

When capacitors are connected in series, the total capacitance is less than any one of the series capacitors’ individual capacitances. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. As we’ve just seen, an increase in plate spacing, with all other factors unchanged, results in decreased capacitance.

Thus, the total capacitance is less than any one of the individual capacitors’ capacitances. The formula for calculating the series total capacitance is the same form as for calculating parallel resistances:

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors’ capacitances. If two or more capacitors are connected in parallel, the overall effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors. As we’ve just seen, an increase in plate area, with all other factors unchanged, results in increased capacitance.

Thus, the total capacitance is more than any one of the individual capacitors’ capacitances. The formula for calculating the parallel total capacitance is the same form as for calculating series resistances:

As you will no doubt notice, this is exactly opposite of the phenomenon exhibited by resistors. With resistors, series connections result in additive values while parallel connections result in diminished values. With capacitors, its the reverse: parallel connections result in additive values while series connections result in diminished values.

Practical considerations

Capacitors, like all electrical components, have limitations which must be respected for the sake of reliability and proper circuit operation.

Working voltage: Since capacitors are nothing more than two conductors separated by an insulator (the dielectric), you must pay attention to the maximum voltage allowed across it. If too much voltage is applied, the “breakdown” rating of the dielectric material may be exceeded, resulting in the capacitor internally short-circuiting.

Polarity: Some capacitors are manufactured so they can only tolerate applied voltage in one polarity but not the other. This is due to their construction: the dielectric is a microscopically thin layer of insulation deposited on one of the plates by a DC voltage during manufacture. These are called electrolytic capacitors, and their polarity is clearly marked.

Reversing voltage polarity to an electrolytic capacitor may result in the destruction of that super-thin dielectric layer, thus ruining the device. However, the thinness of that dielectric permits extremely high values of capacitance in a relatively small package size. For the same reason, electrolytic capacitors tend to be low in voltage rating as compared with other types of capacitor construction.

Equivalent circuit: Since the plates in a capacitor have some resistance, and since no dielectric is a perfect insulator, there is no such thing as a “perfect” capacitor. In real life, a capacitor has both a series resistance and a parallel (leakage) resistance interacting with its purely capacitive characteristics:

Fortunately, it is relatively easy to manufacture capacitors with very small series resistances and very high leakage resistances!

Physical Size: For most applicatins in electronics, minimum size is the goal for component engineering. The smaller components can be made, the more circuitry can be built into a smaller package, and usually weight is saved as well. With capacitors, there are two major limiting factors to the minimum size of a unit: working voltage and capacitance. And these two factors tend to be in opposition to each other. For any given choice in dielectric materials, the only way to increase the voltage rating of a capacitor is to increase the thickness of the dielectric. However, as we have seen, this has the effect of decreasing capacitance. Capacitance can be brought back up by increasing plate area. but this makes for a larger unit. This is why you cannot judge a capacitor’s rating in Farads simply by size. A capacitor of any given size may be relatively high in capacitance and low in working voltage, vice versa, or some compromise between the two extremes. Take the following two photographs for example:

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This is a fairly large capacitor in physical size, but it has quite a low capacitance value: only 2 µF. However, its working voltage is quite high: 2000 volts! If this capacitor were re-engineered to have a thinner layer of dielectric between its plates, at least a hundredfold increase in capacitance might be achievable, but at a cost of significantly lowering its working voltage. Compare the above photograph with the one below. The capacitor shown in the lower picture is an electrolytic unit, similar in size to the one above, but with very different values of capacitance and working voltage:

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The thinner dielectric layer gives it a much greater capacitance (20,000 µF) and a drastically reduced working voltage (35 volts continuous, 45 volts intermittent).

Here are some samples of different capacitor types, all smaller than the units shown previously:

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The electrolytic and tantalum capacitors are polarized (polarity sensitive), and are always labeled as such. The electrolytic units have their negative (-) leads distinguished by arrow symbols on their cases. Some polarized capacitors have their polarity designated by marking the positive terminal. The large, 20,000 µF electrolytic unit shown in the upright position has its positive (+) terminal labeled with a “plus” mark. Ceramic, mylar, plastic film, and air capacitors do not have polarity markings, because those types are nonpolarized (they are not polarity sensitive).

Capacitors are very common components in electronic circuits. Take a close look at the following photograph — every component marked with a “C” designation on the printed circuit board is a capacitor:

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Some of the capacitors shown on this circuit board are standard electrolytic: C30 (top of board, center) and C36 (left side, 1/3 from the top). Some others are a special kind of electrolytic capacitor called tantalum, because this is the type of metal used to make the plates. Tantalum capacitors have relatively high capacitance for their physical size. The following capacitors on the circuit board shown above are tantalum: C14 (just to the lower-left of C30), C19 (directly below R10, which is below C30), C24 (lower-left corner of board), and C22 (lower-right).

Examples of even smaller capacitors can be seen in this photograph:

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The capacitors on this circuit board are “surface mount devices” as are all the resistors, or reasons of saving space. Following component labeling convention, the capacitors can be identified by labels beginning with the letter “C”.

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