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Capacitors

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3.1. Early Capacitor Construction

Capacitors are components that store electric charge and return it, in a similar way that a rechargeable battery does. The key difference is that capacitors rely on electrostatic principles, whereas batteries rely on a chemical process.

The earliest capacitors where discovered as a scientific curiosity, often associated with experiments involving high voltage static electricity. The famous "Leydan Jar", consisting of a simple glass jar with metal foil wrapped around the outside of the jar and similar foil inside, formed a simple capacitor. Electrodes were connected to each foil wrap. It was found that the container could be charged to a high voltage, and the voltage source could be removed. The charge remained in the jar for some time. The jar electrodes could then be touched together to make a visible spark.

3.2. Standard Capacitor Equations

The amount of charge Q depends on the applied voltage V and the capacitance C according to a simple equation

In order to have created a spark, heat energy is needed to create an incandescent spark. The energy equation for a capacitor is 

Energy is stored in a capacitor, and this energy is not lost. Consequently if the applied voltage is changing, charge will flow into and out of the capacitor, creating an alternating current (AC). The time domain equation for this relationship is

3.3. Modern Capacitor Construction

It would be difficult to construct modern electronic equipment with Leydan jars. A more practical approach is to use rectangular metal plates with area A separated by a distance d.

The capacitance obtained is proportional to the area of the plates and inversely proportional to the distance of separation. However the scaling factor, defined as the permittivity of a vacuum 0 is a relatively small quantity, resulting a low capacitance values. For example, imaging two metal plates with X=10, Y=10 mm, separated by a distance of d=1mm. According to the component shown, the capacitance would only be 0.885 pF. In comparison, capacitors used in computer power supplies may have several thousand uF of capacitance. Some "super capacitors" these days achieve capacitance values as high as 1 Farad.

Clearly this simple approach is not adequate, and so an insulating dielectric material can be added between the plates. This has two advantages, the dielectric material can have a higher permittivity   than the permittivity of a vacuum 0 so that the capacitance value will be larger, also a much thinner separation between the plates can be obtained that might otherwise result in a short circuit. 

This relative permittivity r  depends on the dielectric, some typical examples are,

Dielectric Material Relative Permittivity r Comment
Vacuum 1 By definition as a reference
Air 1.00059 Air has low molecular density, hence r is close to 1.
Glass 4.9 to 7.5 Used in early Leydan Jar Experiments
Mica 4.5 to 8.7 Originally used for low loss high frequency capacitors
Porcelain 7.0 Modern high quality high frequency dielectric
Ceramic 4.5 to greater than 1,000 Most common material used today, suits SMD fabrication
Waxed Paper 2.5 Early capacitor, suitable for audio applications
Polystyrene 2.45 to 4.0 Good capacitance stability with temperature and time
Polycarbonate 2.9 Improved dielectric compared to waxed paper
Mylar Film 4.0 Used for high quality audio capacitors
Polypropylene 2.1 Good quality audio capacitors
PTFE (Teflon) 2.0 Microwave dielectric, used for microwave PCB's
Distilled Water 80 Pure water is an insulator, impurities make it conductive
Barium-strontium-titanite 7,500 A ceramic compound.

In recent time, excellent ceramic materials have been developed with relative permittivity values well beyond 1,000. These allow capacitor values up to 10 uF in a 0603 SMD footprint (0.06 * 0.03 inches). These capacitors use extremely small plate separation, and stack multiple plates in parallel to achieve high capacitance values. The total capacitance is proportional to the number of stacked capacitors.

Ceramic capacitors are rapidly becoming the capacitor of choice in almost all electronic circuits involving printed circuit boards (PCB). Different ceramic grades have different characteristics, lower relative permittivity grades have excellent temperature stability and high frequency performance, usually classed as "NPO", whilst other grades are designed for general purpose audio and decoupling with good high voltage tolerance, ranging from 50 Volts to 200 Volts (e.g. X7R). The highest relative permittivity classes are intended for maximum possible capacitance and may have upper voltage limitations as low as 6 Volts, due to extremely close plate separation.

Another popular capacitor style is based on a cylindrical construction, basically the same electrical concept as the stacked plate capacitor, except that two continuous strips of metal foil are wound into a coil with a dielectric sandwiched in-between. 

This style of fabrication is less suited for SMD, and tends to be used for leaded applications. The earliest cylindrical capacitors used waxed paper as a dielectric, and could easily obtain values as high as 0.05 uF with a withstanding voltage rating of 1000 Volts. As a result, this style was widely used in old valve radio receivers and television sets, operating at DC voltages up to 250 V or so in audio coupling circuits.

So far, these capacitors have fixed values, but other variable capacitors were needed in conjunction with inductors to allow adjustable resonant circuits, needed to tune into different radio frequencies in a given band. The earliest variable capacitors used air as a dielectric, and had one stack of fixed plates with an intermeshing stack of movable plates connected to a rotating spindle. Maximum capacitance occurred when the rotating stack meshed fully into the stationary stack, and this capacitance value decreased as the rotating stack turned up to 180 degrees to be completely unmeshed. The image below shows an example variable capacitor, this one has two variable capacitors in one housing. The brass spindle connects to a tuning knob, either directly or through a gear reduced string mechanism. This type of variable capacitor would typically allow an adjustment from 25 pF to 365 pF over a 180 degree rotation. When combined with a fixed inductor, the resulting resonant frequency variation would be equal to the square root of this ratio, i.e. a bit over 3:1. Consequently, a medium wave radio that required a tuning range from 550 kHz to 1,650 kHz was quite feasible.

Air tuned variable capacitors are however physically large, the actual size of the image above would represent one of the smallest versions. Some of the earliest variable capacitors were about the size and shape of a small loaf of bread.

This problem was solved by introducing a dielectric between the moving and stationary plates, usually Mylar film. This allowed miniaturization feasible. All "knob tuned" AM and FM radios today use this form of variable capacitor, due to its prolific use in so many consumer products from 1960 on, with very little conceptual change. Even it is now being phased out by electronic tuning. This new approach allows up-down buttons to change channels, and for radio and TV stations to be programmed. The new variable capacitor is actually a silicon diode, called a  Varicap diode. Varicap diodes can be housed in tiny SMD packages smaller than a grain of rice.   

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