Capacitance: An Overview
By David Herres
We take a look at capacitance: how it is used in electronic circuits and how unwanted capacitance is harmful.
Capacitance, one of the three underlying functions in nature that modify the flow of electrical current (the other two are resistance and inductance) has enormous importance in electronics and cabling. It is highly beneficial in that almost all electronic equipment employs capacitors to filter, select or otherwise modify current in power and signal circuits. And yet at high frequencies, such as we see in data communication, unwanted capacitance is so difficult to eliminate that it actually becomes one of the major limiting factors preventing ideal broadband connectivity, both in cable and within input and output equipment.
What is capacitance? To start, let's take a look at capacitance as an abstract entity and see how it arises and what affects it has on various waveforms at different frequencies.
It is sometimes instructive to consider the water pipe analogy. Resistance is like a constriction in the pipe, impeding fluid flow. Inductance is as if you inserted a large tank in the piping with an air cushion over the water. A steady flow of water (like direct current in an electrical circuit) would pass right through the device not noticing the opposition. In contrast, a pulsating or rapidly reversing water flow would be absorbed by the assembly and be diminished, the effect being more pronounced the faster the fluctuations. Capacitance can be seen as if there were a rubber membrane across the pipe. A steady pressure (DC) would not transmit energy across the pipe except as a pulse when first applied or removed, at which points it would resemble AC with a fast rise time and fall time.
But a rapidly pulsating or reversing fluid flow would be transmitted through the membrane and cause like motion on the other side. AC passes through a capacitor while DC does not. DC passes through an inductor while AC does not. These effects are frequency dependent and also depend upon the amount of inductance or capacitance. Capacitance and inductance are opposites in regard to the way they effect current flow in any circuit of which they are a part.
In this discussion of capacitance for convenience we talk about current flowing through a capacitor, but strictly speaking this is not true. Current enters one lead of a capacitor and exits the other lead but it does not pass through the dielectric layer. At that location it reconstitutes itself as an electric charge between the two plates and that is how energy passes through the device. Current flow in the circuit is a response to the rate of change of the electrical charge within the capacitor.
The schematic symbol for a capacitor is highly appropriate. An ideal capacitor consists of two parallel closely spaced flat metal plates with leads attached. The larger the area of the plates, the greater the capacitance. Capacitance is directly proportional to the area of the plates and inversely proportional to their distance apart. If you double the area of both plates, you double the capacitance. If you cut in half the distance between them, you also double the capacitance.
A third factor that influences capacitance is the nature of the insulating material between the plates. Any insulating material has a dielectric constant. A perfect vacuum has by definition a dielectric constant of 1.0. Dry air is said to have a dielectric constant of 1.0 as well, although it is actually a small fraction of one percent greater. Some insulating materials with their dielectric constants are:
- Vacuum: 1.0
- Air: 1.00059
- Polystyrene: 2.6
- Paper: 3.5
- Mica: 5.4
- Flint glass: 9.9
- Methyl alcohol: 35
- Glycerin: 56.2
- Distilled water: 81
- Class I ceramic: 6 - 500
- Class II ceramic: 500 - 10,000
By using a material such as paraffin-impregnated paper, capacitance can be increased and the capacitor becomes more stable and rugged in a harsh environment. Capacitors can be made up of layers of foil and paper, for example, and rolled into a cylinder for compactness and structural integrity.
Capacitance is a property of any capacitor without regard to the applied voltage or frequency, whether it is in or out of a circuit or on a shelf in a storeroom. Capacitance for any given unit stays the same except that some capacitors degrade with time or vary with temperature.
Some formulas involving factors that determine the amount of capacitance are:
- Capacitance, the ability of any two conductors separated by a dielectric to store electrical energy is given by the equation:
C = Q/V
where Q = charge in coulombs or ampere-seonds
V = potential in volts
C = capacitance in farads.
- Capacitance is also given by:
C = 0.225AK/t(10 to 12th power)
where A = area in square inches of the electrodes
K = dielectric constant
t = separation between electrodes in inches
- Energy storage is:
W = 1/2 C(Vsquared)
where W = energy in joules or watt-seconds
V = potential difference between electrodes in volts
C = capacitance in farads
In many circuits, a capacitor behaves like a resistor. The opposition it offers to the flow of current is called "capacitive reactance" instead of resistance." Capacitive reactance is also measured in ohms and Ohm's Law is fully applicable. The principle difference is that it is frequency dependent. Current flow in a capacitive circuit is dependent not upon amount of applied voltage, but rate of change of that voltage. This is why a waveform is altered in a capacitive circuit.
If you look at a sine wave, you see that where the voltage is highest, at positive and negative peaks, the rate of change is least, and as it crosses the zero line, the rate of change is greatest. For this reason, the current in a purely capacitive circuit is 90 degrees out of phase with the applied voltage.
Two of the formulas that apply to capacitors within a circuit are:
XsubC = 1/2(pi)fC
where XsubC = capacitive reactance
f = frequency in herz
C = capacitance in farads
- Impedance is:
Z = square root of (R squared + X squared)
where Z = impedance
R = resistance in ohms
X = inductive and capacitive reactance, which cancels out at resonant frequency at which the only opposition to current flow is the pure resistance, often close to zero.
Because of their unique electronic parameters, capacitors are very useful, indispensable, in fact, in all sort of equipment. They range from huge water-cooled capacitors used for power factor correction and inductive heating in industrial facilities to clusters of minute units in computer memories.
Typically electronic equipment requires pure stable DC voltages. Since most available utility power is AC, after it is stepped down to the required voltage it must be rectified. The result is a pulsating DC that would not be suitable for audio, video or data to mention a few applications. A capacitor can shunt out the ripple, leaving a smooth nearly pure DC with minimal AC component.
Another useful property of the capacitor is its ability to tune in with great precision a single frequency excluding all others. This is done by means of a resonant circuit. If a capacitor and inductor (coil) are placed in series, they will block all frequencies except for a certain resonant frequency, which the combination will conduct. If they are placed in parallel, they will block the resonant frequency and conduct all others.
We are all familiar with the variable condenser in an old radio which had one set of connected plates mounted on a shaft that could be turned by means of a hand knob on the outside of the cabinet. Another set of connected plates was stationary so that as the shaft turned the capacitance would vary in order to create different resonant frequencies and tune in various stations. The dielectric material was air. (Today's electronic tuners have no moving parts and are more stable, trouble free and cheaper to build.)
Capacitors have other uses as well, based on their unique properties. Many single-phase motors incorporate them during startup. They can be online for a prescribed interval controlled by a timer or they can be switched off by means of a centrifugal switch inside the motor housing when the armature attains a predetermined speed. Capacitors are good at holding a charge and can enable computerized equipment to retain its memory during momentary power outages and they can perform other low power functions such as maintaining clock and calendar function while line power is removed. Other uses for capacitors take advantage of their ability to hold a charge and release it quickly. Photo flash, strobe lights, high-powered lasers and particle accelerators are examples.
We have seen a number of instances where the unique characteristics of capacitors have made them highly useful in diverse ways. But there are situations in which capacitance is unwanted and must be eliminated or minimized to whatever extent is possible. Capacitive reactance or opposition to the flow of electrons greatly decreases in a series circuit as frequency increases. In a parallel circuit, the capacitive effect tends to attenuate the signal. A cable, whether coaxial, UTP Category cable or other, is a capacitor whose
effects become increasingly troublesome as frequency and length increase. In coaxial cable, for example, the center pin and outer braided shield become two plates of a capacitor. Since capacitance is in part a function of plate area, the longer the run of cabe, the greater the attenuation. At moderate frequencies as in CATV audio, video and synchronization signals, such loss is acceptable in moderate runs. If you follow an overhead cable run in a suburban neighborhood, you will see weatherproof enclosures about every 400 feet. They contain amplifiers, which are powered by an AC voltage that coexists with the TV signal in the coaxial cable. (It is filtered out and separated from the signal by means of capacitors.) At higher frequencies, such as in broadband data transmission, the low capacitive reactance (which when vectorially added to resistance is called "impedance") tends to short out the data transmission and so places upper limits on broadband in terms of frequency and cable length.
It is interesting to look at a satellite dish. The microwave signal, gathered by the parabolic dish that is aimed at a satellite in geosynchronous orbit, is so high in frequency that it cannot be conveyed along any type of cable even for the short distance from the focal point of the dish to the frequency converter. It can be transmitted only through a waveguide, which is a rectangular metal tube of prescribed dimensions designed to transmit high frequency radiation without capacitive loss. The waveguide takes the signal to the frequency converter where the frequency is reduced to a level such that it can be brought a limited distance over coaxial cable to the receiver inside the building typically right next to the TV set. The receiver ("cable box") reduces the frequency further to where capacitive loss is not an issue for a short run to the TV set.
Today's local area networks (LANs) operate at speeds up to 100 Mb/s (one hundred million bits per second) and beyond. We are starting to see Gigabit Ethernet, 1000BASE-T, operating at a billion bits per second. High speed digital data pulses originate as square wave signals and ideally retain that waveform. Passing through real world cable, however, they tend to degrade into sawtooth traces. Beyond a certain point these waveforms are not intelligible as digital data. The height of the pulse is also reduced as a function of data rate, cable length and cable parameters. Cable capacitance is the most prominent undesired characteristic and cable manufacturers have show great ingenuity in recent years countering this effect, quite like solid-state engineers who worked in the 20th century to reduce parasitic capacitance between base and collector, which had placed limits on transistor frequency response.
Unwanted or parasitic capacitance also exists in many circuits where high frequencies are found. Radio engineers developed the screen grid in the 1930's to minimize capacitance between cathode and plate in the vacuum tube amplifier, greatly increasing frequency response and audio fidelity. Unwanted capacitance can reside in printed circuits where the traces are closely spaced. Careful planning and routing can minimize attenuation in this area. Recent increases in computer speed have resulted from successful capacitance battles on on the microprocessor front and in bus design.
Unshielded twisted pair cable, such as the commonly used Category 5e with RJ-45 connecting hardware to some extent mitigates the problems of bandwidth limitation Twisting the individual pairs disrupts the parallel path of the conductors lessening the antenna effect and diminishing undesired electromagnetic fields and radiated signals, which cause crosstalk. Further research has led to the development of Category 6 and beyond, and undoubtedly higher transmission speeds will become available in the near future.