A Leyden jar being discharged, from an 1878 science text. This image originally appeared in Augustin Privat-Deschanel’s 1878 “Elementary Treatise on Natural Philosophy, Part 3: Electricity and Magnetism,” D. Appleton and Co., New York, translated and edited by J. D. Everett, p. 571, Fig. 384. In earlier articles about engineering formulas and components, I wrote about the properties of electrical resistance (“Ohm’s Formula One,” Jan. 1 issue) and how early scientists and physicists worked out how to calculate the effects of resistance on electrical circuits (“Current Events,” April 9).
This time, we’ll tackle capacitors.
IT’S ALL GREEK
The Greeks are credited with first recognizing the phenomenon of static electricity. They noticed that a spark could be generated by rubbing amber against a dry cloth — in fact, the word “electricity” is an Anglicized adoption of elektrum, the Greek word for amber. A charged piece of amber might have been an amusing thing to hide under a toga, but static electricity was nothing more than a curiosity to the ancients.
It remained so until Pieter van Musschenbroek, a Dutch professor of mathematics at the University of Leiden in Germany, invented a way to store an electrostatic charge in 1745. He called his device a Leyden Jar. This was the first practical capacitor.
It was a simple glass jar, lined both inside and out with metal foil. The two foil coatings did not extend to the top of the jar, and so were effectively insulated from each other by the glass sides. A lid covered the jar and a metal rod stuck through it into the jar, which was filled with water. When the rod was touched to a rotating metal sphere (used to collect a static charge), the charge was transferred into the jar and stored.
A LARGE CHARGE
Van Musschenbroek’s jar worked fine, but even so, neither its inventor nor anyone else of the time was quite certain why. He had filled the jar with water, believing the electricity was stored in that substance.
In fact, capacitors were originally called condensers, because he and others thought the charge “condensed” out of the air and into the water.
Others, including Ben Franklin, who cheated death while capturing lightning in van Musschenbroek’s bottle, believed the charge was stored in the insulating glass.
As it turned out, neither idea was correct.
Charles-Augustin de Coulomb, a French physicist, worked out a mathematical formula in 1785 that showed the charge was the result of an electrostatic field between the plates of the capacitor. He determined that the strength of the field obeyed the same rules as the Laws of Gravity, which is to say that the field strength diminished proportionally to the square of the distance from it. This became known as Coulomb’s Law and is the basis of all calculations regarding electrical field strengths — such as those used to predict AM and FM radio coverage.
When a voltage source is connected across the two plates of a capacitor, electrons stream out of the source and onto one of the plates, setting up an electrostatic field. The electrons in the field exert a force that is felt across the insulating material, repelling like-charged electrons off the opposite plate and back into the power source. The plate with an excess of electrons thus becomes negatively charged, while the opposite plate is positively charged. The electrostatic field causes current to flow between the plates of the capacitor, even though the material between them (called the dielectric) is an insulator.
This conflicts with Ohm’s Law, which says that there can be no current flow in a true insulator because the resistance is infinite. This conflict is resolved by the unique properties of the electrostatic field in the capacitor, in which electrons on one plate do not actually cross the dielectric; rather, they exert a force on the electrons of the opposite plate, and it is that repelling force that causes current to flow for as long as the charging process continues.
As the process begins, the current flow is highest because that is when there is the largest number of electrons waiting to be bumped around. But as more and more electrons gather on the one plate and more and more are repelled from the other one, the current drops off.
At some point (determined by a combination of the size of the plates and the thickness of the dielectric, as well as the applied voltage) the capacitor charges as much as it can, and no more electrons flow across the field. In essence, then, the capacitor exhibits a sort of variable resistance; the resistance steadily increasing as the charging process continues until it reaches theoretical maximum as the charge is complete and current flow stops.
To differentiate this ambiguous resistance in the capacitor with that of a resistor, the capacitor’s resistance is called reactance, even though, like pure resistance, it is measured in ohms. The unit of capacitance itself is measured in farads, a truncated version of Michael Faraday’s name, in recognition of his work in the fields of electrostatics and electromagnetism.
DC VS. AC
The above example explains the action of a capacitor when DC voltage is applied, but what happens when a capacitor is connected across an AC voltage source? In that case, things change, since AC voltage is a sine wave that cycles from positive to negative and back again, continuously.
Our capacitor still starts to charge up as electrons stream onto one plate and push their counterparts off of the other plate. But after the first one-half of the cycle, the voltage polarity has changed, and the plate of the capacitor that had a negative voltage applied to it, now has a positive voltage, and vice versa.
Of course, the capacitor immediately responds by trying to charge in the opposite direction from what it was doing just a fraction of a second ago and current flows in the opposite direction. But the cycles of the sine wave are unremitting; the capacitor might have time to fully charge before the polarity changes, but then again, it might not.
And that is a function of two things. If the plates are large (meaning a high capacitance value), it will take them a long period of time to fully charge — perhaps longer than one-half cycle of the applied voltage. In that case, there will always be current flow across the capacitor, as the charging process never quite keeps up with the changing polarity of the applied voltage. Likewise, if the frequency is high enough, it might change polarity so fast that even a very small capacitor would not fully charge.
From these statements, we can see that the reactance of a capacitor is inversely proportional to the size of the capacitor and the frequency. The capacitor, then, is a “high-pass” filter, which is to say that the higher the frequency of an applied voltage, or the larger the capacitance of the device, the easier it becomes for current to flow through it. The exact formula is:
where XC is capacitive reactance in ohms; π is 3.14, f is the frequency in Hz (cycles per second) and C is capacitance in farads.
IT’S ALL IN THE DESIGN
Circuit designers can do neat things with such a device.
For one thing, large capacitors are used to “filter” DC voltage that has been converted from the power company’s AC line voltage. The rectifiers that change AC into DC leave large amounts of “ripple” in the DC. The ripple occurs at twice the line voltage frequency, so it can be heard as a 120 Hz hum. The solution is the filter capacitor. Voltage ripples can be thought of as ripples in a pond. As the ripple becomes a trough in the “pond” of our DC power supply, the filter capacitor fills in the trough by giving up its charge. At the peak of the ripple, the capacitor returns to full charge, smoothing out the peak while waiting for the next trough.
All well and good, but that ability can also lead to a dangerous condition when proper safety precautions are not followed.
In a console or a solid-state transmitter, the power supply might only charge the capacitor to 24 or maybe 50 volts. Shocking perhaps, but not lethal. But tube type broadcast transmitters can run on 10,000 or even 12,000 volts. The capacitors in those rigs charge up to the full voltage potential (and in fact, charge to a bit more than that), and 10,000 volts will stop the heart of even the most stout engineer.
Furthermore, high-voltage power supply capacitors are quite large because they are designed to smooth out ripples in circuits that can draw several amps of current. The larger the capacitor, the longer it takes for the charge to “bleed” off when the transmitter is shut down. For this reason, all tube type transmitters are built with “bleeder” resistors across the high voltage power supply. Those resistors draw some current all the time and perform no useful service at all, other than to stay connected across the power supply and bleed off voltage from the filter capacitors when the power is removed (doubtless saving more than a few lives over the decades).
Still, bleeder resistors can fail, and so most high-power transmitters are also equipped with “shorting bars,” which are nothing more than a spring-loaded copper bar that will short the high voltage directly to ground if the door is opened (while also scaring the wits out of the poor soul who makes the mistake of opening the door without turning off the high voltage first).
Capacitors are also used in analog passive equalizers and as speaker crossover networks. Different value capacitors are arranged across an audio source so that the output of each capacitor contains a separate band of frequencies. Adjustable resistors are then used to vary the amplitude of each band to achieve the desired audio characteristics, and the separately adjusted audio bandpasses are joined back together at the output.
Similarly, a capacitor in a dual cone speaker system is placed in series with the wire feeding the tweeter and sized to block all frequencies below a certain point, so only higher frequency sound makes it to that speaker and the bass is confined to the woofer.
Finally, designers long ago learned how to make variable capacitors: ones that could be easily adjusted to have more or less capacitance with the turn of a knob. When coupled with inductors, the result is the tuned resonant circuit, which is what makes radio, and in fact all wireless communications, possible.
From the most mundane to the super sophisticated, every single piece of electronic equipment in use today depends on capacitors. The whole field of electronics would be impossible without them — which just proves that Franklin was right way back in 1752. He really did capture lightning in a bottle.
Jim Withers is owner of KYRK(FM) in Corpus Christi, Texas, and a longtime RW contributor. He has four decades of broadcast engineering experience at radio and television stations around the country.
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