Capacitors 2: DC and AC

by gaussmarkov

Preliminaries

First, let’s summarize some basic electronic simplifications: electrons carry a negative charge and, therefore, repel each other. Because they can move freely within a wire, electrons will distribute themselves uniformly throughout the wire so that there is no discernible polarity along the wire. On the other hand, if they are in the presence of a voltage difference, all electrons will move some amount toward the positive pole because they are attracted to its positive charge. This is direct current (DC) or continuous current.

Second, here is a description of the basic internal structure of capacitors. Capacitors have two metal plates inside them that are separated by an insulating material called a dielectric. In an ideal capacitor, electrons cannot flow across the dielectric. For this reason, a capacitor does not conduct DC as wires or resistors do. However, the plates are close enough that the electrons on one plate can be repelled by the presence of electrons on the other plate. Alternatively, electrons can be attracted to one plate by an absence of electrons on the other plate. Roughly speaking, the total number of electrons in a capacitor is constant so that every electron that enters a capacitor is balanced by an electron that exits.

Battery Analogy

For this reason, capacitors are like rechargeable batteries: by placing a voltage across a capacitor, some electrons gather on one plate and an equal number depart from the other. If the capacitor is then disconnected, it contains potential energy in the form of an electrostatic field across the plates, one with more electrons than the other. Such a capacitor is said to be charged.

If the leads of a charged capacitor are shorted, then the electrons will flow off one plate on to the other to redistribute charge uniformly. If we connect a resistor (instead of a wire) across the leads, then the current of electrons will appear as a momentary voltage difference across the resistor (and capacitor) and the resistor will give off some heat.

In many capacitors, the two plates act symmetrically and the capacitor can be charged with relatively more electrons on either plate. Radial Polarized CapacitorThe polarity of the voltage across such capacitors can be switched causing a corresponding accumulation of electrons on the opposite plate. Polarized capacitors must have the polarity of the voltage across them in only one direction. In other words, electrons should be relatively abundant only on the plate of the lead marked with minus signs on the casing of the capacitor.

As a capacitor is charged, no electrons actually travel through the capacitor. But it is as though they do: for every electron that goes into the capacitor through one lead another electron goes out through the opposite lead. We could say that current flows through a capacitor even though electrons do not. But such current cannot flow forever: as electrons collect on a plate, it becomes more and more difficult to add additional electrons. If the voltage rating of a capacitor is exceeded and too many electrons appear on a plate, then the capacitor breaks down and there is a sudden short as electrons travel from one plate to the other. This can be dangerous.

Alternating Current

An alternating current (AC) is an electrical current with a cyclical magnitude and direction. While DC cannot flow through an ideal capacitor, AC can because the accumulation of electrons on a plate can be reversed so that electrons accumulate on the opposite plate. By repeating such reversals, we can alternate which plate is accumulating electrons and AC will flow “through” the capacitor. The key is to keep changing the direction of the current.

An analogy with a ripple moving across the surface of a tank of water may be helpful. When the wave travels across the surface, the water does not flow. The surface merely rises and falls with each ripple as it passes. Alternating current through a capacitor is similar. The concentration of electrons rises and falls but electrons do not continuously flow in one direction.

Note that the polarity of voltage across a capacitor does not have to change for AC to flow. All that matters is the difference between two voltages:

  1. the voltage across the plates within the capacitor and
  2. the voltage across the leads of the capacitor caused by the source voltage.

If there is a difference, then electrons in the capacitor will redistribute themselves towards matching the source voltage and current will flow. As a result, a polarized capacitor will also conduct AC even though the polarity of the voltage across its leads does not change. As long as the magnitude of the voltage is changing, current will flow through a capacitor.

It may be helpful to think of AC as similar to water moving back and forth in a garden hose. The flow of the water repeatedly changes direction. Now suppose that we hook up two hoses with a rubber diaphragm (an analogy to a capacitor) in between. Water cannot flow from one hose into the other, but it can still move back and forth through the two hoses. In addition, if we add some extra water pressure from one end, this back and forth movement can still occur. It is the changing magnitude of pressure that matters not the changing direction of pressure.

If you would like to see some graphs of how a capacitor reacts to different kinds of AC, then jump to the low pass filters page. The next two sections on this page deal with a basic application of capacitors charging and transmitting AC that does not require discussing the details of the AC.

Coupling Capacitors

Because of their ability to conduct AC and inability to conduct DC, capacitors are often used to connect (or couple) stages of a circuit designed to conduct and alter AC. As such, they are called coupling capacitors. An amplification stage, for example, may place the center of an AC at a value like 4.5V, half of a typical 9V DC voltage supply. This 4.5V is called a DC offset. To contain a DC offset within the amplification stage, capacitors typically appear as “sieves” for AC near the input and output of a stompbox circuit.

[image: Basic Fuzz Face schematic]

Look, for example, at the Basic Fuzz Face circuit. At the input, you will see capacitor C1 with a value of 2.2uF. And at the output, sits capacitor C3 with a value of 0.01uF.

Using the schematic, one can see that there is a DC offset for the AC signal between the coupling capacitors by noting that the -9V power supply is just a couple of resistors away from the AC signal, which is vibrating on all of the connections “inside” of C1, C2, R2, R3, and the 1K GAIN pot at the bottom of the schematic.

An explanation of the DC offset involves describing how transistors can be used to make signal amplifiers. I do not have a companion explanation of transistors written yet, so I’ll just note that the amplification in this circuit works by creating a guitar signal that varies from 0V up to 9V, the range of voltages that one can produce with a single supply voltage like a battery. Because an audio signal tends to vary equally on either side of a resting point, it makes sense to place that point in the middle of the voltage range, at around 4.5V. So the coupling capacitors allow us to feed the circuit an input signal that varies around 0V and to generate an output signal the also varies around 0V.

Capacitor Leakage

Actual capacitors differ from the ideal just described, of course. Two important differences are that real capacitors

  1. have some resistance and
  2. conduct some DC, or leak.

For many situations, these differences can be ignored. However, there is an exception for coupling capacitors that comes up right away in building stompboxes. The symptom is an annoying “pop” sound from the speaker of the guitar amp when switching the stompbox from by-pass into the path of the signal. As R.G. Keen explains in Why does my stompbox pop when I hit the bypass switch?, capacitor leakage can be the cause.

By-passing the stompbox circuit is often accomplished by switching the input and output connections to a wire or trace that runs directly between them. This arrangement is called true by-pass because no electronic components influence the signal of the guitar. When the circuit is by-passed, the outside lead of a coupling capacitor is not connected to anything; the lead is said to be floating. This would not be a problem if capacitors did not leak. The coupling capacitor would remain charged just as when it is connected.

But capacitors do leak and some of the charge maintained while the circuit is connected is lost while it is not. When the floating lead of the coupling capacitor is reconnected to the output, the capacitor faces a supply voltage again and must recharge to return to its operating voltage. As R.G. explains,

“That sudden voltage difference and the charging current that brings the capacitors back to the working voltage is heard in the amplifier as a pop. If the effect has any gain, the input capacitor pop is further amplified by the gain of the pedal into a bigger pop.”

To fix this, we need a pull-down resistor. This is a resistor, typically 1M or higher, connected on one side to the floating lead of the output coupling capacitor and connected to ground on the other side. This high resistance connection keeps the voltage of the output plate of the capacitor at ground level where it is when the circuit is connected. The high resistance value ensures that when the circuit is connected, this pull-down resistor has little effect on the output.

If you look at the Basic Fuzz Face schematic above, you will see that the LEVEL potentiometer will serve as a pull-down resistor and another one is not needed for this circuit. Even when the output is disconnected from the circuit on the wiper of the potentiometer, their is a 500K resistor connecting the floating lead of capacitor C3 to ground.

Many stompbox builders prefer to put a pull-down resistor on the floating lead of the input coupling capacitor as well.

Further Information

R.G. Keen’s How It Works … is a beginner’s guide to understanding what electronics is about written by one of the masters of DIY stompboxes. I don’t recall whether I first saw the battery analogy for capacitors in this article, but the analogy is there along with many other insights. Another of his articles, The Ins and Outs of Effect Bypassing, also contains closely related material.

Also see some of my electronics theory links.


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14 Responses to “Capacitors 2: DC and AC”

  1. Dineshkumar said:

    It’s really good

    I cleared some basic doubts

    Thank you

    Posted 18.09.2007 at 3:11 am

  2. gaussmarkov said:

    That is good news! 😀

    Posted 18.09.2007 at 8:04 am

  3. Jhong said:

    That’s a really big help’ tnx

    Posted 11.12.2008 at 7:29 pm

  4. jabbar said:

    thank Q

    Posted 17.05.2009 at 1:31 am

  5. Brecht Vander Donckt said:

    Hi,

    I’m a Belgian student electronics, it’s a very good summary. Nice work putting it online. Thanks

    Posted 19.05.2009 at 6:49 am

  6. rishi said:

    its very precise and apt ! nicely fed by gauss markov.i m an electrical engg.if som1 has other doubts then i can help.

    rishi
    rishi.jec2008@gmail.com

    Posted 05.06.2010 at 12:41 am

  7. SARA said:

    can you plz tell me y d c cant flow through capacitor

    Posted 21.12.2010 at 7:06 am

  8. selvaguru said:

    it is very useful for ECE students.it is very useful to clarify the doubts about the capacior….

    Posted 14.03.2011 at 4:52 am

  9. ashok said:

    it good

    Posted 14.05.2011 at 12:09 pm

  10. Isha Mir said:

    Excellent….simple nd precise xplanation
    bt i have sm confusion still that how can electrons repel in presence ov dielectric b/w them….plz if anyone knw then ans me….

    Posted 11.11.2011 at 11:36 am

  11. wc said:

    pls hlp

    for a tweeter application utilizing a polarized capacitor………….

    + to + cap-in,

    then -cap-out to + driver in, correct?

    what about electron flow being negative to positve

    i have confused myself, again

    Posted 01.02.2012 at 2:00 pm

  12. k.raja said:

    i have one doubts how to conduts capacitor in ac ..but why did not conducts dc if anybody plz tell me ans..

    Posted 16.02.2012 at 5:57 am

  13. Dilshad said:

    Plz sir guide me…
    How does capacitor block DC??
    Let’s suppose we have a DC source e.g. simple battery.If one plate of capacitor is connected with the -ve terminal of battery then electrons will flow from battery to that plate of capacitor.When electrons reach the plate they will repel the electrons of other plate which is connected to +ve terminal of battery.After this, these repelled electrons will flow from plate to the +ve terminal of the battery.
    So,is’nt the flow of electrons from -ve terminal of battery to one of the plate of capacitor and then flow of electrons from other plate of capacitor to +ve terminal of battery,the current.
    Regards:Dilshad Ahmed Khan
    Thnks in advance.

    Posted 08.03.2012 at 4:53 am

  14. UCHE said:

    IN YOUR CIRCUIT , HOW OR WHEN DOES
    CHARGE ACCUMMULATED ON EITHER OF
    THE PLATES OF CAPACITOR C1 DISCHARGE
    WHEN THE CIRCUIT IS IN OPERATION?

    Posted 01.12.2012 at 11:06 am