### Capacitors store energy electrostatically in an electric field and deliver the stored energy when necessary. Every capacitor has a specified working voltage, and temperature affects the capacitance.

Capacitors are electrical components that store potential energy. They typically contain at least two electrical conductors (plates), separated by a non-conducting insulator (the dielectric). Capacitors are used in nearly every electronic design. They are found in power supplies, amplifiers, oscillators, and even in all-digital circuits as bypass capacitors for the power supply. I want to look here at what capacitors are, how they work, and examine a few pitfalls in using them.

##### CAPACITOR BASICS

**Figure 1** shows two capacitors. The capacitor at the bottom of the photo is about 2” of red and black wire-wrap wire, twisted together. The capacitor on the top is a strip of adhesive-backed copper foil, about 2” long and 5mm wide, attached to one side of a piece of printer paper. There is an identical piece of foil under it, on the other side of the paper.

Neither of these capacitors would be very useful in an actual circuit, though twisted wires are sometimes called a “gimmick” capacitor. I showed these first to illustrate that a capacitor consists of two conductors with an insulator between them. The twisted pair of wires measures a couple of picofarads (pF), and the copper tape measures about 50pF. The equation for calculating the capacitance of a capacitor is given by:

where:

C is the capacitance in farads

A is the area of overlap of the two conductors, in square meters

E is the dielectric constant of the insulator, or dielectric, that separates the conductors

D is the separation of the two conductors, in meters, about 0.0001016 for printer paper.

If you go to college to be an electrical engineer, you will likely encounter this equation in introductory physics before you take any engineering courses. Any two conductors separated by an insulator form a capacitor. This includes traces on a PCB, your finger to a trace on a PCB, if you happen to be touching another trace, and the two wires in an electrical cord. The capacitance may be very small, but it’s there. There is a very old saying in electrical engineering that if you want to build an oscillator, start out by trying to build an amplifier. Although that’s an exaggeration, it’s acknowledgement that there are many potential capacitors in any given electrical circuit, and sometimes you have to manage them to prevent oscillation or instability. Every design has both intentional capacitors and unintentional capacitors that result from the layout and wiring.

The dielectric constant of a vacuum, called Eo, is about 8.8×10^{-12} farads/meter. The relative dielectric constant of any material is Er. For paper, the relative dielectric constant is about 2.3 to 3 (depending on the specific paper used). The value of E in the formula is Eo×Er. So the dielectric value for paper is about 2.3×8.8×10^{-12}=2.024×10^{-11}. Thus, if you plug the values used into the equation, you get about 50pF, which is about what I measured with a capacitance meter.

It might seem odd to use paper as a capacitor dielectric, but many years ago, paper capacitors were fairly common. They used very thin paper and very thin foil, and were rolled into a tube to reduce the size. Paper capacitors are rare now, because there are better materials available, such as polyester film.

##### CAPACITOR CONSTRUCTION

How do capacitor manufacturers make tiny capacitors with capacitance of hundreds or thousands of picofarads (pF), or even tens of microfarads (μF)? You use an insulator with a large dielectric constant, make the dielectric layer very thin, and use a lot of interleaved conductors. **Figure 2** shows how a typical capacitor is constructed. The two plates are actually many plates, interleaved with a very thin dielectric. Think of the figure as being shrunk so about 0.1” long and a fraction of an inch thick; the dielectric spacing is microscopic. And the area of the plates is increased by the number of layers.

A common material for capacitors is ceramic, which has an Er of about 20 to 40, depending on the specific ceramic used. Combining the high Er with microscopic dielectric thickness creates relatively high capacitance in a small package. Other dielectrics are used as well, for example, mica has been used for decades for precision capacitors. For the copper foil and paper capacitor in Figure 1, the capacitance would be about 500pF to 800pF, if I could get a piece of ceramic the same 0.004” thickness as the paper I used (and if I could assemble it without breaking the ceramic, which is unlikely).

##### UNITS OF MEASURE

In a Physics class, capacitance is measured in farads, but practical values used in electronics normally use picofarads (pF, 10^{-12} farads), nanofarads (nF, 10^{-9} farads) or microfarads (μF, 10^{-6} farads). Nanofarad is a more recent unit of measurement; in years past, it was all pF and μF. 1,000 pF = 0.001μF = 1nF. I tend to still use pF and μF, just out of habit. In the really old days, pF was mmF (micromicro farads), which you might find on a very old schematic, such as you will see if you are into restoring antique radios. Obviously, “micromicro” isn’t mathematically correct. A pF is not one millionth of a μF, it’s one thousandth. At the other end of the scale, farad-sized supercapacitors are actually available, and they are used instead of rechargeable batteries in some applications.

##### TOLERANCE

Capacitors have a tolerance, the amount that the capacitance can vary from the nominal value at some nominal temperature. Typical tolerance values are 5%, 10%, and 20% for ceramic capacitors. So, a 0.1μF 10% capacitor may have an actual value of 0.09μF to 0.11μF.

##### TEMPERATURE EFFECTS

Temperature changes capacitance. What matters is how much and how it affects your circuit. Like all electrical components, capacitors have a minimum and maximum operating temperature. There are also categories of temperature coefficients. The International Electrotechnical Commission (IEC) and the Electronic Industries Alliance (EIA) each has standards for this, and there are many temperature coefficient codes. The temperature coefficient is essentially a measure of how much the dielectric characteristics change with temperature. Here are a few of the common codes and what they mean:

X7R (−55/+125°C, ±15%)

X5R (−55/+85°C, ±15%)

Z5U (+10/+85°C, +22/−56%)

Y5V (−30/+85°C, +22/−82%)

Thus, the common X7R capacitors will operate from -55°C to 125°C, and the capacitance will change a maximum of +15% over that range. Note that the temperature variation is added to the tolerance; if that 0.1μF capacitor is at the low end of the tolerance, at 0.09μF, then that is the value that may change 15% over temperature. In other words, over the operating temperature range, it may vary from 0.0765μF to 0.1035μF.

Like everything in the real world, capacitors come with trade-offs. High precision parts cost more than lower precision parts. Parts designed for high-temperature operation, such as automotive and military-grade parts, are more expensive than parts intended for consumer products. Mica capacitors can have very low tolerances, measured as percent tolerance like ±1% or in amount of value change such as ±1pF. Mica is also very temperature-stable. However, the dielectric constant of mica is much lower than that of ceramic, so for a given capacitance and voltage rating, a mica capacitor will be larger. NPO capacitors are also temperature-stable, and are extremely flat over a wide temperature range.

##### WORKING VOLTAGE

All capacitors have a specified working voltage, the maximum voltage that can be applied across the capacitor. Exceeding this value can result in failure, and for a high voltage across a large capacitor, failure can be quite dramatic, with pieces of capacitor all over the place. Trust me on this. Most capacitors can operate briefly beyond their maximum working voltage. But don’t make a habit of it.

##### Q FACTOR

The Q factor, or quality factor, of a capacitor is a function of the effective series resistance of the capacitor. All capacitors effectively have a resistor in series with them, and the value of the resistor goes up with frequency. At low frequencies, the Q factor is not normally a consideration, but at high RF frequencies, the Q factor affects the effective impedance of the part.

##### ELECTROLYTIC CAPACITORS

Electrolytic capacitors are used to get high capacitance, such as tens, hundreds, or even thousands of microfarads, in a small package. An aluminum electrolytic, for example, has a very thin film of aluminum oxide on one plate, which creates a very thin dielectric layer with a high dielectric constant. This allows for the D in the capacitance equation to be very small. Tantalum capacitors are similar though the oxide is different.

Electrolytic capacitors are polarized, and must be wired with the positive end of the capacitor at the most positive voltage in the circuit. Wiring a capacitor backward can result in explosive failure. This is especially true in cases where the capacitor is used to filter a DC power source. There is little current limiting in those applications, and a reversed capacitor is a very bad thing.

Aluminum electrolytic capacitors have larger tolerance than ceramic capacitors; a typical value is -10% to +30%, but can be in the range of -10% to +75% or so. Tantalum capacitors are usually a better, with tolerance more like ceramic capacitors, ranging from ±5% to ±20%.

Aluminum electrolytics also have a more limited life than other types; the capacitors “dry out.” This reduces the capacitance, increases internal resistance (equivalent series resistance or ESR), and decreases working voltage. Elevated temperatures will accelerate this aging.

TDK has a very good paper on construction and use of aluminum electrolytic capacitors [1], and AVX has a similar paper on tantalum capacitors [2].

##### CAPACITORS IN SERIES AND PARALLEL

**Figure 3** shows capacitors in series and in parallel. C1 and C2 are in parallel, and the value of the total capacitance is the sum of the two capacitors, in this case 2.5nF. The maximum voltage that can be applied is the lowest of the two capacitors, if they have different working voltages.

Capacitors C3 and C4 in Figure 3 are in series. The value of the two capacitors is given as:

which is 0.6nF in this case.

##### HOW A CAPACITOR WORKS

To avoid the calculus that you’ll need to understand capacitors in that engineering program I mentioned, I’ll simplify it here: When you apply voltage, such as a battery, across a capacitor, the two plates of the capacitor will have equal and opposite charges. One of those physics problems in that engineering program will likely be calculating the energy storage of a hypothetical capacitor. If you remove the voltage source from the capacitor, the capacitor will remain charged, and the voltage across the capacitor will equal the original voltage source. So, a capacitor acts as a sort of battery.

All dielectrics have some leakage, since there are no perfect insulators. As a result, the charge on the capacitor slowly leaks away, until the capacitor is discharged and there is zero volts across it. But you can draw current from the capacitor, just like you would from a battery.

It might seem like magic that the capacitor can be charged up by the battery and then use that charge to power something, even if it’s only for a few seconds. But the law of the conservation of energy still holds. When you apply the voltage across the capacitor, charging the plates draws current from the battery.

**Figure 4** shows what happens. When S1 is closed, current flows through the resistor and into the capacitor. The resistor represents the impedance of the voltage source and the ESR of the capacitor. There are no ideal voltage sources or capacitors. In an ideal world, closing switch S1 would result in infinite current and immediate charging of the capacitor.

In the real world, however, the value of R1×C1 is the time constant, and after one time constant, the capacitor will be about 63% charged. After two time constants, it will be about 86% charged. Each time constant will add about 63% of the difference between V1 and the current voltage of the capacitor. Thus, the capacitor will never reach the voltage of V1, although it will get close enough that you can’t measure the difference.

You can do this experiment yourself— get a 100µF capacitor and a 33kΩ resistor. As shown in **Figure 5**, connect the resistor and capacitor in series. Connect a voltmeter across the capacitor. Connect the negative side of the capacitor and the free end of the resistor to a 9V battery (be sure to connect the capacitor polarity correctly—the resistor goes on the positive terminal).

You will see the capacitor voltage slowly rise until it reaches the battery voltage. (It won’t quite get there, but close enough that the voltmeter can’t read the difference.) The time constant is about 3 seconds, so you’ll see the capacitor charge to about 5V in about 3 seconds.

If you disconnect R1 from the battery, you will see that the capacitor retains the voltage. It will slowly discharge, depending on how quickly the voltmeter and internal leakage draws down the voltage. If you charge the capacitor and then disconnect the battery and connect R1 to the negative capacitor lead, the capacitor will discharge just like it charged up, logarithmically.

Electrolytic capacitors have higher ESR than other types, which makes them less effective at filtering high frequencies (remember, ESR goes up with increasing frequency). This is why you often see a PCBA with an electrolytic capacitor in parallel with multiple ceramic capacitors on the DC power lines. The smaller ceramic capacitors are to filter faster transients.

##### POWER FILTERING

How might you use power filtering in a practical circuit? **Figure 6** shows a 6V DC voltage with quite a bit of ripple. You might see this from an unregulated 6V power supply, such as an inexpensive wall-mounted power supply. If you put a large enough capacitor across the power supply output, the ripple can be significantly reduced. What happens is that, since the power supply can usually source but not sink current, the capacitor will charge to the peak voltage and hold it while the power supply output cycles to the lower voltage, resulting in an output with significantly reduced ripple.

This works if the time constant of the capacitor and the power supply output impedance is much longer than the ripple frequency (typically 60Hz or 120Hz for a small power supply in the US). The power filter is a low-pass filter, and it works because capacitors pass AC signals but block DC signals.

##### DC BLOCKING

**Figure 7** shows an alternate use of capacitors to block DC and pass AC. The input signal is an AC waveform (maybe an audio tone) riding on a 12V DC offset. This might be generated by a power supply similar to the one in the previous example, or possibly from some kind of signal generator. Let’s say we want to capture the waveform, perhaps to count the transitions or to pass the signal into some other electronic circuit.

Q1 is a transistor wired as an emitter follower. Resistors R1 and R2 bias the base of Q1 to about 3V, and R3 is the emitter resistor. With an AC signal with a 12V bias, directly connecting the signal to the base of Q1 would probably destroy the transistor and definitely would not produce the output you want. But C1 provides a DC block, so the AC signal will pass through but the DC offset will be blocked. The waveform at the base of Q1 will be the AC waveform, but instead of being biased at a 12V offset, it will be biased at the 3V bias at the base of Q1.

How big does the capacitor need to be? The AC impedance of a capacitor is given by this equation:

Xc is the impedance of the capacitor, f is the frequency, and C is the capacitance. Note that Xc is actually a complex number (one of those engineering school concepts), but the equation gives the effective AC resistance. (I won’t go into phase angles or complex/imaginary numbers here.)

If we assume that the impedance at the base of Q1 is the parallel resistance of R1 and R2 (it’s not exactly that, but close enough for this example), then C1 is driving a 6kΩ impedance. So, if C1 is 1nF, then the frequency at which the impedance of C1 equals the 6kΩ input impedance of Q1 is about 26kHz. Accordingly, frequencies below that will be attenuated, and frequencies above that will be passed through with decreasing attenuation as the frequency rises.

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If you’ve seen the schematic of an LM386 audio amplifier circuit or a similar part, you will see a large capacitor (250µF in the LM386 datasheet) between the output and the speaker. This is necessary because the speaker impedance is on the order of a few ohms, but the output capacitor has to pass low audio frequencies. That combination requires a large capacitor.

##### POWER-ON SPIKE

Power-on spike is one thing that can trip up a designer. Going back to Figure 7, suppose that the Q1 circuit is already powered on, and you turn on power to whatever is generating the input signal. There will be a momentary spike of 12V on the base of Q1, as C1 charges up the first time. That may or may not be a problem, but it’s definitely outside the operating intent of the circuit.

In the old days, stereo amplifiers would sometimes “thump” when turned on or off, and those surges would sometimes damage speakers. So, when using a capacitor as a DC block, make sure that any power-on surges can be handled. In the case of this specific circuit, you might put a Zener diode from the base of Q1 to ground, and a resistor in series with C1 if the power-on surge is likely to be a problem. In this specific case, there is nothing to limit the base-collector current from the 12V spike on the base of Q1, which will forward-bias the base-collector junction. Certainly, the larger the DC offset, the more risk there is of damaging Q1 from a sudden power-on spike.

##### SQUARE WAVE AND DC BLOCK

**Figure 8** shows what happens when you put a square wave into a DC blocking capacitor. In this case, I used a signal of 200kHz and a 56pF capacitor. There is a positive spike at the output, when the square wave goes high and a negative spike when the square wave goes low.

This is because the 56pF capacitor and 1kΩ resistor will attenuate frequencies below about 3MHz, and a square wave is composed of a sine wave and a number of higher frequency harmonics. The capacitor passes the higher frequencies, but attenuates the lower frequencies, which includes the baseband 200kHz frequency. Note the negative spike at the falling edge of the input, which can damage some parts. As the capacitor value is increased, the output looks more like the input; at 1μF the output looks nearly identical to the input.

##### CONCLUSION

Capacitors are used everywhere. I hope that this brief tutorial has helped you understand them better—how they work, and how to avoid some potential problems.

Additional materials from the author are available at:

www.circuitcellar.com/article-materials

References [1] to [2] as marked in the article can be found there.

RESOURCES

AVX | www.avx.com

TDK Electronics | www.tdk-electronics.tdk.com

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • JUNE 2022 #383 – Get a PDF of the issue

Sponsor this ArticleStuart Ball recently retired from a 40+ year career as an electrical engineer and engineering manager. His most recent position was as a Principal Engineer at Seagate Technologies.