Capacitor Selection

Impedance versus frequency

$$Z = \text{ESR} + j\left(2\pi f \cdot \text{ESL} - \frac{1}{2\pi f C}\right)$$

Below the self-resonant frequency the capacitive term dominates and the impedance falls at 20 dB per decade. At resonance the reactances cancel and the impedance equals the ESR. Above resonance the ESL dominates and the impedance rises. The self-resonant frequency is

$$f_{SRF} = \frac{1}{2\pi\sqrt{\text{ESL} \cdot C}}$$

Figure 2. Impedance magnitude versus frequency for four 10 µF or 100 nF parts. The ceramic reaches the lowest minimum; the electrolytic is limited by ESR across three decades.

The ESL in the table is the part alone. Once mounted, the loop through the pads, the vias, and the plane adds inductance that usually exceeds the part's own. A 0402 ceramic with 0.4 nH of internal inductance on a pad with 1 nH of via-to-plane inductance behaves as a 1.4 nH part. Package size, pad geometry, and via placement determine the high-frequency behavior more than the capacitor does.

Loss and dissipation factor

Dissipation factor is the ratio of ESR to reactance at the measurement frequency:

$$\text{DF} = \tan\delta = 2\pi f C \cdot \text{ESR}$$

Datasheets give DF at 1 kHz for large values and 1 MHz for small ones. Class 1 ceramics and polypropylene film have DF below 0.1 %; class 2 ceramics 1 to 3 %; aluminum electrolytics 5 to 30 %. Loss matters in three places: it heats the part under AC current, it damps resonances (which is sometimes wanted), and it degrades the Q of a tuned circuit or the accuracy of an integrator.

Leakage

Leakage current is specified as an insulation resistance for ceramics and film (typically above 10 GΩ, or an RC product above 1000 s), and as a current for electrolytics and tantalums, where it is proportional to capacitance and voltage. A 100 µF aluminum electrolytic at rated voltage leaks 10 to 100 µA at 20 °C and several times that at 85 °C. Leakage matters in sample-and-hold circuits, timing circuits, battery-powered hold-up, and any node with a high source impedance.

Dielectric absorption

After a capacitor is discharged and left open, a fraction of the original voltage reappears as charge trapped in the dielectric relaxes back. Dielectric absorption is specified as that fraction. It sets the error floor of sample-and-hold and integrator circuits and the settling time of precision references.

Class 1 and class 2

Class 1 dielectrics (C0G, also called NP0, and the lesser-used U2J and C0H) are paraelectric. Their dielectric constant is low, around 10 to 100, so capacitance per volume is small, but it does not depend on voltage, changes with temperature by a specified small coefficient, does not age, and is not piezoelectric. Class 1 parts are available up to about 100 nF in 1206 and a few microfarads in large packages at high cost.

Class 2 dielectrics (X7R, X5R, X6S, X7S, X8R, Y5V, Z5U) are ferroelectric barium titanate. The dielectric constant is 1000 to 10000, so a 0402 package holds 10 µF, but the polarization that gives the high constant is exactly what makes it sensitive to voltage, temperature, time, and mechanical stress.

The code describes the temperature behavior only, at zero bias. It says nothing about DC bias, and two X7R parts of the same value and rating from different vendors or different package sizes can differ by a factor of two under bias.

DC bias

Figure 3. Capacitance versus DC bias for class 2 ceramics of one nominal value and voltage rating in four package sizes. The smaller package has a thinner dielectric at a higher field and loses more.

Applied DC voltage aligns the ferroelectric domains and reduces the dielectric constant. The loss depends on the electric field, which is the voltage divided by the layer thickness. A manufacturer fits more capacitance into a smaller package by making the layers thinner, so the same 10 µF 6.3 V rating in 0402 sees a much higher field at 3.3 V than in 0805, and loses far more.

Representative values at half rated voltage, for X5R and X7R:

These are ranges across vendors. The only reliable source is the manufacturer's C-V curve for the specific part number, which every major vendor publishes through an online simulator. The rule that follows: choose the voltage rating so the operating voltage is well below half of it, or choose a larger package, or both, and design with the biased value.

A higher voltage rating in the same package does not always help. A 25 V 0603 part and a 10 V 0603 part of the same capacitance may use the same dielectric thickness with different rating margins, or the 25 V part may use thicker layers and fewer of them. The curve, not the rating, is the specification.

AC voltage and capacitance

Class 2 capacitance also depends on the AC signal amplitude. The datasheet value is measured at 1 V RMS (0.5 V RMS for small values). At the millivolt levels of a signal path the capacitance is 10 to 20 % lower; at large AC swings it rises, then falls. In a filter or a coupling position this is a signal-dependent capacitance, which is a distortion mechanism: a class 2 coupling capacitor in an audio path produces measurable second and third harmonic distortion at low frequencies where the voltage across it is significant.

Temperature

Figure 4. Capacitance change versus temperature at zero bias for C0G, X7R, X5R, and Y5V. The class 2 curves shift and steepen under DC bias.

The temperature coefficient of a class 2 part is not a slope. Capacitance peaks near the Curie temperature of the formulation (near room temperature for most) and falls on both sides. The specified ±15 % for X7R is the envelope over the full range at zero bias; with DC bias the whole curve drops and the shape changes, so the combined bias and temperature loss must be read from the manufacturer's data rather than multiplied from the two separate specifications.

X5R stops at 85 °C. Above that the capacitance falls quickly and the part is out of specification. Boards that operate hot, or hot spots near power components, need X7R or X7S.

Aging

Figure 5. Capacitance versus time after reflow for class 2 ceramics. The loss is logarithmic; the datasheet value is referenced to 1000 hours.

Ferroelectric domains relax over time, and class 2 capacitance falls by a constant percentage per decade of hours after the last time the part was heated above its Curie temperature. Typical rates:

The marked value is the value at 1000 hours. A part measured one hour after reflow reads 5 to 15 % high on the same basis; a part in service for 10 years (about 10^5 hours) reads 5 to 10 % below marked. Reflow above about 125 °C de-ages the part and restarts the clock, which is why incoming inspection of aged parts shows low values that recover after assembly, and why a rework on one capacitor changes its value relative to its neighbors.

Piezoelectric and microphonic effects

Barium titanate is piezoelectric. A class 2 capacitor under AC voltage vibrates and can sing audibly (the whine from a converter with a large ceramic output capacitor at an audible switching or burst frequency). The reverse also holds: mechanical vibration or shock applied to a class 2 part with DC voltage across it generates a voltage. In a low-noise amplifier input, a reference bypass, or a high-impedance sensor node, a class 2 capacitor is a microphone. Class 1 ceramics and film are not piezoelectric.

Mitigations for singing: a lower-dielectric-constant part (X7R sings less than X5R at the same value), a larger package with less strain per volt, two parts in series or on opposite sides of the board so their strains cancel, film or polymer parts for the offending value, or moving the switching or burst frequency out of the audible band.

Cracking

Figure 6. Cross-section of a flex crack. Board bending puts the termination in tension and the crack starts at the termination edge and runs diagonally through the electrode stack.

Ceramic is brittle. Two mechanisms crack it.

Flex cracks come from bending the board after the part is soldered: depaneling, screwing the board into a housing, connector insertion, pressing a button, or a bowed board pulled flat by screws. The stiff solder joint and termination hold the ends while the board bends under the body, and the crack starts at the inner edge of the termination. Larger packages are more vulnerable because they span more of the bend; 1206 and larger parts are the usual casualties, and 0402 and smaller rarely flex-crack.

Thermal shock cracks come from heating the part faster than the ceramic can equalize: hand soldering a large MLCC with an iron, wave soldering without preheat, or a reflow profile with too steep a ramp. The crack forms internally and is invisible.

A cracked part may measure correctly. The crack becomes a failure when moisture and DC bias drive electrochemical migration along it, over days to months, and the part turns first leaky and then short. On a power rail a shorted ceramic is a fault current path; on a battery-powered product it is a dead battery or a fire.

Mitigations, in order of effectiveness:

1. Keep MLCCs out of high-stress zones: within about 5 mm of board edges, V-scores, tab routes, mounting holes, and connectors, and away from anywhere the board is pressed. See Figure 9, and Whole-board flex below for the board's own bending.
2. Orient the long axis of the part parallel to the bend line (parallel to the nearest edge or score), which puts less differential strain across the terminations.
3. Use soft-termination parts (a conductive polymer layer between the termination and the ceramic that absorbs strain; every major vendor offers them) for parts that must sit near stress or that would cause a hazard if shorted.
4. Use open-mode or series-electrode construction for parts on a battery or mains-derived rail, where a short is a safety event. Open-mode parts keep the electrodes away from the termination edge so a flex crack does not bridge them; series-electrode parts are two capacitors in series inside one body, so one crack does not short the part.
5. Put two parts in series on a critical rail if the safety case requires it.
6. Use a smaller package: two 0603 parts in place of one 1206.
7. Control the depaneling method (a router or a laser rather than breaking a V-score by hand) and the assembly torque.
8. Never hand-solder an MLCC larger than 0603 without preheating the board.

Whole-board flex

Figure 7. A long, narrow board supported at its ends bends about its short axis. Surface strain runs along the length and peaks at mid-span, so a capacitor placed lengthwise there takes the full strain across its terminations.

Edge zones are not the only source of bending. The board as a whole flexes whenever it is loaded between supports, and its shape sets the direction. A long, narrow board, a board supported only at its ends, and a board with a connector that is mated by hand all bend about their short axis: the surface stretches along the length, most at the middle of the span, and the bend line runs across the width. A square board supported at four corners bends in both directions, and a cantilevered board (a mezzanine or a card supported along one edge) bends most at its root, where it meets the support.

Consequences for placement:

• Identify the flex axis from the aspect ratio and the mounting before placing large ceramics. On a long, narrow board the long axis of every MLCC of 0805 or larger should run across the board, parallel to the short edge, so it sits parallel to the bend line.
• Keep large ceramics away from the middle of an unsupported span and away from the root of a cantilever. Near a standoff or a stiff edge the curvature is small.
• Add standoffs, a stiffener, or a support rib where a large MLCC must sit in a high-curvature region, and specify the maximum board deflection in the mechanical drawing if the enclosure can press on the board.
• The same applies during assembly: a long board held at one end while a connector is pressed in at the other has been bent, and the in-circuit test fixture that pushes pogo pins into it has bent it again. Fixture supports go under the largest ceramics.
• Boards that will be flexed in service (press-fit, handheld, anything with a keypad) should specify soft-termination or open-mode parts for every MLCC of 0805 and larger regardless of placement.

Voltage rating and derating

Class 2 ceramics do not have a hard derating rule the way tantalum does; the rated voltage can be applied continuously without a wear-out mechanism, and the failure rate rises with voltage and temperature in the usual way. The derating is set by capacitance: the operating voltage must be low enough on the C-V curve that the remaining capacitance does the job. In practice that means operating at 30 to 50 % of rated voltage for capacitance-critical positions and up to 80 % for positions where any capacitance is enough. Automotive and industrial guidelines commonly require 50 % for class 2 ceramics on rails that see transients.

Class 1 ceramics have no bias dependence and are used up to 80 % of rating with the same transient margin considerations as any other part.

What ceramics are good for

• Decoupling and bypass at every frequency above a few hundred kilohertz, where nothing else has the impedance.
• Switching converter input and output filters, with the value computed at bias and the ripple current rating (a thermal limit, usually generous) checked.
• Timing, filters, sample-and-hold, and precision analog: C0G only.
• Snubbers and resonant circuits at high frequency: C0G, and the AC current rating must be checked because ceramics have a small thermal mass.
• Any position where low ESR, small size, and no polarity matter and the biased value is acceptable.

Liquid electrolyte parts

The liquid electrolyte is the part's cathode and also its weakness. It evaporates through the seal, and as it does, ESR rises and capacitance falls until the part is out of specification. The rate follows an Arrhenius relation, and the rule of thumb is that life doubles for every 10 °C below the rated temperature:

$$L = L_0 \cdot 2^{\frac{T_{rated} - T_{core}}{10}}$$

where L0 is the rated life at rated temperature (the "2000 h at 105 °C" on the datasheet) and Tcore is the actual core temperature, which is the ambient plus the self-heating from ripple current through the ESR. A 2000 h, 105 °C part at a 55 °C core temperature has an expected life of 2000 × 2^5 = 64000 hours, about 7 years of continuous operation. The same part at 85 °C has 8000 hours, less than a year. The manufacturer's calculator includes the ripple heating term and the voltage derating term and should be used in place of the rule of thumb.

End of life for a liquid electrolytic is a specified drift: typically capacitance down 20 to 30 %, ESR up by a factor of two to three, and leakage above the initial limit. The part does not usually fail catastrophically at end of life; it stops filtering, and the circuit it filters fails. The exception is reverse voltage, overvoltage, or excessive ripple, which generate gas until the vent opens and the part expels electrolyte.

Leakage current rises with temperature and time in storage. A liquid electrolytic that has sat unpowered for years has a degraded oxide and draws high leakage when first powered until the oxide re-forms. Parts stored more than two years should be reformed with a current-limited supply before use, and a product that will sit in inventory should specify long-shelf-life parts.

Polymer and hybrid parts

Solid polymer aluminum capacitors replace the liquid with a conductive polymer. ESR is a few tens of milliohms, flat over temperature, and there is no dry-out mechanism, so life is set by the polymer's slow oxidation and is much longer. The costs are higher leakage (tens to hundreds of microamps), lower voltage ratings (typically to 100 V, commonly 35 V and below), a tighter limit on overvoltage and surge, and price. Polymer parts fail short under sustained overvoltage, which matters on a rail with transients.

Hybrid parts use polymer with a small amount of liquid electrolyte, which heals oxide defects and keeps leakage low, at the cost of a slightly higher ESR than pure polymer and a return of the temperature dependence at the extreme cold end. They are the current default for automotive and industrial rails where low ESR, low leakage, and long life are all needed.

What aluminum electrolytics are good for

• Bulk energy storage: hold-up through a supply interruption, the input reservoir of a mains-powered supply, and the input of a converter fed through a long cable, where the capacitor absorbs the cable's inductive energy.
• Low-frequency filtering below about 100 kHz where the capacitance per cost is unmatched.
• Damping. A liquid electrolytic's ESR in parallel with a ceramic bank damps the LC resonance of an input filter, which a pure ceramic bank does not.
• Positions where a fail-open at end of life is acceptable and a shorted part is not.

Derating

Operate liquid electrolytics at or below 80 % of rated voltage for life, and at a ripple current below the rated value adjusted by the datasheet's frequency and temperature multipliers. Polymer parts are commonly derated to 80 to 90 % of rating and must not see transients above rating. Both types should be selected for a core temperature that meets the life target, which usually means the largest can that fits rather than the smallest that meets the capacitance.

Manganese dioxide tantalum

The MnO2 cathode has a failure mode that defines the technology. A defect in the oxide carries current, the local heating converts the MnO2 to a lower oxide that is conductive, the fault grows, and the tantalum anode ignites in the oxygen released by the MnO2. An MnO2 tantalum fails short and, with a low-impedance source, burns. The failure rate is strongly voltage dependent, and the traditional derating rules follow:

• Operate at 50 % of rated voltage or less. Below 50 % the failure rate falls by roughly a factor of ten for each further 10 % of derating.
• Limit the surge current with series impedance. The traditional rule for a low-impedance source is at least 1 Ω per volt of applied voltage in series for full reliability, or accept a higher failure rate with 0.1 Ω per volt. On a converter output this is often impractical, and polymer parts are used instead.
• Do not use MnO2 tantalum directly across a battery or a low-impedance rail without series resistance or a fuse.
• ESR rises by a factor of two to three at -40 °C and the ripple current rating is low.

Polymer tantalum

The polymer cathode does not release oxygen and self-heals by becoming non-conductive at a defect. Polymer tantalums are benign in failure, tolerate surge current, have an ESR of tens of milliohms that is flat over temperature, and can be derated to 80 to 90 % of rating. Leakage is higher than MnO2 and the voltage ratings are lower (commonly to 35 V, with 50 to 75 V available). Polymer tantalum has replaced MnO2 in most new designs where the cost is acceptable.

Niobium oxide

Niobium oxide capacitors are a lower-cost relative of MnO2 tantalum with a benign failure mode (they fail to a high resistance rather than a short). Capacitance per volume and voltage ratings are lower. They are a drop-in for MnO2 tantalum in low-voltage positions where the ignition risk is unacceptable and polymer is too costly.

What tantalums are good for

• Bulk capacitance in a thin profile where an electrolytic can does not fit.
• Positions needing a stable value over temperature with moderate ESR: filters below 100 kHz, hold-up, and reference bypass where the microphonic effect of a ceramic is a problem.
• Damping a ceramic bank, using the ESR of a polymer tantalum in parallel.
• Long-life products, since there is no dry-out.

The polarity mark on a surface-mount tantalum is a stripe on the positive end, the opposite convention from an aluminum electrolytic (stripe on negative). Reverse polarity beyond a small fraction of rated voltage destroys the part, and a reversed MnO2 tantalum is an ignition source.

Safety capacitors

Capacitors that bridge mains to earth (Y class) or mains line to line (X class) must be rated to the safety standard (IEC 60384-14) for the position, because their failure mode is a shock or fire hazard.

Y capacitors are limited in value by the allowed earth leakage current of the product class (a few nanofarads for equipment with a protective earth, less for double-insulated). Both classes are usually film for X and either film or a specially rated ceramic for Y. An ordinary capacitor of adequate voltage rating in an X or Y position is a compliance failure and a hazard.

Decoupling in more detail

The purpose of a decoupling capacitor is to be a low impedance between a power pin and its ground pin over the frequency band where the device draws transient current. That impedance is set by the capacitor's ESL plus the mounting inductance up to the frequency where the plane takes over, and by the capacitance only below the self-resonant frequency. Consequences:

• A capacitor 10 mm from the pin has 5 to 10 nH of trace inductance in series with it and is not decoupling anything above a few megahertz. Placement at the pin with the shortest via to the plane is the specification.
• The smallest package with an adequate biased value gives the lowest ESL. A 0402 100 nF part is a better decoupling capacitor than a 0805 100 nF part.
• Multiple capacitors of the same value in parallel divide the ESL and ESR. Multiple capacitors of widely different values create anti-resonances (Figure 8).

Figure 8. Impedance of a 10 µF and a 10 nF ceramic in parallel, compared to two 10 µF parts. Between the two self-resonances the pair forms a parallel tank with an impedance peak.

The traditional decade-spaced set (10 µF, 1 µF, 100 nF, 10 nF) was a response to the high ESL of leaded parts and to the ESR that damped the anti-resonances. With modern MLCCs the ESR is low, the anti-resonance peaks are sharp, and a bank of the same value in the smallest package is usually the lower impedance. Where a mixed set is used, keep the values within a factor of ten of each other and confirm the impedance with the manufacturer's models.