Parasitics and Capacitor Selection, Part 6: Capacitance

Since we’re now halfway through the series, it’s probably a good time to look at the nameplate parameter for capacitors – the capacitance itself.

In most capacitor applications, such as bypass and decoupling, the parasitic inductance and resistance associated with the technology determines the best solution; and, as long as the capacitance falls within a certain value range, it’s not all that critical. However, in other applications, such as tuning and antenna matching, it’s the single most critical parameter. Typically, when a capacitor is being used as a bulk capacitor within the required range of capacitance, more is better.

Let’s digress for a moment to discuss how standard capacitance and voltage values are defined, though.

Standard voltage ratings for capacitors tend to follow the R5 Renard Series, which was originally used to subdivide decade intervals in a geometric progression. For example, to subdivide 10 into “n” geometric steps, one would use the nth root as the scaling factor so that each value in the series is given by Equation 1, in which “b” is equal to the number of interval values required and “i” is the interval of that series.

Using this equation, if b = 5, the interval values, to two significant figures, are: 1, 1.6, 2.5, 4.0, 6.3, 10, 16, 25, 40 , 63, 100…

For maximum capacitor voltage ratings, R5 Renard Series ratings are still used in IEC specifications; however, many American manufacturers standardize the “6.3” values at 6, 60, 600, etc. and intersperse additional values from a 1-2-5 series to provide 20, 50, 200, 500, etc. maximum voltage options.

The standard sequence of values for capacitors, resistors, and inductors was also set by a Renard-type series, but with an added proviso that requires the values needed to provide seamless coverage between two arbitrary values for common tolerances (e.g., ±5%, ±10%, ±20%, etc.). So, if you have a technology that has a typical manufacturing capability to achieve a ±20% capacitance tolerance, the range between 1 and 10 can be spanned in six steps (using b = 6 in the equation above) such that, to two significant digits, the maximum tolerance of one value dovetails or overlaps with the minimum tolerance of the next.

The series using 6 intervals for a ±10% tolerance is referred to as E-6; similarly, E-12 (using b = 12 in Equation 1) works for a ±5% tolerance, while E-3 works for a ±20% tolerance. This system can be extended to finer and finer tolerances, with E-24 series working equally well for ±2.5% tolerances and E-48 for ±1.25% tolerances. However, the fine tolerances adopted for precision devices were 2% & 1%. So, for E-48 and higher orders, three significant digits are required to define unique values. As such, some of the values for precision resistors were tweaked slightly to improve overlap.

This tweak was then retrofitted to the lower orders, but had only a small effect – namely, requiring that a few values be rounded up rather than to the nearest value in two significant digits. That’s why we currently have 3.3 and 4.7 as standard values for capacitors and inductors rather than the more mathematically elegant 3.2 and 4.6. Ultimately, though, establishing standard values just provides useful buckets in which to group component size; they are not driven by any unique electrical requirement.

Table 1

Calculated Values vs. Adopted Values for E-3, E-6, E-12, & E-24 series.

Calculated Values vs. Adopted Values for E-3, E-6, E-12, & E-24 series.

Additionally, while the foregoing history of the numbers we use every day appears to be of academic interest only, there can be ramifications for logistics that users need to be aware of. Let’s say that, year-on-year, a manufacturer of a standard E-6 series capacitor is able to squeeze 20% more capacitance into a certain size package at a given voltage rating. If the previous maximum rating was 68uF that won’t be enough to get to 100uF, but it would be enough to achieve an E-12 value of 82uF, so the manufacturer includes this option (retaining a standard E-6 ±20% tolerance) in the series; as, since more is better in most decoupling applications, a designer may choose this value for a certain application.

This program may be revisited in the not too distant future to identify and evaluate potential alternatives, but by that time – given typical advances in capacitance and voltage capabilities – most manufacturers will offer a standard 100uF rating. Working with the bill of materials (BOM) alone and trying to keep to the “special” 82uF value referenced would certainly lead to availability issues at that point, but since the value “buckets” are geometric rather than arithmetic and are based on a more-is-better approach, there’s typically no issue associated with selecting a capacitance value twice as large as an original design for a given application. So, using a 100uF capacitor in lieu of an 82uF capacitor would be considered a straightforward substitution, especially since the ±20% tolerance would overlap with the 82uF nominal.

Bulk capacitors, which provide reservoirs of energy for silicon devices (e.g., ASICs, FPGAs, etc.) to draw on instantaneously, are the most typical application that follows the “more is better” capacitance rule. In fact, if the bulk capacitor application is a “brick wall” that uses many capacitors in parallel, an extra capacitor is often beneficial; as, apart from adding capacitance, it will also reduce the overall ESR, which will improve noise filtering in power supply output applications. One caveat to this general rule is when a capacitor is in the output stage of a low dropout (LDO) voltage regulator. In this case, too low an ESR can cause instability or oscillations in the circuit.

For any given capacitor technology at a certain voltage rating, going to a higher capacitance value will result in a lower ESR device. So, in this case, one would want to select the next lowest capacitance when considering substitutions. In general, though, the larger the capacitor, the less critical the value may be in the application. For example, further up the capacitance scale, at the farad level for supercapacitors, most technologies are supplied with a single tolerance option ±80/±20. In essence, this is akin to having a guaranteed minimum value (GMV) specification since the maximum is not an issue.

With regard to mid-range capacitance values (spanning 0.1uF to 10uF), if the capacitors are configured with inductors, resistors, or both into LR, LC, or LCR filter circuits, then the values of all the components will be interdependent with respect to the required filter characteristics. In most cases, E-6 values are chosen for the capacitors, but with a tighter 10% (E-12) tolerance to keep them within the application window.

Additionally, since we’re discussing the requirements for substituting or upgrading capacitors, when two capacitors are connected in parallel, the total capacitance in a system is additive (see Equation 2). When capacitors are connected in a series, the total capacitance in a system can be derived using Equation 3.

If C1 = C2, then Ctotal is half of this value; and, as each capacitor supports its rated voltage, the voltage rating of the system is double that of a single element. An example of this can be seen in the AVX FlexiSafe™ capacitor design. FlexiSafe capacitors feature a rugged ceramic chip with flexible terminations built to withstand high thermal and mechanical shock environments, and their internal electrodes have a cascade design that actually forms two capacitors in series within a single ceramic body. The benefit of this design is that, in the event of an external high current arc or pulse – even one that creates a short on one side of the element – a FlexiSafe capacitor will continue to function normally. It’s possible to tell when this happens, though, because, after the event, the in-circuit capacitance will actually double.

Figure 1

AVX FlexiSafeTM capacitor design

AVX FlexiSafeTM capacitor design

When connecting electrolytic capacitors (like tantalum) in parallel or in a series, the capacitors will be polar, but a standard series configuration (+ – + – ) will similarly result in a capacitance value that’s half that of an individual element with the voltage rating doubled while the system remains polar.

One can also put polar capacitors in series back-to-back to achieve a non-polar configuration. Non-polar tantalum capacitors were developed a long time ago by putting two tantalum elements into a sleeve and connecting the outside of the elements in a common cathode configuration with a positive stub wire at each end welded to axial or radial leads. This is identical to putting two standard tantalum capacitors in a circuit, connecting the two negative leads together, and using the two positive leads as the outside circuit connections.

Additionally, this is typically less costly than a discrete device with an internal common-cathode configuration. When connecting two tantalum capacitors of the same rating in a common-cathode configuration, the total capacitance will be half that of an individual unit and the voltage rating will be that of an individual unit, but bi-directional (non-polar) in the circuit.

Finally, to complete our discussion of capacitance tolerances, we’ll need to consider low value capacitors. Lower capacitance values have a higher self-resonant frequency. This makes them particularly well suited for microwave and RF applications, which typically require very specific values with tight tolerances, especially when using a capacitor individually as a notch filter or for an antenna matching application. In the latter case, high precision thin-film capacitors can replace the E-48 system typical of high precision resistors and, unlike resistors, can actually adopt a linear value system, going from 0.1pF to 2pF in 0.05pF increments with +/-0.02pF tolerance.

This not only provides many more nominal value options above 2pF, but can also provide custom values in between these for critical matching. Using this same technology, thin film inductors use the E-12 series for fractional nH inductances, but with ±0.05nH tolerances available for nominal values of 1.2nH and lower. Moreover, AVX’s multilayer organic (MLOTM ) technology is able to provide 0.1nH increments for nominal values of 1.3nH and lower at +0.05nH tolerances.

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