Electronic Design

Turn Capacitors And Inductors Into "Active Passives"

When designers think of passive components, they think of manufacturing tolerances for inductors and capacitors that are typically ± 20% or ± 10%. That's okay in theory, but not when these components are used in an actual application. Applying dc bias to a ceramic capacitor or current to an inductor, at a particular frequency, changes the characteristics of these components. Hence, the name "active passives." For example, a 10- µF , 0603, 6.3-V capacitor can measure as low as 4 µF with 1.8-V dc bias at -30º C. A 3.3- µH inductor can measure as low as 0.8 µH when used in the actual application at 85º C.

Also, component manufacturers are becoming aggressive and perhaps releasing parts that are just good enough to keep up with competitors in the size-versus-value war. This is analogous to various practical situations — for example, a car manufacturer specifying 30 mpg in EPA tests, while real-life driving conditions bring 20 mpg. The consequence is more frequent trips to the gas station than you expect.

This example can be extended to portable power systems. Every component used in the various blocks within the system directly influences system performance. Key performance metrics in portable power systems include battery life, solution size, system resource friendliness, etc. For example, in portable power systems, more-frequent device charging negates the "portable" usefulness.

The system designer already took the first step toward achieving the key performance metrics by choosing a switching regulator to power various system blocks. The next step is to ensure the selected switching regulator works at peak efficiency. Key performance metrics for a switching regulator are efficiency, accuracy, and output-voltage tolerance (including transients, voltage ripple, solution size, etc.). To meet these performance metrics, the switcher IC must be a team player along with the external components.

External components for a switching regulator are typically an inductor, an input capacitor, and an output capacitor. Just like any game that requires team coordination for victory, the external components and the switcher must be matched and coordinated to meet the performance metrics expected of a dc-dc converter solution.

When designing switching regulators, compensation is optimized for a range of values for the inductor along with the input and output capacitors. The output-current capability of the part also depends on many factors, one of which is the inductance value.

This article addresses the key parameters that are affected, and what the system designer must know, when selecting external components for the smallest and most-efficient solution in a portable power system.

Let's focus on ceramic capacitors. They're ideal for portable applications when it comes to size, cost, and performance. And they're well-suited for high-frequency applications due to their low equivalent series resistance (ESR) and impedance at the switching frequency. Low ESR minimizes output voltage ripple, and the low impedance yields excellent filtering characteristics. Capacitors using Y5V-type dielectric have a poor temperature coefficient and can drop in value by 80% at 85 ºC . They're not recommended for portable applications, so this section will concentrate on X5R/X7R capacitors.

Figure 1 shows the history of case sizes for a 10- µF , 6.3-V, X5R ceramic capacitor. The key advantage of using a smaller case size is the savings in the board area for a switcher, and the height of the total solution. At present, major mobile-phone manufacturers have a maximum height limit of 1.2 mm for components used in the phone. As phone models slim down further, this limit can be expected to drop. Today's ceramic capacitors are well poised to meet this requirement.

So far so good, but does the system designer need to know something more about ceramic capacitors? Absolutely! For instance, dc-bias effects in ceramic capacitors must be considered when choosing capacitor values and case sizes. An improperly selected capacitor can wreak havoc in the system design from a stability viewpoint. Typically, dc bias occurs in ferroelectric dielectrics (Class 2), such as X5R, X7R, and Y5V capacitor types.

The basic formula for a ceramic capacitor is:

C = K × \[(S × n)/t\]

where C = capacitance, K = a constant, n = number of layers, S = overlapping area, and t = layer thickness.

The factors affecting dc bias are K, layer thickness, percentage of rated voltage, and grain size of material. An electrical field across the capacitor "polarizes" the inner molecular structure, which causes a temporary change in the K constant and, unfortunately, only lowers it. Smaller-case-size capacitors have a bigger percentage drop in capacitance with dc bias. The higher the dc bias voltage, the greater the percentage drop in capacitance for a particular case size. System designers must be careful when replacing a 0805 capacitor with a 0603 capacitor for space savings — unless the converter is tested with the intended type of capacitor. Or, the 0603 capacitor is recommended in the datasheet.

Figure 2 shows the effect of dc bias on several different capacitors over the ambient temperature range for a typical portable application. Looking at the dc bias characteristics, you can see that a 10- µF , 6.3-V, 0603 capacitor from manufacturer A has a capacitance value of 5.75 µF at 1.8-V dc bias and -30º C. Notice the distinction between capacitor and capacitance. Capacitance is the actual value of the capacitor as seen by the application. The same capacitor from manufacturer C has a capacitance value of 3.5 µF under the same conditions. In fact, the 4.7- µF capacitor from manufacturer A is almost as good as the 10- µF unit from manufacturer C.

So, you can see that capacitance-value curves should be requested from manufacturers at the application's intended dc bias voltage. For example, a system designer using a 2.5-V output voltage must look at dc bias curves at 2.5 V. Minimum capacitance values from the stability viewpoint of a switcher can be found in datasheets of switchers. The difference between manufacturers also must be considered when specifying dual sources of capacitors for the bill of materials (BOM) of a portable power solution.

These decisions should not be left to the sourcing people unless they're well advised of what to look for. Capacitor manufacturers love to show separate curves — one for the capacitance change with temperature, and one for the capacitance change with dc bias. However, they don't show them together, which is really what's needed for a specific application. Combined curves should be requested from manufacturers for the most common voltages used in the system.

Some of the common voltages for a baseband core microprocessor are 1.3 V, 1.5 V, and 1.8 V. I/O and hard-disk drives use 1.8 V, 2.5 V, or 3.3 V. Output voltages for an RF power-amplifier supply can range from 0.8 to 3.4 V.

When it comes to input capacitors, the input voltage range must be considered. For a lithium-ion battery this runs from 3 to 4.3 V, and can be as high as 5.5 V when chargers are plugged in.

The impedence/ESR versus frequency curves also are important from a system viewpoint. A capacitor used in a 2-MHz switcher may not be the ideal choice for a 5-MHz switcher. The capacitor's resonant frequency is a key specification with regard to switcher design. Output-voltage ripple is minimized when the switching frequency gets close to the output capacitor's resonant frequency.

For example, a 4.7- µF and a 10- µF 0603 capacitor have a resonant frequency in the range of 2 to 3 MHz. But resonant frequency is about 6 MHz for a 1- µF 0603 capacitor, and close to 10 MHz for a 1- µF 0402 capacitor. At frequencies higher than the resonant frequency, the impedance is inductive in nature. If it's not properly compensated, stability issues will ensue, and ripple increases in the switcher. Last but not least, manufacturing tolerances for ceramic capacitors are specified/tested at 1 V rms or 0.5 V rms at 1 kHz, whereas in the application, the conditions are very different. Nominal values of capacitors are much lower at lower rms voltages. For a typical switcher, the ripple voltage is in the 5- to 30-mV range.

The three most important points in inductor selection for portable power applications are size, size, and size. Real estate on mobile-phone boards is scarce, especially with all of the features being added to phones, such as MP3 players, TV, and video capabilities. Adding features will drain more current from the battery. Therefore, higher-efficiency solutions are sought for blocks that are conventionally powered by linear regulators or connected directly to the battery. Using magnetic buck converters is the first step toward the higher-efficiency solution. And, as the name implies, an inductor is required.

Key specifications for an inductor, apart from size, are inductance value, dc resistance of the winding (DCR), saturation current rating, rms current rating, ac resistance (ESR), and Q factor at the switching frequency. Depending on the application, the type of inductor — shielded or non-shielded — is important, too.

Similar to dc bias in capacitors, a 2.2- µH inductor from manufacturer A can be very different from manufacturer B's device. The inductance value versus dc current over the temperature range is a very important curve to request from manufacturers. The saturation current rating (I SAT) can be found by looking at this curve. Typically I SAT is specified as the dc current at which the inductance value drops by 30% of its nominal value. Some inductor manufacturers don't specify I SAT . They may specify a dc current for a 40 ºC rise in temperature from the ambient.

DCR effects conduction losses, impacting efficiency at higher output currents. ESR increases with operating frequency, impacting switching losses that dominate at lower output currents. ESR is indirectly proportional to the Q factor. An inductor with a low ESR will have a high Q factor at that frequency. Why should the system designer be worried about the ESR and Q factor when the inductor meets all of the other specs?

As switching frequencies rise above 2 MHz, added emphasis must be placed on ac losses in inductors. Inductors from different manufacturers that are comparable in datasheet specs like I SAT and DCR may have very different ac resistance at the switching frequency, leading to a marked difference in efficiency at light loads. This information is crucial for enhancing battery life in portable power systems, since the system spends most of its time in sleep, standby, or low-power modes.

Since inductor manufacturers don't usually supply ESR and Q factor information, designers should request it. Inductance versus current is also usually given only for 25 ºC , and should be requested for the operating temperature range. The worst-case condition is typically 85 ºC .

Figure 3 shows the ac resistance versus frequency for a number of inductors. Let's consider using one in an example buck converter with the following specifications: FSW = 2 MHz, VIN = 5.5 V, L = 2.2 µH , VOUT = 1.5 V, I = 0 to 600 mA, and ΔI = 289 mA (calculated). Referring to Figure 3, the 2.2- µH inductor has a DCR at low frequency of 0.2Ω and an ESR at 2 MHz = 1Ω. The dc loss and ac loss due to the inductor can be calculated using the following equations:

DC loss = I2 × DCR

AC loss = ( dΔ I2 )/12 × ESR

Looking at the equations, at higher output currents the low frequency or dc losses will dominate, and at lower output currents the ac losses will dominate. ΔI is the peak-to-peak ripple current in the converter, and its magnitude is the same at high and low output currents for continuous conduction modes of operation. After going through the math, it can be seen that at I = 600 mA, 91% of total losses in the inductor is dc loss. And at I = 50 mA, 93% of total losses in the inductor are ac losses.

Figures 4a (ESR) and 4b (Q) show inductors from manufacturer A (Low ESR and high Q) and B (High ESR and low Q). Also shown are efficiency curves for a 2-MHz converter using these inductors (Fig. 4c). Judging from the data, even though manufacturer A has a higher DCR, it offers a better efficiency at light loads.

Depending on the application, shielded or unshielded inductors may be chosen. Typically, shielded inductors are used for portable applications that have to meet stringent EMI specifications.

Last but certainly not least, there are two types of inductors based on the manufacturing methods. The first type is the traditional wire-wound coil type. The newer type is a chip inductor. Chip inductors are becoming increasingly popular due to size and height advantages. Mounting speed during PCB assembly is also one of the advantages touted by chip (multilayer) inductor manufacturers. System designers have to consider some key aspects of chip inductors when selecting a switcher solution. Inductance versus dc current over temperature is a key parameter that can be significantly different between a coil and chip inductors. Figure 5 shows the cross-sectional image of a wire-wound and a chip inductor.

Referring to Figure 6, it can be seen that, in general, a coil-type inductor has a flat inductance curve over dc current and temperature until the saturation current. After that, there's a sharp roll off with current. Typically, a 10 to 20% drop occurs in ISAT at 85 ºC compared to 25 ºC .

At 25 ºC , chip inductors have a higher initial inductance value than their nominal values. The chip inductor starts rolling off in inductance as soon as current increases. Therefore, in most cases, the definition of the ISAT rating doesn't apply to chip inductors. The rms current rating that specifies temperature rise determines the current rating for chip inductors. A drop in inductance with temperature, with no dc current, is another characteristic of chip inductors.

With regards to actual inductance values, system designers must be careful to select the right inductor and follow datasheet guidelines for minimum inductance. The wrong inductor can affect stability, cause sub-harmonic oscillations, and/or reduce the switcher's output-current rating. As with the case of ceramic capacitors, designers should focus on inductance value for operating conditions rather than nominal inductor values.

How do you select the current rating of the inductor for a magnetic buck converter?

If the IRMS rating of the inductor is greater than the required output current, the easiest way is to select an ISAT rating greater than or equal to the switcher's maximum current limit. However, as we've seen for chip inductors, we must search for a minimum inductance value for stability and output-current requirements. Choosing a higher value chip inductor — for example, 3.3 µH instead of 2.2 µH— to meet inductance requirements is a losing proposition as higher-value inductors have a much sharper roll off for the same case size.

Also, differences exist among chip inductor manufacturers. For example, manufacturer A can use a low-permeability material and have a gradual change in inductance. However, such an approach needs more layers. As a result, it will have higher DCR compared to manufacturer B, who uses a high permeability material and has a sharper roll-off — but with a lower DCR.

The author's intent for this article is to present information that can be used in real-world scenarios. It also informs system designers and component procurement engineers about the data that should be requested from component manufacturers during the component selection process.

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