Getting the Most Out of Ceramic Capacitors

Although higher switching frequencies in modern dc-dc converters allow the use of lower-valued capacitors, designers continue to choose tantalum capacitors for such applications. However, the latest high-CV ceramic capacitors can do more than others in many cases. Besides meeting the performance goals, ceramics can save space and cost in your converter designs. While the potential for lowering cost is good, it comes at a price. The designer must perform a few calculations to get the most out of the ceramic capacitors.

The choice of capacitor depends on many parameters. Based on its equivalent circuit, the most important parameters are:

• Capacitance (C)
• Equivalent serial resistance (ESR)
• Equivalent serial inductance (ESL)
• Maximum effective current allowed through the capacitor (I_RIPPLE)

Many dielectric materials are available for ceramic capacitors, but the X5R dielectric in MLCC technology, by Taiyo Yuden, is probably the most interesting. While X5R provides high CV with very low ESR and ESL, the trade-off is a substantial amount of tolerance on capacitance values.

Table 1 lists the capacitors discussed in this article. Also included for comparison is a high-performance tantalum capacitor from Sanyo. (Tantalum capacitors with better performance are available; however, they're either larger or not available in SMD packages.)

Looking at the characteristics of the 10µF and 47µF X5R capacitors provided in the data sheets, you can see that temperature and the applied voltage produce a considerable variation in capacitance, which is in addition to the unit-to-unit variation allowed by the specified tolerance. These variations are depicted in Table 2, which gives the minimum capacitance values corresponding to different values of applied voltage.

The Minimum C value combines the effects of capacitance variation due to initial tolerance, temperature, and applied voltage. The main limitation of the X5R dielectric is its low value of maximum capacitance. That value becomes even lower with increasing values of applied voltage.

From this table, you can see the most important advantage of ceramic capacitors — their ESR is 10 times lower than that of tantalum types, and their ESL is five times lower. Typical ESR is the value measured from the characteristics. For safety, the maximum ESR includes a 50% margin to allow for temperature variation.

A capacitor's maximum effective current, called “ripple current” by manufacturers, is defined as the real current going through a capacitor. This current generates the ESR joule loss, which in turn causes an elevation of temperature: Pj = ESR(I²real).

Manufacturers specify a maximum ripple current to limit the temperature rise, but the amount of rise depends partly on your board. Exceeding the ripple-current rating is acceptable if your system's maximum ambient temperature is low. You must measure the temperature elevation, of course — useful information in cases with unspecified maximum ripple current.

It's now clear why ceramic capacitors support higher ripple currents — their ESR is very low. They support several amperes, which is much more than usually necessary.

Ripple Generation

It's easy to differentiate between spikes and ripples. Ripple is a variation of the output voltage at the switching frequency, caused by the ac component of current going through the capacitor. Spikes are high-frequency, low-energy damped oscillations. Note: this discussion applies only to converters operating in continuous current mode (CCM). In other words, the inductor current does not go to zero during each cycle.

You can determine a capacitor's ripple voltage by calculating the voltage generated in its equivalent circuit:

In power electronics, the capacitor placed near an inductor is called a filter capacitor, and its role is to filter the ac component of current flowing through the inductor (Figs. 1 and 2). Thanks to the inductor, the ac current seen by this capacitor is low with respect to its average current (see C_OUT in Fig. 3). Filter capacitors include the output capacitor of buck and forward converters, and the input capacitors of boost and buck-boost converters.

Calculation of ΔV_c

To calculate ripple in a capacitor, you first linearize the current and then integrate it. Next, you calculate the minimum and maximum values, and take the difference. For 0 < t < ton = αT.

The i_COUT waveform of Fig. 3 shows the shape of current through the capacitor.

Because the constant K represents a continuous voltage, it is equal to zero. This parabola is minimum when the derivative equals zero. In Fig. 3 you can see that ic(t)= 0 at t = αT/2. So,

You can easily sketch this parabolic function: vc(0) = 0; vc(αT/2) is minimal; ic(T) = 0.

For ton < t < T,

Because the constant K represents a continuous voltage, it is equal to zero. This parabola is maximum when the derivative equals zero, which occurs at t = (1-α)T/2. So,

You can easily sketch this parabolic function: vc(αT) = 0; vc((1-α)T/2) is maximum; ic(T) = 0.

Calculation of ΔV_esr

vesr(t) = ESR*i(t)

The current waveform is trapezoidal, so you can write:

Calculation of ΔV_esl

For 0 < t < ton, the trapezoidal current shifts the ripple up:

For ton < t < T,

In a similar way, the trapezoidal current shifts the ripple down.

As we see can in Fig. 3, the total ripple is equal to the sum of the two components:

C_out for Step-Down Converter

Consider a step-down converter defined as follows:

Because the current filtered by a filter capacitor is low, it is usually easy to minimize ripple voltage without recourse to an additional output filter. As you can see in Table 3, even the lower capacitance ceramic gives better performance than the big tantalum. The contribution of ESL to the total ripple is negligible, thanks to the great reductions in capacitor ESL achieved in the last 10 years. With tantalum, the main ripple component comes from ESR.

So, is a 10µF capacitor acceptable? If you consider ripple only, then it definitely is acceptable! However, in practice, it's important you take into account the dynamic performance the system requires. So now, what is the maximum speed and magnitude of current steps the converter will have to face?

If the output current is almost constant (varies less than 30% of its nominal value, for instance), then a 22µF capacitor is acceptable. However, if the output changes too rapidly, you just might find that a 100µF output capacitor is necessary. (For French Telecom, most dc-dc converters are qualified with the following dynamic load: a current step within 20µs, from 0.1Inom to 0.6Inom or from 0.5Inom to 1Inom). For cases such as this, you'll probably find that a tantalum capacitor is a good choice for your application.

Cin for Step-Up Converter

Consider a step-up converter defined as follows:

Looking at Table 4, ceramic capacitors give better performance. Because the input doesn't support a high current step, a 10µF capacitor is sufficient.

Tank Capacitor Ripple in CCM

Tank capacitors are located before or after switches (switches in the form of a transistor or diode). Such capacitors see an ac-current component higher than the average current (see current in Fig. 4 or Fig. 5). Notice that you can't remove a tank capacitor. Otherwise, the dc-dc converter would not work at all. Indeed, a tank capacitor can serve as a practical replacement for the perfect voltage source found in the theory of converters. Because the ac current seen by such capacitors is very high, their application should receive special care. Tank capacitors include the output capacitor of boost and flyback converters, and the input capacitor of buck, flyback, forward, and push-pull converters. As an example, consider the output capacitor (Cout) of a step-up converter. Iout is the dc current in the load.

Calculation of ΔV_c

Because the dc component of current is null in a capacitor, you have: Icout(t) = iD(t) — Iout (see Fig. 5). You can easily integrate the current during toff.

For ton < t < T,

and

Ic(t) = -I_OUT

gives

Calculation of ΔV_esr

Because the current is trapezoidal, we can write: ΔVesr = ESR * ΔIc

With ΔIc = Ipk and Ipk = Iout + ΔI_L/2, it becomes:

ΔV_esr = ESR* (I_OUT + ΔI_L/2)

Calculation of ΔV_esl

Let's derive the current during each phase of time:

For 0 < t < ton, the slope of current is linear and equal to ΔIL/ton:

For ton < t < T, the slope of current is null. So,

Vesl2 = 0

Finally, we get:

Cin for Step-Down Converter

Consider the same design in Table 5:

Examining Table 5, you instantly notice that the ripple voltage for a tank capacitor is more substantial than that for a filter capacitor. The reason is the large amount of ac current through a tank capacitor, which “sees” the peak value of that current. Again, even a 22µF ceramic capacitor exhibits better performance than a tantalum type. If noise injection in the source is not an issue, 10µF should be enough.

Cout of Step-Up Converter

Consider the same example looking at Table 6. The output of a step-up converter is the most difficult to filter, because it exhibits high real current, and the capacitor must support dynamic regulation.

Spikes

Spikes are high-frequency sinusoidal oscillations in the megahertz range, generated during the actuation of a transistor or diode switch (Figs. 1 through 3, on page 24). If no precaution is taken, these spikes can be much higher than the ripple. Their magnitude depends on the many parasitic elements present in the active devices and in the PCB⁴. Because these spike magnitudes can't be calculated without measuring the board's parasitic elements, they will not be discussed further.

Note that spikes are much higher in a tank capacitor than in a filter capacitor. The reason is very simple: current cannot vary instantaneously in the filter's inductor. To filter those spikes you need a high-frequency capacitor — the famous “100nF” value. In fact, that value is a bad habit from prehistoric times. You will get better performance with a 10nF X7R ceramic capacitor that exhibits a 50 MHz resonance and 0.38nH ESL.

Spike amplitudes can be reduced to an acceptable level if the layout is properly drawn, the ESL of the capacitor is low (less than 1nH), you don't forget the high frequency filtering capacitor, and (if necessary) you slow the switching time of the switches³.

Example

Let's compare a ceramic capacitor and a postcap capacitor as they're used in the design of a +5V boost converter, based on a MAX1790 IC operating at 650 kHz, as shown in Fig. 6, on page 27. As you can see in Table 7, an X5R capacitor costs less and saves pc-board area.

A Closer Look

The good performance of X5R capacitors allows you to save space and cost, especially in the case of filter capacitors. For tank capacitors, the use of ceramics would seem limited to low output power, but a closer look leads to the conclusion that ceramics are a good choice for filtering noise — when placed in parallel with the large-value tantalum or postcap capacitor used to absorb current transients. The use of ceramics is certainly growing.

The preceding material should make it possible for you to calculate noise in a switching converter. Even when an IC manufacturer provides you with a “Plug-and-Play” converter, a calculation of noise will help you in optimizing the circuit.

References

1. Wuidart, L., Topologies for Switched-Mode Power Supplies; STM application note.

2. Ferrieux et Forest, Alimentation à découpage, Edition Dunod.

3. Input and Output Noise in Buck Converters, application note available on Maxim Web site.

4. Lenoir, Eric, Layout Considerations for Nonisolated DC-DC Converters, application note available on Maxim Web site.

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