Choose the best inductor, capacitor for DC/DC converters in portables
Keywords:power dissipation? DC/DC converters? regulator? switching converter? output capacitors?
By Christophe Vaucourt
Texas Instruments
As the form factor of wireless handsets, PDAs and other portable electronics continue to shrink while their complexity level continues to grow, design engineers face an increasing number of problems with battery life, board space and heat or power dissipation.
Efficiency is often the main objective when using DC/DC converters. Many design requirements involve converting the battery voltage to a low supply voltage. Although a linear regulator can be used for this, it cannot achieve the efficiency of switching regulator-based designs. This article will cover some of the most common issues designers have to face when trading off solution size, performance and cost.
Large vs. small signal response
Switching converters are based on fairly complex regulation schemes to maintain high efficiency during heavy and light loads. Modern CPU core supplies require a fast and friendly, large-signal response of the regulator. For instance, when a processor is switching from idle to full speed operation mode, the current drawn by the core can rise very fast from tens of microamps to several hundred milliamps.
As the load conditions change, the loop rapidly responds to new requirements to keep voltage within the regulation limits. The amount and rate of load change determines whether the loop response is called a large-signal response or a small-signal response. We define the small-signal parameters based on a steady-state operating point. Consequently, variations below 10 percent of a steady-state operating point are considered as a small-signal variation.
In practice, the error amplifier is in slew limit and it does not control the loop because the load transient is occurring faster than the error amplifier can respond, so the output capacitors satisfy the transient current until the inductor current can "catch up."
Large-signal response temporarily takes the loop out of operation. However, the loop must respond gracefully going into and out of large-signal response. The wider the loop bandwidth, the faster the load transient the loop can respond to.
Figure 1: Inductor selection. |
Even though the regulation loop, from a small signal prospective, may show enough gain and phase margin, the switching converter can still exhibit instability and ringing during line or load transients. When selecting external components power supply designers need to be aware of these limitations.
Inductor selection
The basic buck regulator in Figure 1 will be used to illustrate the inductor selection.
For most TPS6220x applications, the value of the inductor will be in the range of 4.7?H to 10?H. Its value is chosen based on the desired ripple current. Usually, it is recommended to operate with a ripple of less than 20 percent of the average inductor current. Higher V_{IN} or V_{OUT} also increases the ripple current as shown in Equation 1 below. Of course the inductor must be able to handle the peak switching current without saturating the core, which translates to a loss of inductance.
At the expense of higher output voltage ripple, small value inductors result in a higher output current slew rate, improving the load transient response of the converter. Large values inductors lower the ripple current and reduce the core magnetic hysteresis losses.
The total coil losses can be combined into the loss resistance (Rs), which is connected in series with the ideal inductance (Ls). This is resulting in the simplified equivalent circuit shown Figure 2 below:
Even though the losses in Rs are frequency dependent, the DC resistance (RDC) is always defined in datasheet specifications. This is dependent on the wire material used or the construction type of SMD inductors and is found at room temperature by a simple resistance measurement.
The size of the DC resistance RDC directly influences the increase in temperature of the coil. Prolonged exposure to levels exceeding the current rating should thus be avoided.
The total losses of the coil consist of both the losses in the DC resistance RDC and the following frequency dependent components:
- The losses in the core material (magnetic hysteresis loss, eddy-current loss)
- Additional losses in the conductor from the skin effect (current displacement at high frequencies)
- Magnetic field losses of the neighboring windings (proximity effect)
- Radiation losses
All these loss components can be combined into a series loss resistance (Rs). This loss resistance is primarily responsible for defining the quality of the inductor. Unfortunately, mathematical determination of the loss resistance Rs is impractical. Thus, inductors are usually measured over the entire frequency range with an impedance analyzer. This measurement provides the individual components XL(f), Rs(f) and Z(f).
The ratio of reactance (XL) to total resistance (Rs) of an induction coil is known as the quality factor Q, shown in Equation 2 above. The quality factor is defined as a quality characteristic of the inductor. The larger the losses are, the poorer the inductors acts as an energy storage element.
The quality-frequency graph of Figure 3a and Figure 3bhelps designers select the best inductor construction for the particular application. Based on the measurements results, the operating range with the smallest losses (highest Q) can be defined up to the quality turning point. If the inductor is used at higher frequencies, the losses increase rapidly (Q decreasing).
Figure 3a (left) shows Q vs frequency in Hz. Figure 3b (right)Rs () vs. frequency (Hz). |
A properly designed inductor will degrade efficiency by only a small percentage. Different core materials and shapes will change the size/current and price/current relationship of an inductor. Shielded inductors in ferrite material are small and don?t radiate much energy. The choice of which style inductor to use often depends on the price vs. size requirements and if any radiated field/EMI requirements.
Figure 4: TPS62204 (1.6V) efficiency vs. load current vs. input voltage. |
Output capacitor
Removing output capacitors saves money and board space. The basic selection of the output capacitor is based on the ripple current and ripple voltage as well as on loop stability considerations.
The effective series resistance (ESR) of the output capacitor and the inductor value directly affect the output ripple voltage. The output ripple voltage can be easily estimated based on the inductor ripple current and output capacitor series resistance (ESR).
Thus, a capacitor with the lowest possible ESR should be selected. For example, 4.7 to 10?F capacitors in X5R/X7R technology show an ESR value in the range of 10m. Smaller capacitors are acceptable for light loads (or in applications where ripple is not a concern).
The TI control loop architecture allows designers to use their desired output capacitors and compensate the control loop for optimum transient response and loop stability. The internal compensation works best with one set of operating conditions and is sensitive to output capacitor characteristics.
Figure 5: TPS62204 load transient performance. |
The TPS6220x series of step-down converter has internal loop compensation. Due to this, the external L-C filter has to be selected to work with the internal compensation. For this device, the internal compensation is optimized for an LC corner frequency of 16kHz, that is 10?H inductor and 10?F output capacitor. As a general rule of thumb, the product L*C should not move over a wide range when selecting a different output filter. This is important when selecting smaller inductor or capacitor values that move the corner frequency to higher frequencies.
During the time between the application of the load transient and the turn-on of the P-MOSFET, the output capacitor must supply all of the current required by the load. Current supplied by the output capacitor results in a voltage drop across the ESR that subtracts from the output voltage. The lower the ESR, the lower the voltage loss when the output capacitor supplies load current. To minimize the solution size and to improve the load transient behavior of the TPS62200 converter, it is recommended to operate with 4.7?H inductor and 22?F output capacitor.
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