**Inductors in automotive DC-DC converter applications need to be carefully selected to give the right combination of cost, quality, and electrical performance. In this article, Smail Haddadi, Field Applications Engineer, offers guidance on how to calculate the specifications needed and which trade-offs are possible.**

## Buck or Buck-Boost Switching Regulators

There are approximately 80 different electronic applications in automotive electronics which each need their own stabilized power rail, derived from the battery voltage. This can be done with large, lossy ‘linear’ regulators but the efficient approach is to use a ‘buck’ or ‘buck-boost’ switching regulator as this can be 90+ percent efficient and compact. Switching regulators of this type require an inductor and selecting the correct part can sometimes seem a little mysterious as the calculations required originated in 19^{th}-century magnetics theory. Designers would like to see an equation into which they can ‘plug-in’ their performance parameters and get the ‘right’ inductance and current rating so that they can simply select from a catalog of parts. However, it is not that simple: some assumptions have to be made, trade-offs considered and often multiple design iterations worked through. Even then, the perfect part may not be available as standard with the design needing re-work to see how an off-the-shelf inductor might fit.

## Buck Regulator

Let’s consider the buck regulator (Figure 1) where V_{in} is the battery voltage, V_{out }is a lower voltage processor power rail and SW1 and SW2 alternately open and close. The simple transfer function equation is V_{out} = V_{in}.T_{on}/(T_{on} + T_{off}) where T_{on} is when SW1 is closed and T_{off }is when it is open. The inductor does not figure in this equation, so what effect does it have? In simple terms, the inductor needs to store enough energy while SW1 is on to allow the output to be maintained while it is off. Energy stored can be calculated and equated with the energy required but practically there are other things to be considered first. The alternate switching of SW1 and SW2 causes current to ramp up and down in the inductor which forms a triangular ‘ripple current’ on the average DC value. The ripple current is then sunk into C1 which releases it when the SW1 is off. The current through the ESR of the capacitor produces output voltage ripple. If this is a critical parameter, and the capacitor and its ESR are fixed by size or cost, this might set the ripple current and inductor value.

**Figure 1. **Basic buck converter

## Modern Buck Converters

Often choosing the capacitor offers flexibility. This means that if the ESR is low, the ripple current can be high. However, this causes problems of its own. For example, if the ‘trough’ of the ripple touches zero at some light load and SW2 is a diode, as it often is, it stops conduction for part of the cycle and the converter enters ‘discontinuous conduction’ mode. In this mode, the transfer function changes and becomes more difficult to stabilize optimally. Modern buck converters normally use synchronous rectification where SW2 is MOSEFT and can conduct drain current in both directions when it is on. This means the inductor can swing negative and maintain continuous conduction (Figure 2).

**Figure 2.** Conduction modes of a buck converter

The peak-to-peak ripple current ΔI can be allowed to be high in this situation and it is set by the inductance value according to ΔI = ET/L. E is the inductor voltage applied for time T and it is easiest to consider what happens in the off time for SW1, Toff, when E is the output voltage. ΔI is maximum at this point because T_{off} is maximum with the highest input voltage from the transfer function. For example: for a maximum battery voltage of 18 V, an output of 3.3 V, a peak-to-peak ripple of 1 A and a switching frequency of 500 kHz, L = 5.4 µH. This assumes that there is no voltage drop across SW1 and SW2. The load current has not figured in this calculation.

A brief search of the catalogs might show multiple parts with a current rating that matches the desired load. However, it is important to remember that the ripple current is superimposed on the DC value which means that in the example above, the inductor current will actually peak at 0.5 A above the load current. There are different ways to rate inductors for current: either as a thermal or magnetic saturation limit. Thermally limited inductors are often rated for a given temperature rise, typically 40 ^{o}C and can be run at higher currents if cooling is available. Saturation must be avoided at the peak current and the limit reduces with temperature. It is necessary to carefully examine the inductor data sheet curves to check whether it is thermally or saturation limited.

Inductor loss is also an important consideration. Losses are mostly ohmic and can be calculated when ripple current is low. At high ripple levels, core losses start to predominate and these are difficult to predict as they depend on waveform shape as well as frequency and temperature. The real test in on a prototype, as this might show that lower ripple currents are necessary for best overall efficiency. This would require more inductance and perhaps a higher DC resistance – it is an iterative process.

## High-Performance HA66 Series

A good starting point would be the high-performance HA66 series from TT electronics (Figure 3). It has a range including 5.3 µH part rated for saturation at 2.5 A, allowing a load of 2 A with the +/- 0.5 A ripple. The parts are ideal for automotive applications, with AECQ-200 certification from a company with a TS-16949 approved quality system.

**Figure 3. **The HA66 series of inductors from TT Electronics

**References**

- http://www.ttelectronics.com

This information has been sourced, reviewed and adapted from materials provided by TT Electronics plc.

For more information on this source, please visit TT Electronics plc.