The Application of SMD Inductors in Low-Power Power Supplies

Ultra-low power or ultra-high power switching power supplies are not as easy to select as conventional switching power supplies. Currently, standard inductors are manufactured to suit mainstream designs and may not adequately meet the requirements of some specialized applications.

A key challenge lies in the selection of inductors for ultra-high efficiency Buck circuits. A typical example is small-sized battery-powered devices requiring long operation times. In such circuits, engineers often face the conflicting demands between battery capacity (cost and size) and the Buck converter’s size and efficiency.

To reduce the size of the switching power supply, it is ideal to choose the highest possible switching frequency. However, switching losses and the losses in the output inductor increase as the switching frequency rises, which can become the main factors limiting efficiency. These conflicting demands significantly increase the complexity of circuit design.

Inductor Requirements for Buck Circuits:

For engineers, ferromagnetic components (inductors) are often the first nonlinear devices they encounter. However, it is difficult to predict inductor losses at high frequencies based on manufacturer data. This is because manufacturers typically only provide parameters such as open-circuit inductance, operating current, saturation current, DC resistance, and self-resonant frequency. For most switching power supply designs, these parameters are sufficient, and selecting a suitable inductor based on them is relatively easy. However, for ultra-low current, ultra-high frequency switching power supplies, the nonlinear parameters of the magnetic core are very frequency-sensitive. Moreover, frequency also determines the coil losses.

In ordinary switching power supplies, core losses are almost negligible compared to DC I²R losses. Therefore, except for the 'self-resonant frequency' (which relates to frequency), inductors typically lack other frequency-dependent parameters. However, in ultra-low power, ultra-high frequency systems (such as battery-powered devices), these high-frequency losses (core losses and coil losses) usually far exceed the DC losses.

Magnetic dipoles with approximately similar directions and close proximity influence each other and form “alliances.” Although these dipoles are physically separated by binding material, their magnetic fields are interconnected. These “alliances” are called “units.” The boundary of a unit is the dividing surface between the internal alliance and external dipoles. Dipoles outside this boundary find it difficult to join the alliance inside. This boundary is known as the “unit wall.” This model is often used to explain many fundamental parameters of magnetic cores.

When a magnetic field is applied to the core (i.e., current flows through the coil), units with different directions interact. When the applied current generates a sufficiently strong external magnetic field, units near the coil experience a stronger magnetic field and join together first, forming larger units. Units deeper inside the core remain unaffected initially. Under the influence of the magnetic field, the unit wall between joined and unaffected units continuously moves toward the core center. If the coil current does not reverse or stop, the entire core eventually becomes unified. This unification of all magnetic dipoles in the core is called “saturation.” The B-H hysteresis loop provided by manufacturers shows the process from initial magnetization to saturation. If the current decreases, units tend to return to their initial free state, but some remain joined. This incomplete transition is known as remanence (visible in the hysteresis loop). Remanence causes stress during the next unit joining, resulting in core losses.

The hysteresis loss per cycle is given by:

WH=mH×∮dI

where the integral represents the area within the hysteresis loop from initial inductance to peak inductance and back. The energy loss at switching frequency 

PH=F×mH×∮dI

While calculating these AC losses seems straightforward, it becomes very complex at high frequencies and moderate flux densities. Every circuit includes parameters that influence core loss but are difficult to quantify, such as parasitic capacitances, PCB layout, drive voltage, pulse width, load conditions, input/output voltages, etc. Unfortunately, core loss is highly sensitive to these factors.

Each core material has a nonlinear conductivity that causes loss. This conductivity induces “eddy currents” within the core under an applied magnetic field, leading to losses. At constant flux, core losses approximately scale with frequency raised to the power ????,where the exponent ???? varies depending on core material and manufacturing processes. Inductor manufacturers often fit core loss curves with empirical formulas.

The magnetic flux density ???? in a forward-switching circuit can be expressed as:

Bpk=4×A×N×fEavg

 where:

$B_{pk}$Bpk = peak AC flux density (Tesla)

Eavg = average AC voltage per half cycle

A = core cross-sectional area (square meters)

N = number of coil turns

$f$$f$ = switching frequency (Hz)

General Overview of Magnetic Core Inductors and Loss Testing:

Typically, manufacturers of magnetic materials provide the rated inductance coefficient $A_L$ of the core. The inductance $L$ can be easily calculated using the formula:

L=N2AL

whereN$N$ is the number of coil turns, and ALAL is proportional to the doping level of the magnetic material as well as the ratio of the core’s cross-sectional area to the magnetic path length.

The total core loss equals the core volume multiplied by the peak flux density $B_{pk}$ and the frequency, measured in watts per cubic meter (W/m³). Core losses depend heavily on the core material and manufacturing process.

Core Loss Testing Equipment and Methods:The most effective way to test inductor performance is to place the inductor in the final switching power supply circuit and measure the circuit efficiency. However, this requires the final circuit, making it inconvenient for early-stage testing.

A simpler testing method exists to evaluate core loss at the design stage (at the intended switching frequency):

• The core is placed in series with a low-loss dielectric capacitor (e.g., silver-coated mica).
  
• This forms a series resonant circuit driven by a resonant mode signal. The capacitor’s value is chosen to resonate at the inductor’s switching frequency.
  
• A network analyzer (or alternatively, a signal generator with an RF voltmeter or power meter) measures the test parameters.
  

At resonance, a low-loss magnetic core behaves like an $L-C$ resonant circuit, and losses can be modeled as a pure resistive element (including coil and core losses).

In the test setup, terminals A and R connect to 50Ω resistors, making the open circuit (excluding the inductor) equivalent to an oscillator with a 150Ω load. The network analyzer shows:

20×log(RA)=20×log(15050)=−9.54 dB

Typical test parameters include a 2000 pF capacitor, inductance around 2.5–2.8 mH, and a test frequency of 1 kHz. Note that the permeability of magnetic materials is a nonlinear frequency-dependent function, so results may differ at higher frequencies.

Experimental Data on Core Losses:

• A single-layer Fe-Ni-Mo laminated core with relative permeability of 125 mH, wound with 16 turns of 10/44 multi-strand wire.
  
• A two-layer Ni-Fe-Mo powdered core with doping level 250, wound with 8 turns of 10/44 multi-strand wire.
  

Measured inductances: 2.75 mH and 2.78 mH respectively. Although the first coil has twice the number of turns, its cross-sectional area is half that of the second coil. Both exhibit high losses under the same signal amplitude, with equivalent resistances of 360Ω and 300Ω respectively.

In contrast, another inductor (2.5 mH), using Micrometals’ very low doping material (Carbonyl T25-6, relative permeability 8.5) with 34 turns of 10/44 multi-strand wire, shows an equivalent loss resistance of only 22,000Ω under the same test conditions, indicating significantly lower losses.

Inductor Selection for Low-Power Switching Supplies:

Selecting inductors for low-power, high-efficiency switching supplies requires special attention. Standard device datasheets and selection tables often lack sufficient detail. Most inductors use ferrite cores (non-low-loss materials), which are gradually being phased out in low-power, high-efficiency applications.

A relatively simple loss-testing setup allows designers to compare inductors’ performance at the intended switching frequency before final selection.

To achieve low-loss inductors, select materials with low doping levels to reduce magnetic field strength parameter $B$, choose low-loss cores, and consider using multi-strand wires. It is also advisable to use magnetic components recommended by chip manufacturers or consult with magnetic material experts to meet specific design needs.