Switched-mode power supplies are becoming ever more widespread. The semiconductor manufacturers have made their contribution, offering a wide range these integrated circuits with simplified circuit design. Care must be taken in the selection of the appropriate power inductor storage choke to fully utilize the advantages of switching regulators.

This article is split in two chapters:

**calculation of power inductors****example of high current inductor types**

further read: **Selection of the Storage Inductors for DC/DC Converters**

**Power Inductors Calculations**

The selection of cores and windings of storage chokes are optimized for use in switching converters and DC-DC converters.

Leading manufacturers of storage chokes following recommendations from various switching converter IC manufacturers, e.g. National Semiconductor, Linear Technology, STMicroelectronics, Texas Instruments, Exar, Diodes, MPS, ON Semiconductor, Semtech, Maxim and a special customized solutions can be found in their reference design guidelines.

**Toroidal Core Types**

Toroidal storage chokes are ideal from the EMC perspective: The magnetic field lines mainly pass through the core. The stray field and associated coupling in neighboring conductor tracks or components remain small.

In the field of switching converters, storage chokes serve to buffer electrical energy and, at the same time, to smooth the output current. The energy stored in the core in this process is:

To enable high energy storage and to minimize the resulting core losses, the toroidal core volume is divided into many electrically isolated regions. The iron powder used in our storage chokes therefore has three-dimensional, uniformly distributed, microscopic air gaps, which prevent eddy-current losses.

The disadvantage of reduced permeability is balanced by greater maximum energy storage and lower losses. Furthermore, these cores are extremely well suited for use in applications with high DC premagnetization.

**Data book specifications**

*Open-circuit inductance L _{0}:*

If the inductor is operated without DC premagnetization or with only a small AC current, the open-circuit inductance L_{0} results.This value may be measured with sufficiently sensitive inductance measuring equipment for small AC voltages e.g. 0.1โ0.5 V and a fixed measuring frequency between 1 kHz and 100 kHz, depending on the inductance value.

*Inductance rating L _{N}:*

In addition to the small AC voltage amplitude, the specified DC current is superimposed and the resulting inductance measured.

*Current rating I _{N}:*

The DC current, for which the inductance and wire thickness are specified and whose specifications are optimized. As shown in graph on Figure 2., inductance only saturates with a much larger current.

*DC resistance DCR:*

The windings resistance value is measured with an ohmmeter at an ambient temperature of +25 ยฐC.The test current for resistance measurement is a small DC current, which does not lead to a significant temperature increase in the wire. As values in the milliohm range are measured here, a 4-wire measurement must be made to minimize measurement errors.

*Magnetic field energy E:*

The energy, for which the core data and windings of the coil is optimized. This is specified in microjoules.The following simple and practically proven formulae can be used for dimensioning a storage choke. A brief extract from the extensive core material program and the following table should provide an overview of the choke dimensioning process. Depending on the application, further specifications from the core material data spectrum may be necessary.

*Iron core material data:*

The table 1. shows an overview of the most commonly used materials and their applications.

*Operating temperature:*

The operating temperature of the iron powder core may be from โ55 ยฐC to +125 ยฐC. Prolonged core operation above +75 ยฐC however results in increased losses.

*Insulation voltage:*

The protective coating of the toroidal core uniquely identifies the core material and serves to protect against environmental effects and provides electrical isolation from the windings. Epoxy resin coatings are used and an insulation dielectric strength of 500 VDC is achieved as standard. Higher insulation voltages can also be offered.

A_{L} value: For every size of core an A_{L} value is specified to simply calculate the winding turns for the required choke; the tolerance is ยฑ10%.

The standard means of measuring the A_{L} value is at B = 1 mT and f = 10 kHz.

- d
_{a}= outer diameter - d
_{i}= inner diameter - h = height
- l = effective magnetic length
- A = effective magnetic cross-sectional area
- V = effective magnetic volume l
- W = winding wire length for 1 turn

*Storage Choke Calculation:*

*Storage Choke Calculation:*

The following demonstrates how a storage choke can be calculated for a switching converter application:

Example: switching converter (step-down controller โ storage choke)

**Requirements:**

Inductance rating L_{N} = 100 ยตH Current rating (DC) I_{N} = 1 A Peak current through the inductance I_{max} = 1.5 A Ripple current = 20% of I_{max} = 0.3 A (see Chapter III/Applications) Switching frequency f = 52 kHz

A maximum AC flux density B_{AC} = 0.05 T is recommended for iron powder cores (to ensure low core losses). Also the inductance should be selected so the ripple current does not exceed 20%โ30% of the maximum current.

** Step 1 : Choice of the core material** and the necessary core volume (V). As the switching frequency is just 50 kHz, we firstly select the material 3W7538 with ยต

_{r}= 75.

Selected core: 3W7538, as switching frequency < 70 kHz; core no. 13 d_{a} = 12.7 mm; d_{i} = 7.7 mm; h = 4.83 mm

Magnetic data: l = 3.19 cm; A = 0.112 cm2; V = 0.358 cm3 A_{L} value: 33 nH/N^{2}

**Step 2**:** Required winding turns**

- L in nH
- A
_{L}value in nH/N^{2}

The final number of winding turns must be increased as a result of current dependent permeability. The correction factor for the A_{L} value is determined from the โeffective permeability against DC premagnetizationโ graph (see Figure 3.).

At H = 1724 A/m on the graph in Figure 3. โ Effective permeability with DC premagnetization = 80% of the initial permeability.

To be certain that the full inductance rating of 100ยตH exists with a DC current of 1A, the final number of winding turns is calculated as:

** Step 3**:

**Determination of the DC resistance**

The wire diameter can be ascertained from the relevant wire tables for the required current of 1A, e.g. AWG 22 (d = 0.6 mm). This limits the self-heating of the wire to less than +10ยฐC.

The DC resistance of the windings is given by:

*Step 4*: Check for max. AC field flux density

- Inductance rating L in H
- Ripple current ฮI in A
- Core cross-sectional area A in cm
^{2} - Winding turns N
- Peak voltage of the choke U
_{s}in V (during โtโ) - Duration of peak voltage t in s

*Step 5*: Calculation of core losses

The losses in the core material may be calculated from the following formula:

- Frequency f in Hz
- AC field flux density B in mT
- Core losses P
_{C}in mW/cm^{3}

For our examples this leads to:

The total core losses of the selected core are:

The losses in the windings equal:

The total losses of the storage choke are low at around 370mW and the choke calculated is well suited for the application.

**High Current Inductor Types**

**SMD NiZn Ferrite Core Storage Choke**

SMD storage chokes with highly dynamic and low loss NiZn ferrite cores are suitable as chokes in switching control applications up to a clock frequency of approx. 10MHz and offer high current loading capacity and low DC resistances.

There are a multitude of construction types available for the different types of application:

- Magnetically shielded series
- Unshielded versions series

**Data book specifications**

*Inductance L: *Different measurement conditions apply for the different construction series. The inductance is stated at a certain test frequency and measurement voltage (see data sheet).

*Current rating IN:* The current rating of the inductor is specified as the DC current at which inductor exceeds the permitted tolerance limits (DL) or the self generated heating (DT) exceeds a certain limit. The smaller of the currents defined by the two conditions is termed the current rating of the inductor. This is how ever not the saturation current, which is higher than the current rating.

*DC resistance DCR: *The windings resistance value is measured with an ohmmeter at an ambient temperature of +20 ยฐC. The test current for resistance measurement is a small DC current, which does not lead to a significant temperature increase in the wire. As values in the milliohm range are measured here, a 4-wire measurement must be made to minimize measurement errors.

*Operating temperature: *The ambient temperature when operating the SMD NiZn series of storage chokes at full current rating load should generally range from โ40 ยฐC to +85 ยฐC. The self-heating of the component must be taken into account at higher ambient temperatures in order that the permissible solder joint temperature is not exceeded or the wire insulation damaged. The wire used can withstand a temperature of up to +150 ยฐC. The ferrite core itself may be used over a far greater temperature range (approx. โ50 ยฐC to +250 ยฐC [Curie temperature]). However, in this case, the tolerance limits of the inductor may be exceeded due to the temperature dependence of permeability.

Operating temperature = ambient temperature + self-heating < +125 ยบC

The above curve on Figure 5. assumes that self-heating is permissible up to a maximum temperature sum (component + ambient temperature) of +125 ยฐC. The current must be reduced above an ambient temperature of +85 ยฐC. The curve below is intended for critical applications, in which the coil itself should only generate a small amount of self-heating.

*Insulation resistance:* The insulation resistance between windings and coil core is more than 100 Mโฆ for a test voltage of 500 V_{DC}<sub>DC</sub>.

*Saturation current I _{sat}:* The saturation current is the DC current at which the zero current inductance is reduced by a certain percentage.

The percentage of inductance decrease is however not standardised and can be defined differently for each package type. In datasheets โ and especially when comparing data from different manufacturers โ very close attention must be paid to the definition point. A printout of the measurement curve โInductance versus DC premagnetizationโ is better still. Here the user can, for example, check in detail how the inductor behaves in the case of overload or at the moment it switches on. An example for a standardised curve is shown in Figure 6.

*Volt-ยตsec product: *As a result of their effective magnetic area A_{eff}, storage chokes can only be driven to a maximum value โ the so-called Volt-ยตsec product. The following calculation rule applies for the step-down controller to determine the necessary Vยตsec product of storage chokes:

- E
_{t}= V-ยตsec - U
_{in(max)}the maximum input voltage in Volts - U
_{out}the output voltage of the controller - f the switching frequency in Hz.

With increasing switching frequency, the necessary Vยตsec product of the storage choke becomes lower; however, with increasing input voltage it becomes higher. This relationship is again illustrated in Figure 2.48 below.

**Practical tips:**

For some types in the SMD NiZn SMD chokes manufacturers also provide Vยตsec specification in their datasheets. If this information is missing, it can be read off from the measurement curve โInductance versus DC current premagnetizationโ. Here you locate the inductance plateau where you read off the associated current and residual inductance values and calculate the Vยตsec product as follows:

- L
_{res}in ยตH - I
_{max}in A.

**Ferrite storage chokes**

For ferrites, the saturation curve shows a very steep decline beyond a certain DC current value (โ**hard saturation**โ). For this reason it is recommended to reduce the Vยตsec product calculated in this way and therefore to then optimise inductor selection.

**Iron powder core storage chokes**, Superflux, WE-PERM etc. have a constant decrease in inductance due to the DC-premagnetization (soft saturation). As a rule:

**NiZn storage choke core material parameters**

The NiZn (WE-PD) core material parameters are described by the following power loss formula:

The corresponding curve is shown in Figure 8.

**Power Loss and Temperature Increase in the Component**

Now the power loss can be approximately determined, the question arises of the temperature rise of the component in operation. Measurement curves can be generated for the rise in temperature of the components with DC currents. Here the questions are to be resolved:

**How was the component measured?**

- mounted on a PCB with a lot of copper (= cooling element!)
**OR** - only the component via a thin and poor heat-conducting connection

**After what time was the temperature read off from the component **(thermal time constant !)

The following approximation formulas can be useful in the design phase; however they do not obviate measurement under real operating conditions. Determination of total power loss in the storage choke:

a) Copper losses:

b) Core material losses from empirical formulas

This results in the total power loss (without further losses such as the skin effect etc. โฆ):

**Temperature increase in the component (large surface)**

- Ptot in (W)
- surface area A in (mm2)

**NiZn Power Ferrite Core Double Chokes**

NiZn power ferrite core double chokes (Figure 9.) with two separate windings expand the standard spectrum of storage chokes with more features.

**Features:**

Two separate windings on a common ferrite core

- Available in a 1 : 1 winding (standard), but also in other winding ratios (customer-specific)
- Bifilar winding for minimal stray inductance / high coupling factor โข (k ~ 0.985 โฆ 0.990) or separate layer winding with increased leakage inductance
- Operating voltage up to 80V
_{DC} - Isolation voltage 100V
_{DC}max

**Applications:**

- SEPIC switching controllers (functional principle โ see Chapter III/7.4)
- CUK switching controller (switching controller with negative output voltage)
- Switching controllers with second, unregulated output voltage (auxiliary voltage)

**Operating temperature:**

The ambient temperature of double choke under full rated current load is usually between โ40 ยฐC and +85 ยฐC. The self-heating of the component must be taken into account at higher ambient temperatures in order that the permissible solder joint temperature is not exceeded or the wire insulation damaged.

The wire used can withstand a temperature of up to +150 ยฐC. The ferrite core itself may be used over a far greater temperature range (approx. โ50 ยฐC to +250 ยฐC [Curie temperature]). However, in this case, the inductance tolerance limits may be exceeded due to the temperature dependence of permeability.

**Electrical characteristics**

*Rated current: *The self-heating for the pair of windings passing maximum current should not sum to more than +40ยฐC. This is a conservative number, datasheet specification may differ per type and manufacturer.

Rated current is determined for each winding, which passes current on its own, leading to a temperature increase of up to +20 ยฐC and is specified as IN1 and IN2 respectively. If both windings pass their rated current at the same time, this leads to self-heating totaling +40 ยฐC.

*DC resistance:* Correspondingly, the specification for the winding resistance of the two individual windings is found from individual measurements. Attention: Please compare the datasheet specifications carefully โ often the parallel configuration of the two windings is found in the literature as rated current / DC resistance, which suggests a higher rated current and lower DC resistance. In practice this is of course, not the application for this series of chokes!

*Saturation current: *In the case of the double choke with the same inductance, it is sufficient if just one of the windings carries the saturation current. The second winding is inevitably reduced in its inductance. The value is identical for the same inductance; the saturation current per winding is specified for dissimilar inductance values.

**TPC โTiny Power Chokeโ SMD storage chokes**

TPC โTiny Power Chokeโ of storage chokes (Figure 10.) is usually for applications for which the packing density and the package height is important. This design enable to produce the smallest wire-wound inductors in dimensions such as 2.8 x 2.8 x 1.0 mm.

These chokes are mostly used for switching controllers that have several outputs integrated in one IC, e.g. LTC3544B. (Figure 11.) This IC has 4 outputs at which different voltages, output currents and switching frequencies are adjustable.

The core material used is typically NiZn and is therefore suitable for switching frequencies up to 10 MHz. The saturation current is defined as a โ35% inductance drop in relation to the zero current inductance, which is usually typical for inductance in this small package. Magnetically shielded versions as on Figure 10. are suitable for switching controllers for example in mobile applications.

**SMD High-Current Inductors**

Laptop computers and motherboards of modern computers are equipped with processors, whose clock frequencies may be 1 GHz or more. Processor manufacturers rely on low supply voltages in order to maintain losses in integrated circuits within tolerable limits and to attain the required switching speeds. These lie between 1 โฆ 3.3 Volts depending on the processor generation.

Components require large currents at the same time. Current inputs of up to 60A per processor are not a rarity and cannot be handled by well known switching regulators. The so-called multiphase switching converters fulfill the intelligent power management concept required. Because of the high switching frequency and the output current requirements, one needs only small inductance with high current capability and low losses. SMD high-current inductors are suitable for these applications.

The core material used for high current inductors may require high-purity alloy of various types of iron powders, which shows significantly lower core losses than conventional iron powder cores.

*Thermal aging: *Thermal aging can lead to the destruction of the organic binder used, especially at high operating temperatures with standard iron powder material. A thermal avalanche effect can consequently occur, which may finally destroy the core material. For standard iron powder materials and those not thermally treated for reasons of their production process, the rule of thumb applies that the maximum temperature of +125 ยฐC measured at the component should not be exceeded for a prolonged period. Nevertheless, modern materials with practically no thermal aging are now also available by leading manufacturers.

The core material of high current inductors can withstand high temperatures up to +200ยฐC or even higher.

* Flat wire types. *High current inductors can use a rectangular flat wire, which proves to be a major advantage over conventional round wire designs in terms of AC resistance loss. A flat wire (Figure 13.) inside the choke is used in place of the conventional round wire.

Flat wire windings offer the following advantages:

Large wire surface โ thus low high-frequency losses (skin effect)

- Low winding capacity โ hence high self-resonant frequency
- Low DC resistance โ thus low self-heating at high prolonged currents
- High packing density and therefore smaller component size than comparable chokes with round wire (Figure 2.57)
- High operating temperature up to max. +150 ยฐC

Through the combination of low-loss core material and flat wire windings inside the core, achievable performance of SMD high-current inductors can be:

- Small SMD component size such as 6.6 x 7.3 mm2, 10.5 x 10.0 mm2 or 13.5 x 12.8 mm2 with a height of 3.4 mm to max. 4.9 mm.
- Open-circuit inductance L
_{0}, tested at 100 MHz with 0.25 VAC - Inductance rating L
_{N}at current rating I_{N}and self-heating < +50 ยฐC - Min. inductance at max. current I
_{max}and self-heating < +100 ยฐC - Min. DC windings resistance DCR
_{max}at Ta = +25 ยฐC

Figure 15. shows the typical behavior of SMD high-current inductor 0.82 ยตH choke 13.2 x 12.8 x 6.2 mm.

The component has an inductance of 0.65 ยตH at the specified rated current of 27 A and demonstrates typical self-heating of +50 ยฐC. The inductance is very stable under current load; the limiting factor is the self-heating of the component. Even at a current load of 50 A the inductance does not drop more than 30% from the open-circuit inductance. The self-heating is well over +100 ยฐC, however.

Flat wire, low core loss inductors represents a highly dynamic and robust types of storage chokes, especially suited for use in high-current switching converters and multiphase or polyphase converters. Additional application areas are in high-current interference suppression chokes and as a replacement for rod core chokes.

**Radio Interference Suppression Choke**

Radio interference suppression chokes use usually iron powder toroidal cores with a very low stray field. High current loading capacity is achieved through high saturation magnetization. The useable maximum upper frequency range of this component extends from a few MHz to approx. 30 MHz depending on the type.

The impedance-phase curve against frequency of a typical toroidal core choke is shown in Figures 16. and 17.

It may be seen from Figure 17. that the resonant frequency is at 4.1 MHz. Above 4.1 MHz the capacitive character of the choke predominates, at 30 MHz the impedance has fallen to approx. 200 โฆ. The impedance is almost linear (Figure 16.) up to the resonant frequency of 4.1 MHz.

Due to the frequency dependence of complex permeability, calculations are only feasible in limited frequency bandwidths and sufficiently far (in the linear range) below the resonant frequency. Figure 18. shows the equivalent circuit of the choke in the 25 kHz to 1 MHz range, Figure 19. the equivalent circuit in the 1 MHz to 5 MHz range. The values were found using an impedance analyzer, calculating on the basis of the componentsโ equivalent circuit. Due to high non-linearity, the equivalent circuit can be simulated over a wide frequency range with just 3 components.

From the measurement curves impedance and phase an increase in eddy-current losses and a decrease in the complex permeability can be seen.

the impedance can be calculated as a function of frequency. The broken line in Figures 18. and 19. are the simulated curves with the values given by the equivalent circuits. It shows that without considering the complex permeability and its frequency dependence, the calculation can be performed with limited accuracy.

**Practical tip:**

Here another word on the saturation of the ferrite ring: The effective core cross-sectional area is inversely proportional to the saturation current and proportional to the impedance. This means that wherever possible, the larger core cross-section area should be chosen.

**Metal Composite Inductors**

Latest metal composite inductors (Figure 20.) come with a remarkably higher energy density compared to the ferrite inductors. This leads to 30% โ 50% smaller case sizes which, for example, serves the trend for downsizing high current ECU power circuits. Furthermore, smaller case sizes also have the pleasant side-effect of being less prone to get damaged in harsh or vibrating environments. A true plus in terms of long term reliability.

**DC Bias Characteristics**

Excellent magnetic saturation characteristics of metal composite inductors (i.e. Ferrite core = 0.4T vs. Metal Composite Type = above 1.5T) render it difficult to magnetically saturate, which in turn is resulting in good inductance vs. current performance, without a substantial drop off. In comparison, ferrite inductors do not only suffer from a fairly quicker inductance drop off.

Their inductance also suffers the undesirable effect that it varies with temperature, whereas the performance of their metal composite counterparts is stable over the entire specified temperature range. Naturally, the qualification of applications using ferrite inductors needs increased effort compared to metal composite inductors due to consideration of different temperature ranges.

Low loss characteristics of metal composite vs ferrite inductors assist realization of high efficiency power circuits such as ECU and makes thermal design considerations simple.

**High Mechanical Shock and Vibration Robustness**

Ferrite inductors consist of several sintered parts being constructively composed with an air gap inside the body, whereas metal composite inductors are based on a monolithic design without air gap.

Due to that assembled structure, the ferrite typesโ resistance to vibrations is limited to <4G to maximum 10G. Opposed to that, the monolithic structure of the metal composite inductors leads to a significantly higher vibration resistance โ up to 50G, depending on the inductor type. This may be advantage for harsh environmental, high vibration applications such as automotive, industrial or aerospace/defense electronics.

**Low EMI Noise**

Also in terms of a lower leakage flux outside the power inductors, the point goes to the metal composite types: Their monolithic structure causes by far less leakage as the magnetic flux simply is concentrated inside the inductor housing. See figure 23.