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• What capacitor and inductor are the best for a switching power supply? - Inductor- : Reading and Understanding Inductor Specifications and Equivalent Circuits

What capacitor and inductor are the best for a switching power supply?

# Reading and Understanding Inductor Specifications and Equivalent Circuits

## Inductor – Part 1－

Keyword Inductor Power inductor Inductor specifications Nominal inductance Self-resonant frequency DC resistance Rated current Saturation current Temperature rise current Inductor equivalent circuit Parasitic components DC resistance Copper loss Iron loss Insulation resistance Inter-wire capacitance Inductor Q Resonance point

－In discussing " What capacitor and inductor are the best for a switching power supply?", we have until now considered various aspects of capacitors, but from now we shall move on to explain inductors.
When constructing a switching power supply, an inductor is one vital component. However, we sometimes hear that magnetic components, including inductors, can be hard to understand.

There certainly are not a few people who are not comfortable dealing with magnetic components. But, switching power supplies have become an indispensable component, and cannot be avoided. Here we would like to answer queries to deepen the reader's understanding of inductors.

－Well then, please explain what should be understood before anything else.

Well, to start with the basics, I'd like to explain how to read the specifications of an inductor. The first thing I'd like to say is that even if a specification name is the same, often the conditions assumed for the specification differ among products and among manufacturers. And similarly, for a given specification, one manufacturer may guarantee a maximum value (max.) and a minimum value (min.), while another manufacturer may present only a typical value (typ.). Hence some care is needed when selecting inductors or when comparing and examining similar devices.

－So one has to take care to confirm conditions of the specifications.

そThat's right. It should be kept in mind that if the numerical values as presented are compared directly, major problems can result. Anyways, let's have a look at a specific example. The following is an excerpt from a Taiyo Yuden catalog.

Of course, the nominal inductance is a vital parameter. As indicated in the last column, the measurement frequency is 100 kHz, and the tolerance is ±30%.

The self-resonant frequency frequency is the limiting frequency for functioning as an inductor. The minimum value of the self-resonant frequency is guaranteed. The value indicates that the device will function down to the lowest specified frequency.

The DC resistance is mainly the resistance of the windings, and is indicated with a tolerance of ±20%.

The rated current is another parameter for which conditions must be checked. One such condition is the saturation current; in the case of this inductor, the maximum value of the saturation current for which the inductance changes by -30% is indicated. Depending on the manufacturer or product, the condition stipulated may be between -10% and -30%.

As another rated current, the temperature rise current is stipulated. This is the maximum value of the current at which the temperature rises by 40℃ when a direct current is applied; here again, the condition varies between 20℃ and 40℃ depending on the manufacturer or the product.

There is another separate matter to be considered regarding rated currents. This is the fact that, depending on the manufacturer or the product, both the saturation current and the temperature rise current may not be indicated. In general, when only one is indicated, it can be assumed that as a rated value, the smaller of the two is presented, but to be on the safe side it is a good idea to check with the manufacturer.

Rated currents are important parameters, and so we shall explain them in a little more detail. The following diagrams indicate the characteristics for saturation and temperature rise in relation to maximum values, typical values, and margins.

We use an example to further explain the saturation current. The reasoning is the same as for the temperature rise current. In the example, the saturation current is specified to be the current resulting when the direct current is gradually increased until the inductance changes by -30%, that is, falls by 30%. There is always deviation in values among inductors, and indeed among samples of any kind. The typical value (typ.) is a representative value given this deviation. The guaranteed value indicates the allowed maximum value and/or minimum value. Consequently, they have a certain margin with respect to the typical value. Upon actually measuring values, many are found to be close to the typical value, but there are also units with values close to the maximum and minimum values.

Upon examining the typical, maximum and minimum values, the extent of the margin should be clear. And, by comparing characteristics and specified conditions, it should be evident whether the conditions imposed are strict or not.

－Well, why is it that the specified conditions for the same characteristic differ among products and manufacturers?

There is no single, simple reason, but it may be because manufacturers disagree about which conditions are appropriate when considering the required performance of an application circuit or the need to ensure safety. Of course, level settings with respect to product performance, characteristics, quality, and reliability, as well as price considerations, are probably related.

－Apart from this, is there anything else that needs to be understood right from the start?

In addition to understanding specifications, equivalent circuits and the various components must also be grasped to understand the basic characteristics of inductors. Previously, when discussing capacitors, we described the parasitic components ESR and ESL and their effects. Inductors also have similar parasitic components.

We will explain this using an equivalent circuit. Rdc is a DC resistance, mainly that of the windings, and is also called the copper loss. This is a component in series with the inductor. Rac is the loss due mainly to the core material, and is called iron loss. As indicated for capacitance and resistance, there is a frequency characteristic. When the frequency is high, the impedance falls, and the loss is increased. Insulation resistance is a DC resistance that pertains to leakage currents. Capacitances occur due the fact that wiring is insulated with films of urethane or some other insulator, and so in the windings, conductors are separated by insulating material, that is, they have the same structure as a capacitor. This interwire capacitance is the main capacitance, and has a great effect on the resonance point.

The Q factor is an index representing the inductor performance. It is the value obtained by dividing X (=ωL) by R (Rac), and indicates the amount of loss for a given frequency. From the equation, it should be clear that when R (Rac, the iron loss) is small, the Q factor is high.

The basic characteristics of an inductor are represented by a graph plotting resistance/impedance versus frequency. This is an example of an inductor 6 mm on a side, of height 2 mm and with inductance 4.7 µF. The red line is Rac, the iron loss. The blue line is the impedance, and the green line is X (ωL).

As explained above, a capacitance is present, and so there is a resonance point. The green line, representing X, indicates the characteristics of the capacitance itself at frequencies above the resonance point, but as the frequency rises, this impedance falls. Rac increases as the frequency rises. Rdc is the value of Rac for a direct current (zero Hertz).

These are the characteristics of a given inductor, but it should be kept in mind that the parasitic components will differ depending on the inductor materials and structure.

－Well then, having reviewed the basics, next we'd like to ask about the types of inductors used in power supplies.