In the previous tutorials, we have discussed the basic concept of an inductor, properties of an inductor and different types of inductors. Now it's time to know how to select an inductor for a given circuit. Fortunately, different types of inductors are designed to suit specific applications. Thus, for any application, there is either exclusively one type of inductor available, or there are at most two or three types to choose from. Check out the previous article to learn about the different types of inductors and their applications. For most common applications, solenoid coils, toroids, or pot cores are preferred. To select between them, the following considerations are important:
- If the circuit requires the use of multiple inductors that must or may have some mutual inductance, solenoid coils can be used. Solenoid coils are inexpensive, widely available, and easy to design and troubleshoot. However, solenoid coils are generally quite bulky compared to other types of inductors. Still, these may be preferred first if electromagnetic interference or mutual inductance is not a major circuit concern.
- If the circuit does not require mutual inductance or there is no electromagnetic interference of the inductor with any other component of the circuit, then toroids should be preferred first. Toroids are small in size, have a high inductance value and have almost no electromagnetic interference. If mutual inductance is desired between different coils, they can be wound on the same core.
- Pot Cores offer similar advantages to toroids. However, these are quite expensive due to their complex construction. It is not easy to find pot cores for high power applications. Pot cores also have limited exposure to air circulation, so they can experience heating issues. Still, the potentiometer cores are very robust, offer better shielding and can be mounted more easily on printed circuit boards.
When selecting an inductor for a given circuit, choosing the type of inductor is quite simple. The important concerns in selecting an inductor are always the desired characteristics. First, for any circuit, a desired value of inductance is provided or needs to be derived by the engineer. An inductor of the same nominal value needs to be chosen. The next important thing that needs to be considered is tolerance. It must be verified that variation in inductance will not affect the performance of the circuit. Consequently, an inductor with suitable tolerance must be chosen.
The rest of the parameters can be circuit or application specific. Essentially, it is important to check the saturation current of the selected inductor. The saturation current of the chosen inductor must be at least 1.5 times or twice the DC or RMS current levels to which the inductor may be exposed in the circuit. To ensure the desired performance of the inductor, the incremental current and maximum DC current must also be checked. Factors such as saturation current, incremental current and maximum DC current play a crucial role, especially when the selected inductor has a ferrite core.
If the circuit needs to be very power efficient, such as in coupling applications or power supply circuits, DC resistance, impedance, and quality factor are important properties to check. Similarly, in frequency-sensitive circuits like filter circuits, the self-resonant frequency of the inductor plays an important role. Similarly, in temperature sensitive circuits, inductance temperature coefficient, resistance temperature coefficient, ambient temperature range, operating temperature range, and Curie temperature are important factors that must be essentially checked. The issue of electromagnetic interference can be resolved most of the time by choosing the correct inductor type, i.e. toroid or potentiometer core, if EMI has to be avoided.
Standard values of inductors
Just like resistors and capacitors, inductors are also available in standard values, according to the E Series. To learn more about standard values of resistors, capacitors, inductors and Zener diodes, check out the following article, “Basic Electronics 08 – Reading of Value, Tolerance and Power of Resistors”.
Series and parallel combination of inductors
It may not be possible to always obtain the exact value of the required inductance. In this case, a combination of series or parallel inductors can be used to obtain the desired inductance. When inductors are connected in series, their equivalent inductance is the sum of the inductances as follows:
L Series = L 1 + L 2 + L 3 + . . . .
When inductors are connected in parallel, their equivalent inductance is given by the following equation:
1/L Parallel = 1/L 1 + 1/L 2 + 1/L 3 + . . . .
The equation for combining inductances in series is derived from the fact that the sum of voltage drops across all inductors connected in series will equal the applied voltage while the same current passes through all inductors in the branch. The equation for the series combination of inductances is derived as follows:
V Total =V L1 +V L2 +V L3 + . . . .
-EU Series * di/dt = -L 1 * di/dt + (-L 2 * di/dt) + (-L 3 * di/dt) + . . . .
L Series = L 1 + L 2 + L 3 + . . . .
The equation for parallel combination of inductances is derived from the fact that the sum of currents through all inductances connected in parallel will equal the total current, while the voltage across them will remain the same. The equation for parallel combination of inductances is derived as follows –
I = i1 + i2 + i3 + . . . .
1/L Parallel * ∫V.dt = 1/L 1 * ∫V.dt + 1/L 2 * ∫V.dt + 1/L 3 * ∫V.dt + . . . . .
1/L Parallel = 1/L 1 + 1/L 2 + 1/L 3 + . . . .
The above equations are derived considering that the inductors do not have any mutual inductance.
Mutual inductance
Practically all inductors have some mutual inductance. Electromagnetic interference is very apparent in the case of solenoid coils, while toroids, potentiometer cores and transmission line inductors are well shielded to show any significant mutual inductance. The mutual inductance between two inductors depends on the value of their inductance and the coupling coefficient between them. It is measured in the same unit as inductance and is denoted by the letter 'M'. The following equation gives the value of mutual inductance between two inductors –
M = k*(L 1 *EU 2 ) 1/2
Here, k is the coupling coefficient. It can have a value from 0 to 1. If two inductors are well shielded and do not present electromagnetic interference, the value of k is 0 and there is zero mutual inductance between the inductors.
Mutual inductance is very apparent when inductors (particularly solenoidal coils) are connected in series. Mutual inductance can be additive or subtractive. When inductors are connected close to each other so that current flows through them in the same direction, they reinforce each other's magnetic fields. Therefore, the mutual inductance is additive in this case. The following equation gives the effective inductance in this case –
L = L 1 + L 2 + 2M = L 1 + L 2 + 2* k*(L 1 * L 2 ) 1/2
When inductors are connected close to each other so that current flows through them in opposite directions, the magnetic fields across the inductors oppose each other's magnetic fields. In this case, the mutual inductance is subtractive. The effective inductance, then, is given by the following equation –
I = I 1 + I 2 – 2M = L 1 + I 2 – 2*k*(L 1 * I 2 ) 1/2
In the next article, we will discuss reading inductor packages.
