The Complete Guide to Inductor SPICE Models: From Impedance Curves to the Top 3 Failure Modes (Engineers Must Read!)

We all learnt the concept of inductance when we were in our high school physics class where we saw how a solenoid develops voltage where there is a change of current that goes through it. The basic function of an inductor for a filter is to provide an in-line high impedance path (as shown in Figure 1). The impedance of an inductor increases with frequency; this is defined by Eq. 1.

where Xl is the impedance of the inductor, L is the inductance value and f is the frequency of concern.

Figure 1 The function of an inductor in a filter is to provide a high impedance path

An inductor is an energy storage device, the energy stored in an inductor is given by Eq. 2.

Where EL is the total energy stored in an inductor, ˪ is the inductance value and i is the current going through the inductor. One misconception that engineers often have is that the energy is stored in the wires of an inductor. After all, according to Eq. 2, there must be current present in an inductor to store energy. Current is defined as a form of charge movement in the inductor (conductor), right? No, this is not true. Energy in an inductor is largely stored in the air, not in the wires. Again, Eq.2 is developed and simplified to help engineers with circuit analysis. It does not show the fact that energy is stored in the field and the field exists predominantly in the space. We can easily prove this by comparing the energy storage capability between an inductor without an air gap and an inductor with an air gap. We are not going to spend much time discussing this since it is beyond the scope of this work. But understanding the fact that energy is stored in the air surrounding an inductor is crucial because it helps us understand the coupling mechanism and bypassing of an inductor, which will be discussed in detail later.

Figure 2 Understanding that energy in an inductor is stored in dielectrics such as air is important. Shown, REO Edge Wound Inductor

A basic inductor can be modelled as a circuit using the SPICE simulation tool in Figure 3. It should be noted here that we call the whole circuit an inductor, rather than the inductor symbol that we all learnt in school. This is important as, a schematic symbol provides little information on the physical structure of a component, which often limits our understanding of what is actually happening in an electromagnetic field. A basic first-order model such as the one shown in Figure 3 cannot represent more complex phenomena such as skin effect, proximity effect and saturation. But in the frequency range of a few kHz to a few MHz, which is often the spectrum of interest for power and electronics engineers, this simplified model is often sufficient for a f ilter design. The important point here is that an inductor is always associated with its parasitic capacitance due to the turn-to-turn winding structure. It is only inductive until its self-resonance point (which is defined in Eq. 3 below). After the self-resonance point, an inductor behaves more like a capacitor.

where L is the inductance value and C is the capacitance value. In Figure 3, L1 is the inductance value of the inductor, C1 represents the turn-to-turn winding capacitance, R1 is the inductor winding resistance, which is associated with copper loss (i²R loss), R2 is what we call leakage resistance. You can treat R2 as a form of natural damping in the inductor. Putting a leakage resistance in a SPICE model is important. It has been found that without the resistor in this model, sometimes the circuit that we try to simulate will not stabilise.