Of all the components that go into a circuit, magnetics seem to have the most complexity in terms of several factors including construction, parasitics, linearity, and variations. Unlike capacitors and resistors which tend to be standardized, inductors are more of a custom design based on application. Textbook circuit analysis leads to believe an inductor value is picked as if it were sitting there on the shelf in an unlimited selection of available parts. In reality, there are often various inductors lying around that will provide the desired circuit value; however, the design may not be optimal in terms of other operating parameters including voltage, current, power, and/or frequency. As the number of windings grows, the complexity expands exponentially. Therefore, having the ability to simulate an inductor in a circuit model can provide a much easier way to analyze a circuit.
Inductors, like most components, have a voltage and current relationship. In the most basic form, this relationship is linear as the voltage determines the rate of change of current in an inductor. For the most part, an inductor value is simply a basic version with linear behavior in a simulation program such as LTSPICE. However, like all components, parasitics make inductors deviate to a nonlinear behavior. The basic inductor parasitics are series resistance RDC and parallel capacitance CP (See Reference 2 Modeling Non-Ideal Inductors in SPICE.)
Equivalent Inductor Schematic2
The resulting behavior of the inductor changes with frequency as shown in the following inductance impedance curve2 .
As frequency increases, the impedance approaches the resonant frequency of the inductance combined with the parallel capacitance. These parameters affect the accuracy of the simulation model when compared to the actual component as shown.
Another nonlinearity that inductors exhibit is due to core saturation. The inductance value actually changes with applied current2 and voltage as shown in the following two figures.
Inductor versus Current2
The BH curve shows the second nonlinearity in an inductor4 . At first this curve can be intimidating mostly because B [volt-seconds] and H [ampere-turns] are foreign entities with uncommon units such as Gauss and Oersteds respectively. In reality, this curve is quite simple. Applying volts for a period of time means walking up the curve. As the amount of B increases, the lower curve starts to extend horizontally along the H axis which is also related to increasing current. In general, the device is becoming a short circuit with unlimited current. The only way to reset the inductor is to walk back down the BH upper curve. The hysteresis between the upper and lower curve is the power lost to the core. Finally, the operating point of an inductor with DC offset is shown as the asymmetric minor loop.
LT SPICE has both flux based and a hysteretic model4 . For further detail on inductor nonlinearities, refer to Reference 3 which goes into detail on magnetics design.
Transformers and coupled inductors can also be modeled using SPICE. The simplest forms are several inductors bound together with a coupling statement which is a line of text that starts with a “K” and is inserted in the schematic or netlist.
Using a K Statement to Couple Inductors and Make a Transformer5
Reference 6 explains even more on the K statement and coupling inductors in SPICE however it does get rather complex as well.
Some of the more standard transformer designs have SPICE model libraries that you can use. Reference 7 has basic and standard model libraries available.
Modeling often provides an insight into circuit behavior on a much faster scale than a hardware build and evaluation. As for magnetic devices, this not only assists in the analysis, it can help to avoid a lot of deep mathematical calculations as well as prolong the build on a custom component.
- How to create a transformer using LTSpice
- Modeling Non-Ideal Inductors in SPICE, Martin O’Hara Technical Manager, Newport Components, U.K. November 8 1993
- SPICE modeling of magnetic components
- LTspice: Simple Steps for Simulating Transformers by Gabino Alonso
- Transformers, LT wiki
- Wurth LTspice Transformer Library