Use PSpice to model distributed-gap cores
PSpice software lets you create magnetic-core models that simulate nonlinear magnetic devices (Figure 1). These simulations are useful for observing hard-to-measure magnetic parameters such as core flux density, especially when you cannot quickly procure a sample device. The required inputs to the PSpice magnetic-core model are initial permeability of the core material, data points from the B-H magnetization curve, and the physical properties of the core, such as magnetic-path length, cross-sectional area, and air-gap length.
All of the needed inputs for the magnetic-core model are typically available from core manufacturers' data sheets. However, in the case of a distributed gap with powder cores such as MPP or KoolMu, you need to determine the equivalent air gap to model the core using PSpice, because it relies on the air-gap length as input data to the model. Using the conservation of flux and manipulating Ampere's Law for a magnetic circuit with an air gap result in: 1/UE=(1/UI)+(LG/LE), where UE is the effective permeability of the core, UI is the initial permeability of the core material, LG is the length of the gap in centimeters, and LE is the magnetic-path length of the core in centimeters. Assuming that the initial permeability, UI, of the core is high, which is typical of distributed-gap cores, then the term 1/UI drops out, and you can rearrange the equation to solve for the gap length as LG=LE/UE. Using the magnetic-path length, LE, and effective permeability, UE, that the core manufacturer's data sheet specifies, calculate the equivalent air-gap length of the distributed gap-core for use in the PSpice model.
As an example, take the KoolMu 77310-A7 toroidal powder core from Magnetics Inc ( www.mag-inc.com). Because the data sheet does not specify the initial permeability of the KoolMu core, arbitrarily use 5000. (This parameter is insignificant in the model due to the air gap.) Use the magnetization curve for the KoolMu material and mark the data points in Table 1.
Physical data for the 77310-A7 core shows a magnetic path length of 5.67 cm, cross-sectional area of 0.331 cm2, and effective permeability of 125. From this data, you calculate the effective air-gap length of 0.045 cm. Enter this data into PSpice for the core model.
A quick and easy way to verify the accuracy of the model is to create an inductor in PSpice using your magnetic-core model. Place the inductor in a series-tuned RLC circuit (Figure 2). Using PSpice, run an ac sweep of the circuit, and use a probe to find the resonant frequency, fRES. Using the resonant frequency, you can calculate the measured inductance of the PSpice model as LMEAS=1/(4×π2×fRES2×C). If your magnetic-core model is correct, this should be close to the expected inductance calculated as LEXP=(N2)×AL, where N is the number of turns, and the core data sheet typically supplies the inductance factor, AL.