Last update: 4 July 2022
This blog post summarizes the results from my Jupyter notebook, which can be viewed here. The notebook is hosted on Github.
The Jupyter notebook examines coupled inductor circuits. Numeric and symbolic solutions are obtained for the voltages and currents in the circuits. The first circuit specifies the inductor values and the coupling in terms of mutual inductance. The second circuit is of a traditional transformer circuit where the turns ratio is given and the coupling constant is assumed to be 1.
A coupled inductor has two or more windings that are connected by a magnetic circuit. Coupled inductors transfer energy from one winding to a different winding usually through a common core. The efficiency of the magnetic coupling between both the windings is defined by the coupling factor k or by mutual inductance. The coupling constant and the mutual inductance are related by the equation:
Where k is the coupling coefficient and in spice the value of k can be from -1 to +1 to account negative phase relation. Phase dots are drawn on the schematic to indicate the relative direction of the windings. In LTspice the phase dots are associated with the negative terminal of the winding.
Coupled inductor circuit 1 is shown below. The circuit was drawn in LTspice and both the schematic and net list were exported. The inductors L1 and L2 are coupled with a mutual inductance of 0.5j.
Coupled inductor circuit 2 is shown below. This circuit has two independent voltage sources and a transformer. The turn ratio of the transformer is specified as 1:2 and the coupling constant is assumed to be 1.
For both circuits, the solutions obtained with Python were verified with results obtained from LTspice.
Reference: https://en.wikipedia.org/wiki/Inductance#Mutual_inductance
