Bifilar winding - this name applies to two different types of windings:
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Magnetically coupled windings are used whenever there is a need to exchange energy or signal between different parts of an electromagnetic circuit. Hence, they are used in transformers, coupled inductors, electric motors and generators, etc.
For this reason, certain windings are wound with multiple wires run together so that the wire-to-wire spacing can be a small as possible. This is important for example in pulse transformers and common-mode chokes.
Becaues of the proximity of conductors, a component with bifilar windings (and multi-filar) have increased parasitic capacitance (self-capacitance), which can become problematic at high frequency, do to self-resonance effect.
Non-inductive winding is not used for electromagnetic energy transfer. A typical application for non-inductive winding is a wire-wound shunt resistor, used for current-to-voltage conversion (i.e. the voltage drop across a resistor is directly proportional to the current flowing through it).
An ideal shunt resistor should introduce only pure electrical resistance, without any parasitic inductance or parasitic capacitance because they affect the linearity of voltage drop with respect to frequency and harmonics.
But typically a significant lenght of wire is required in order to obtain the given value of resistance, and if the wire is wound on some former it has the shape of a coil and thus it might have a non-negligible value of inductance (and capacitance).
In order to reduce the inductive effect two wires can be wound together (bifilar) at the same time. Then if one end is joined electrically, then current is made to flow “clockwise” in one wire, and tracing back the same path “anticlockwise” in the second wire. The magnetic fields from both wires cancel out to a great extent and the total parasitic inductance is minimised.5)
A more complex way of achieving even lower parasitic inductance is the Ayrton-Perry winding, which is not bifilar and more difficult to make.