# Mutual Inductance

Posted by in on 3-13-13

In addition to mutual capacitance, there is another, often more important mechanism for circuit interaction in high speed digital design – mutual inductance.  Mutual inductance is present wherever there are two loops of current.  These current loops produce magnetic fields which interact with one another proportionally to the rate of change of current within the loop.

Modeling Mutual Inductance

Mutual inductance is the proportionality factor by which a voltage is induced in a circuit in response to the current change in another circuit.  Just like in mutual capacitance, there is no need for these circuits to be physically connected for them to suffer the effects of this coupling.  As depicted in the figure above, mutual inductance can be modeled as a small transformer between the two circuits in question.  With a few basic assumptions, the induced voltage in a circuit can be given by the equation below.

Mutual Inductance

Due to the large current fluctuations inherent in high speed digital designs, they are especially susceptible to mutual inductance related coupling.  It is also important to keep in mind that the effect on an individual circuit is the superposition of the mutual inductance across all other circuits.  So, great care must be taken, particularly in high speed designs, to avoid major mutual inductance problems in your design.  A couple of things to keep in mind: 1) magnetic fields are vector quantities, so flipping the direction of current flow flips the polarity of the magnetic field (and the resulting induced voltage) and 2) coupling due to this mechanism is highly dependent on loop orientation – orienting a circuit parallel to the local lines of magnetic field strength of another circuit results in zero noise coupling from that particular circuit.