Digital Circuit Boards: Mach 1 GHz

1.17 Self- and Mutual Inductance

The terminology used in describing mutual inductance is very similar to that used to describe mutual capacitance. When magnetic flux is generated in a circuit, some of the flux crosses into other circuits. For an ideal inductor, the flux that is generated stays in that component. The ratio of flux to current in one geometry is called self-inductance. This is the fundamental definition of inductance.

The definition of mutual inductance is the magnetic flux coupled into a second circuit for a current flowing in a first circuit. The coupling can be of either polarity and depends on conductor geometry. Our interests will be the coupling between traces on circuit boards. The notation that is used is the double subscript such as L₁₁, which means the ratio of magnetic flux generated in loop 1 by current in loop 1. The notation L₁₂ means the ratio of flux in loop 2 to the current in loop 1.

N.B.

The inductance per unit length of a circuit trace can be derived from the capacitance per unit length by recognizing that the velocity of transmission is (LC)^−1/2 = c/ ε _R, where is the velocity of light.

The cross coupling that occurs in digital circuits goes in both directions. This coupling involves both electric and magnetic fields. This problem is discussed in Chapter 3.