## The Way Home

Form a loop of wire about 2 in. in diameter. Measure its inductance. Now, squash the sides of the loop together, forming a long, skinny loop (Figure 1). When you squash the loop, you decrease its inductance. This simple experiment proves an important point: Inductance is not a property of the wire alone; it is a property of the shape of the entire current path around the loop. Current always makes a loop. If it goes out, it must find a way back home. The shapes of both the outgoing and the return paths affect the observed inductance. (courtesy EDN Magazine)

By the way, measuring inductance is simple. For example, a small inductor connected to the output of a 50-Ω square-wave generator creates a small voltage pulse on every step edge. A bigger inductance creates a bigger pulse. If you want to get quantitative about it, the value of the unknown inductance, L, is related to the total area, A, under the observed pulse: L=A(R/ΔV), where L is the unknown inductance in henries, A is the area under the observed pulse in volt seconds, R is the source impedance of the pulse generator in ohms, and ΔV is the peak-to-peak step size of the generator in volts.

To explain why inductance changes with the shape of a loop, I must draw your attention to the pattern of the magnetic field surrounding the loop. Consider separately that part of the field generated by current flowing in the outbound half of the loop and that part of the field caused by current in the return path.

As you squeeze the loop into a long, skinny shape, the magnetic fields generated by the outbound and return paths mimic each other but with opposite polarities and slightly different positional offsets. Inside the loop, the fields reinforce, but at points remote from the loop the fields nearly perfectly cancel. The closer you bring the outbound and return pathways, the more perfect the cancellation.

Field cancellation matters because it is the total energy, E, stored in the magnetic field surrounding the conductors that determines the inductance. In mathematical terms, E=½LI2, where E is in joules, L is in henries, and I is the current flowing through the inductor in amps. Better cancellation reduces the magnetic fields surrounding the conductors, decreasing the total energy, E, thus decreasing the inductance. Squeezing together the outbound and return pathways reduces the inductance and, because the total magnetic field intensity surrounding the conductors shrinks, squeezing the wires also reduces emissions.

Inside a connector the same principle applies. As signal currents propagate through the signal pins of a connector, equal but opposite currents propagate simultaneously through the power and ground pins. The closer you place the power and ground pins to the signal pins, the less inductance your signals perceive as they traverse the connector. Less inductance means a lower magnetic field strength, less crosstalk, and less EMI. That's why good connectors have a lot of power and ground pins.

In a board with solid power and ground planes, imagine a typical surface-mounted bypass capacitor layout. Consider the current loop formed starting at the VCC plane, going up through the power via, through a pad, through a bypass capacitor, and back down through another pad and ground via to the ground plane. The closer you place the two vias, the less inductance this structure exhibits. Shorter, smaller capacitors are therefore better.

If you change your layer stack to squash the planes up close to the surface of the board, right under the capacitor, you get another tremendous benefit. The fields generated by currents flowing in the body of the capacitor now tend to cancel the equal and opposite fields generated by currents circulating in the power and ground planes. Capacitors pressed down against the power and ground planes exhibit low inductance and low B-field radiation. This benefit is a good reason to locate power and ground on layers 2 and 3 of your board, minimizing the spacing between the planes and the bypass capacitors.