## Proximity Effect

Is there a model of "Proximity Effect" in strip lines or microstrips that is caused by the current generated forces of adjacent conductors? I would guess it could cause frequency dependent attenuation.

Thank you.

Thanks for your interest in High-Speed Digital Design.

You are correct that the proximity effect does play a role in determining the patterns of current flow (and therefore the attenuation and characteristic impedance) of microstrip and stripline transmission lines.

The proximity effect for PCB traces takes hold at rather low frequencies on the order of a few Megahertz. Below that frequency the magnetic forces due to changing currents in the traces are too small to influence the patterns of current flow. At low frequencies current in a PCB follows the path of least RESISTANCE. The path of least resistance for current flowing in a PCB trace fills the volume of the trace, flowing uniformly throughout the conductor. The path of least resistance for that same current as it returns to its source through the power and/or ground planes spreads out in a wide, flat sheet, tending to occupy as much of the surface area of the planes as possible on its way back to the source. That's the least RESISTANCE path.

Above a few Megahertz, the magnetic forces become VERY significant, and the current flow patterns change. Above a few Megahertz the INDUCTANCE of the traces and planes becomes vastly more important than their resistance, and current flows in the least INDUCTANCE pathway. We can state the general principle of least-inductive current flow in a number of equivalent ways:

- Current at high frequencies distributes itself to neutralize all internal magnetic forces, which would otherwise shift the patterns of current flow.
- In more technical terms, the component of the magnetic field normal to a (good) conductor is (nearly) zero. (If the normal component is non-zero, eddy currents build up within the conductor to neutralize the normal component of the field).
- In terms of minimum-potential energy, current at high frequencies distributes itself in that pattern which minimizes the total stored magnetic field energy.
- In terms of inductance, current at high frequencies distributes itself in that pattern which minimizes the total inductance of the loop formed by the outgoing and returning current.
- The current in two round, parallel wires is not distributed uniformly around the conductors. The magnetic fields from each wire affect the current flow in the other, resulting in a slightly non-uniform current distribution, which in turn increases the apparent resistance of the conductors. In parallel round wires we call this the proximity effect.

All of the above viewpoints are correct, and they are all equivalent.

Above that frequency where magnetic effects take hold, the patterns of current flow attain the minimum-inductance configuration and do not vary further with frequency (except for the skin effect, mentioned below).

For example, in a typical 70-ohm microstrip configuration you will see at high frequencies the current distributed fairly uniformly around the circumference of a signal-carrying PCB trace, with slightly more current flowing on the side nearest the reference plane, and slightly less on the back side. The increase in resistance due to this effect (above and beyond simple consideration of the skin depth and trace circumference assuming a uniform current distribution) is on the order of about 30 percent, a percentage that remains fixed as a function of frequency.

On the reference plane beneath the trace, you will see another a similar effect. At high frequencies the RETURNING SIGNAL CURRENT FLOWING IN THE REFERENCE PLANE flows most heavily right underneath the trace, with wide tails of residual current falling off rapidly to each side as you move perpendicularly away from the signal-carrying trace. The exact distribution of current in the planes depends on the trace geometry, but not on the operating frequency (assuming your operating frequency is high enough to have attained the minimum-inductance flow pattern). Because the returning signal current at high-frequencies flows in a finite area of the reference plane the effective resistance of the reference plane must be non-zero. The total resistive circuit losses due to the high-frequency pattern of current flow in the reference plane totals approximately 30 percent of the PCB skin-effect trace resistance, a percentage that remains fixed as a function of frequency.

Modern 2-dimensional electromagnetic field solver software automatically takes the proximity effect into account.

A more serious source of high-frequency attenuation, in the range from 10 MHz up to 1 GHz, is the skin effect. The skin effect forces current to flow only in a thin layer around the circumference of the conductors (or the surfaces of reference planes). The thickness of the current penetration layer (the skin depth) changes appreciably with frequency, creating noticeable changes in the attenuation of long traces.

So when does all this attenuation stuff matter? In PCB traces shorter than 12", at frequencies of up to 1 GHz, you can generally ignore all trace losses. They just aren't significant enough to worry about. For longer traces, or at higher speeds, the skin effect becomes very significant. At frequencies above 2 GHz (for typical PCB trace geometries) the skin effect is superceded in importance by the effect of dielectric absorption.

Best Regards,

Dr. Howard Johnson