(Note: Part 1 of this article is available at:
When transient current is forced into a drain or ground wire, resistance and inductance combine to produce a voltage drop, Equation 1:
is the resistance of the cable and XL
is the inductive impedance of the cable, both in ohms.
The resistance of the wires, shown in Table 2, is dependant upon the length and diameter of the wire (more on the electrode/earth resistance later).
Here, the resistance is "dc resistance" since it is observed only in cases of direct (non-ac) current flow. The frequency (Hz) of the current has an indirect effect upon the resistance, due to the skin effect. When an alternating current flows in a conductor, a back EMF is created in the center of the conductor, which opposes the current flow. This restricts the current to flow only at the outer surface of the wire, effectively removing the core of the wire from the circuit. The effective depth of current flow is called the skin depth, and can be calculated by Equation 2:
where δ ?'is the skin depth in mm, ρ ?'is the resistivity of the conductor, f is the frequency in MHz, μR is the relative permeability of the conductor and μo is 4π-10-7 NA2. Table 3 lists the skin depth for copper wires at certain frequencies.
Most lightning current energy is below 10 kHz. While there is some energy at 100 kHz, very little remains above 1 MHz. In this case, the design point for frequency might be at least 10 kHz, which means that conductors over 0.052" (1.3 mm) thick (representing a skin depth of 0.026" (0.66 mm) on each side of the conductor) have reduced conducting efficiency.
The 10-kHz resistance of the conductor, with only the outside 0.026" (0.66mm) of the conductor contributing to current flow, has a significant effect on larger-diameter cables. The effective conductor sectional area at 10 kHz, compared to the dc or actual area is given in the curve of Figure 5.
(Click to enlarge image)
While increasing diameter increases the effective area, the increase in effective area is associated with the circumference of the wire, not the sectional area.
The skin-depth effect means that copper straps about 1/16" (1 mm) thick will tend to outperform round wire of the same cross-sectional area, since the full cross section of the strap will conduct high current. Admittedly, wire (particularly stranded wire) is much easier to install, join, and change direction than straps. Flat-braid cable is a good alternative for vibration resistant and highly efficient grounding, which is why it is commonly used in aircraft-grounding applications.
Another aspect of impedance is the series inductance and its effect on creating voltage drop. The inductance of a wire is predominately related to its length and weakly related to its diameter. An estimate of a wire's self inductance is Equation 3:
where L is the length in meters, and d is the diameter of the wire in mm. The inductance of some typical wire lengths and diameters is given in Table 4
, along with the inductive impedance (calculated by 2π
(Click to enlarge image)
The length of the cable increases the impedance dramatically. Larger-diameter cables have slightly less impedance, due to the larger surface area. The benefit of larger diameter is less significant for resistive impedance, due to the skin-depth effects.
Bonding refers to the electrical connection of metal objects with conductors that serve as a flow path for lightning current. Typical current-flow paths can include metal structural steel, reinforcing bar, metal conduit, dedicated lightning-protection system cables, metal plumbing and piping, power-grounding wires and electrical conductors. Since these metal objects may find themselves in the lightning path, just as in a cable, current-flow voltages can be created along their lengths due to resistance and inductance, so that the voltage nearest the current injection point is significantly higher than at other nearby metal objects. If a person or equipment is connected between these points, hazardous voltages can exist. Bonding of adjacent metal objects reduces this voltage, and provides a redundant current-flow path.
In many cases a protector should be bonded to a ground plane, which usually consists of at least a peripheral ground around the area to be protected. Often a ground grid is used to provide low impedance across the ground plane. To intercept lightning, overhead grounded shield wires can also be bonded to this ground plane.
The extent of bonding relates to the risk of a direct strike to the structure, susceptibility of equipment, and the likelihood of injury to personnel. Consult local codes and practices of other contemporary structures. Make sure that the bonding is made with appropriate wire and terminals, and is made between the appropriate objects. In some cases, "hidden" internal bonding, such as reinforcing bar, can be cost effective. However, testing with current injection is usually needed, particularly when the lightning protection infrastructure is unknown, or the building was not designed for high lightning-risk device deployments.
H. Grounding resistance: never low enough
Lightning is essentially a current impulse which is trying to return to earth. The term grounding sometimes means a wire connected to an equipment chassis that is run in parallel with the power lines, to assist in tripping over-current devices and reducing voltage on the chassis in case of power line faults. While these grounding wires are sometimes involved, grounding here refers to the connection to the soil, which (hopefully) will be the preferred path of lightning current.
Electrode resistance also deserves focused attention. For electrical power entry, a minimum of twenty-five ohms is sufficient in most locations. However, recommendations of 10 ω or 5 ω?'are common. In some deployments, the goal is an incredibly low 1 ω. What value of electrode resistance is sufficient or able to solve our lightning problems?
Assume that we have to contend with a 90th-percentile lightning current of about 100 kA, and that using multiple current-flow paths we have managed to get the lightning current to share into five extremely low, 1 ω earth electrodes. This means that we would have about 20 kA into each electrode. The voltage of the 1 ω electrode would be approximately 20 kV (by V = IR). Now if you were spanning between this "ground" point and another more distantly "grounded" object, you would experience a very objectionable impulse. If electronics circuits span these "grounds", damage would most likely result (this voltage is sometimes called ground-potential rise).
But wait a minute! Even when we had five 1 ω electrodes and developed 20 kV, as explained above, what's happening? The problem isn't the wires or the electrodes, it's the soil. Try as we might, it is virtually impossible to drain lightning into the soil with negligible voltage. So how do we protect people and electronics?
First, during high lighting current flow, the ground will be at an elevated voltage compared to other locations and grounds. There are three elements to a practical solution:
1. Extend your ground bonding plane to include all equipment required to be protected. This frequently means enclosing the protected equipment in a shielded structure, usually implemented as a "mesh" Faraday cage.
2. Ground this structure at numerous points to provide redundant and reduced, albeit imperfect, earthing.
3. Suppress or ground the entry of ALL conductors at this structure where they enter. Don't forget that water pipes, air conditioning lines, structural steel and other "on-electrical" conductors need the same grounding as signal and power lines.
Figure 6 represents various mounting configurations for installing in-line protectors.
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(A) Locating the protector in a panel or bulkhead provides the best grounding and shielding. A strain-relief loop is required for a rigid cable. The connector can also 'piggyback' on bulkhead feedthroughs.
(B) Attaching the protector to a ground bar or panel surface still provides superior grounding and enables high-density cable runs. The cable should include a drip/strain-relief loop. Mounting is usually accomplished with a bracket or M8 bolt.
(C) Grounding the protector with a wire jumper or strap still provides good grounding, and is the easiest method. A lug, bracket or M8 thread can be used. This method allows the cable to flex and run in any direction. A large ground wire should be used.
Unless properly protected, lightning transients can wreak havoc upon electronic systems. By understanding the role and importance of the key parameters discussed in this article and by following these design guidelines, it is possible to effectively mitigate the consequences of lightning transients and to protect electronic devices. Minimizing the impact of lightning transients not only extends electronic system life and reliability, it has the added benefits of reducing capital equipment, operating and maintenance costs.
About the author
George M. Kauffman is Vice President of Engineering at Nextek, Inc., Littleton, MA (www.nexteklightning.com). For the past five years, he has has overseen NexTek's engineering team, developing new lightning-arrestor and DC power-conditioning products. George is a recognized leader in the lightning-protection industry and holds multiple patents in the EMC field. His technical expertise assures that each product line exhibits optimal technical performance characteristics.
Prior to NexTek, George spent eighteen years at Digital Equipment Corporation in numerous roles including manufacturing, product development, product management and software development. George holds both a BS in Mechanical Engineering and an MS in Engineering Management from the University of Massachusetts/Amherst. He is registered in Massachusetts as a Professional Engineer.