Introduction to antenna surge protection

Contents

• Foreword and Disclaimer
• Conclusions / Abstract / Summary
• Lightning
• Basic taxonomy and ideas
  
  • Lightning Protection Zones
  • Equal potentials
  • LPS downconductor resistance
  • Earth resistivity
  • Lightning strike statistics and risk assessment
  • Cone and Sphere method of LPZ0b demarcation
• Example scenaria/buildings
  
  • Brick and mortar + safe separation distance
  • A skyscraper
  • A tower of steel
  • A ship
  • A substation
• Troublesome examples - reality bites
  
  • The one proper way
  • An alternative, old, improper way
  • Building with no LPS, solution #1
  • Building with no LPS, solution #2
  • Building with no LPS, solution #3
• More complex cascaded protection of a signal line
• A closer look at some theory
  
  • Electric field intensity, gradient of potential
  • Inductive coupling
• References
  
  • The Dehn bible
  • The Dehn catalogue
  • Kniska = a PDF booklet of lightning protection (Dehn CZ promo)
  • Rosa and Grover
  • A master's thesis on substation earthing
  • Personal contacts

This HOWTO was inspired by a debate at a Meinberg agents meeting earlier this year. Hence the Meinberg antennas in some of the pictures, and hence the focus on antenna placement, protection and small-signal coax cabling.
Note that I am not a Meinberg employee, I've merely been a techsupport for their hardware for two decades or so, in a "regional agent company". In a legal sense, I do not speak for Meinberg.

I am neither a licensed engineer in the business of lightning protection, nor in fact an EE graduate. From a professional perspective, I'm a hobbyist with 20 years of practice on jobs in neighboring areas.
If you'd appreciate professional advice for your particular circumstances, or a second opinion, by all means do contact a licensed lightning protection practitioner in your area / in your application field.
For quality reading, refer to the IEC/EN 62305 norm, and/or official documentation by Dehn or other vendors of relevant surge arrestors and other lightning protection hardware.

In most countries, any installations related to lightning safety, especially on the outside lightning protection system of a building, are subject to official inspection/approval, and should be designed by a licensed project engineer.
Lightning safety serves to protect human lives and to prevent damage to property.

While I technically do have access to the EN 62305 (Czech mutation), there's an online resource that I find more useful / richer in examples: I will refer to it as the Dehn Bible - officially the Lightning Protection Guide. And there's more - just see the references.

Fasten your seatbelts.

A rare close-range picture and video, showing upward leaders growing to meet the branching downward leader.
(source publication, raw slo-mo video data)

A difference of potentials worth up to hundreds of millions of Volts accumulates in the atmosphere, and finds a way though the storm clouds to discharge itself into ground, via a beautiful branching jagged arc.
The arc does not flash into existence all at once, it "crawls" at a finite velocity, or rather, takes a sequence of short jumps. This effect, apart from being visually appealing, should also help us understand some of the "best practices", tools and lore of modern Ligtning Protection System design.

In the picture and video above, it's interesting to note how the tips of the "leaders" get dragged by corona (the publication speaks in detail about "streamers" = individual "rays" in the corona). The corona seems to siphon charge from local "pockets of lower resistance", and provides enough energy (current) for the developing channel to stay ionized = conductive.

Footage by the Slow Mo Guys - thunderstorm at the sea in Singapore

YT vid by Robert Patterson, containing a snippet of footage from National Geographic

A YT short published by StoryfulNews, showing an amazing upward lightning strike in Kansas

There's more on YouTube, these are just a few examples.

Apparently, lightning bolts are typically negative and growing downward in the characteristic branching fashion, but in rare cases the atmosphere is positively charged, in that case the lightning grows upward, and consequently (?) the branching leader is not observable from the ground. Some sources just say that positive lightnings are not branching... There's a whole science and taxonomy on the topic.

Points to remember from this chapter:

• Lightning crawls across the sky, finding path of least resistance in the atmospheric "soup" of rainy clouds.
• The path is by no means linear. The leading channel is branching, and the lightning is in no way guaranteed to strike the highest point far and wide.
• When one of the branches of the leader connects with an opposite-going upward leader, the main conductive channel thus established quickly drains the initial difference of potentials, thus typically depriving other branches of the lightning of their "steam". I.e., typically just one leader of the bunch connects to ground - this one then remains energized / ionized and drains some more energy from the clouds up above, for as long as some secondary discharges high up in the clouds keep the main channel alive by feeding it with additional energy.

A larger busbar by Dehn

A smaller busbar by nVent

In principle, a busbar is just a metal bar with screw terminals, suitable as a central interconnect point for wires arriving and departing in various directions.
There are various sorts, either for stand-alone use, or as an internal accessory for mounting inside plastic circuit breaker boxes etc.

The word "equipotential" does not refer to a particular construction arrangement. It refers to function in the block schematic: "serving the equalization of potentials".

The "wiring" aspect of equipotential bonding is codified as part of IEC 60364-4-41 and IEC 60364-5-54. Lightning protection aspects are detailed in IEC/EN 62305-3 (external protection) and 62305-4 (internal protection).

Equal potentials of the Protective Earth, i.e. a common reference ground, is a key concept in surge protection. The systemic protection approach hinges on this.
Equal potentials for every exposed earth inside the house.
Only connected to the outside LPS ground at about the terrain level.
Thus, if a lightning strikes the outside LPS, this one combined common ground in the basement does still jump up (due to earth resistance), but the whole house "jumps up and settles down en bloc", so that no harm (injury / fire hazard) is done to anything and anyone inside the house, as long as any outgoing/incoming wiring is "clamped" by surge-arrestors to this single PE potential within the house.

The peak current of a lightning strike, with a 99% confidence, is specified to be below 100 - 200 kA, depending on Lightning Protection Level (AKA LPS class). There are 4 LPL's = LPS classes, depending on detailed risk assesment.
Read: think of what happens at 100 - 200 kA, considering the resistances outlined below.

This initial peak may have a half-life of a millisecond or so, but more follows and it can take several seconds for the ionized channel to die completely. (Typically it dies in a fraction of a second.)

Metal	Resistivity ρ [Ω·m]	Ω/m, 16 mm2	Ω/m, 50 mm2	Ω/m, 100 mm2
Copper	1.68 · 10-8	1.05 · 10-3	0.34 · 10-3	0.17 · 10-3
Aluminium	2.65 · 10-8	1.66 · 10-3	0.53 · 10-3	0.27 · 10-3
Iron	9.70 · 10-8	6.06 · 10-3	1.94 · 10-3	0.97 · 10-3
Stainless steel*	69.0 · 10-8	43.1 · 10-3	13.8 · 10-3	6.9 · 10-3

Resistivity values for some typical metals, used for LPS construction
* stainless steel: 18% Chrome, 8% Nickel

Imagine a small house, with two down-conductors, 10m each, made of 50 mm² zinc-galvanized steel (iron). Combined, that's about 10 milliOhms from the tip of the lightning rod to the earth termination system's attachment clamp.
If I recall correctly some comments from an inspector at our premises the other day, such a value would be a miracle, unless all the joints are welded. But let's take this optimistic value. Ignoring inductance, the resistive voltage drop would be 2 kV peak for a 200 kA lightning strike.

The IEC/EN 62305 mandates minimal conductor cross-sections for the LPS, and minimal counts / maximal spacing of down-conductors along the perimeter of the building.

The minimal "safe bet" cross-section is 16 mm² copper. For the lower Lightning Protection Levels (LPS classes), Aluminum and even steel are theoretically okay too, at 16 mm².
Stainless steel is not suitable at 16 mm² cross section, for the down-conductor role.
It is interesting to note that 16 mm² of copper is worth the same as 100 mm² of steel, resistance-wise. It would appear that a "plausible maximum" for conductor resistance might be about 1 milliOhm per meter of length, but the primary problem is not residual voltage. The primary concern is heat-up by the lightning current. Standard steel at 16 mm² at 200 kA in LPS class 1 would melt. Therefore, apart from resistivity, mass and melting temperature are other factors. We could try some math with energy, thermal capacity and melting point, but ahh well... let's just trust the norm on this.
There's a neat table in the Dehn Bible on page 97. Downconductor spacing is on page 95.

So much for the outside LPS, its cross-sections and materials.
Time to take a short look at the ballpark of grounding ("earth termination").

Material	Resistivity ρ [Ω·m]
Sea water	0.3
Swamp	5 - 40
River/lake water	10 - 100
Dirt/clay	20 - 200
Humid sandy soil	200 - 400
Concrete	150 - 500
Dry sandy soil	1000 - 2000
Rocky soil	100 - 3000
Gravel/sand	2000 - 3000
Weathered rock	< 1000
Sandstone	2000 - 3000
Granite	up to 50 000

Resistivity values for some geological materials (soil and others).
Sources: the Dehn Bible on page 122,
Roman Bursik's master's thesis on page 27
Recommended minimum earth electrode construction: Dehn Bible on page 292.

Although the Dehn Bible mentions some formulas for ballparking the earth electrode resistance for different constructions of the electrode, it's still kind of difficult to get your hands on a practical number.
In the Dehn Bible on page 128 (ish), there is a chart or two, showing values of R_E for several values of earth resistivity. For ρ between 100 and 400, and a grounding conductor (electrode) buried in a length of 10 m, the resulting resistance was somewhere in double digit Ohms.

Times something like 100 kA, ho hum...
Note that this is referring to earth termination. In a building with a properly interconnected system of LPS earth and inner PE GND, and with arrestors in place, people and hardware in the building are pretty much safe. But, upon a lightning strike, the earth resistance translates into a gradient of voltage in soil around the building (earth termination) which can be dangerous. This is called a step or stride voltage.
We'll probably revisit this sub-topic briefly when debating earth termination around large buildings and in substations.

The following animated picture is a little tangential in our context.
Considering what's been said so far, guess what may arrive at the ends of the communication link between the two houses. Mind the arrestors at the signal cable's entry point into each building, and think about their role.

Protection of communication links in general

Statistical lightning density across Germany, average 1999-2011
Scale: <0.6 .. <3.0 strikes to earth per km² per year
Source: found on page 34 of the Dehn Bible
Original source: Siemens Blitz-Informations-Dienst
Appears closely related to a domestic German supplement No.1 to IEC/EN 62305-2.

The statistical density of strikes is a key factor in risk assessment and Lightning Protection Level categorization. The "Lightning Protection Level" seems synonymous with "Lightning Protection System class".
The IEC/EN 62305 dedicates a whole part 2 (i.e. "62305-2") to risk management. A rich topic in its own right - let's call it out of scope in this howto :-) You may want to check chapter 3 in the Dehn Bible.
Suffice to say, that the LPS class is an important intermediate variable, used as a parameter in various rules in Lightning Protection System design, as per IEC/EN 62305-3.

Lightning Protection Level (Ligtning Protection System class)	I	II	III	IV
Max peak lightning current / statistical confidence	200 kA / 99 %	150 kA / 98 %	100 kA / 95 %	100 kA / 95 %
Min peak lightning current [1] / statistical confidence	3 kA / 99 %	5 kA / 97 %	10 kA / 91 %	16 kA / 84 %
Rolling sphere radius	20 m	30 m	45 m	60 m
Cone α for h=20m [2]	22°	39°	49°	55°
Building height for cone α=22° [2]	20 m	30 m	45 m	60 m
Mesh size (grid spacing)[3]	5 x 5 m	10 x 10 m	15 x 15 m	20 x 20 m
Spacing of downconductors	10 m	10 m	15 m	20 m
Safe separation ki	0.08	0.06	0.04	0.04

Some LPS design parameters dependent on the LPS class.
Notes:
1. no clue why the minimal values are ordered in reverse, and what do they matter to dimensioning
2. for the cone method, there's a neat chart (nomogram) and a table, specifying the dependency of α on LPL and bulding height. See the Dehn Bible on pages 69 and 71.
3. for LPS designs where the outside LPS air termination is formed by a grid of conductors - typical for larger buildings.
For downconductor cross-sections and permissible temperature rise, see a table in the Dehn Bible on page 97.

While the table above mostly deals with LPS design parameters that are off topic in this howto, the rows highlighted by blue background are relevant to anyone who needs to place an antenna. These values give you a clue, how far the "shade" under the air termination reaches - also known as the LPZ0b, see the next chapter.
If unsure what your LPS class is at a particular site, be careful = brace for the worse case.

• LPZ0 a = unprotected outdoor space
• LPZ0 b = outdoor space partially protected (shaded) by a taller nearby LPS air termination.
  LPZ0b is the preferred zone for installation of antenas!
• LPZ0 c = a zone around buildings, looking like a tunnel, defined by 0-3m vertically above terrain and 0-3 m horizontally adjacent to the outside walls of the building. It is related to potentially dangerous levels of step/stride voltage and touch voltage. See the picture above. LPZ0c is a little tangential to the topic of this howto, mentioned only for the sake of completeness.

To define the reach or coverage of LPZ0b, there are two methods: the older cone method and the newer rolling sphere method. See the two pictures below.

LPZ0b using the older cone method

LPZ0b using the modern rolling sphere method

A tall brick and mortar building, including an explanation of separation distance

Q: Can I ground the antenna to the outside LPS?
A: Absolutely not! Read on for details (separation distance).

What's wrong with the antenna? Well in 2D, it doesn't heed the separation distance sketched in that same picture :-)
Which will be explained below.

Safe separation distance means, how far away from the outside LPS it is safe to place... whatever it is that needs to stay out of harm's way. Such as, an antenna on the roof, or stuff inside the building.
The point is, that the outside LPS itself becomes live during a lightning strike. The downconductors have a resistance, which means that gentlemen Ohm and Kirchhoff attend the party thrown by Mr. Ampere, giving rise to some ugly Volts as a product of the lightning current. Worse yet, the LPS also has an own inductance, which means that Mr. Henry tends to steal center stage for a few microseconds right at the start, where he merrily launches the unpopular Mr. Volta through the ceiling... producing an ugly voltage pulse, corresponding to the leading edge of the lightning current, where the Δi/Δt is the steepest.

The canonical/codified formula to calculate safe separation distance seems largely "empirical".

It incorporates a combination of three coefficients:

• k_i is derived from the LPL / LPS class (this is the inductance-related coefficient)
• k_c called a partitioning coefficient, depends on geometric arrangement of especially the downconductors. For large buildings, it requires some complex calculation. There's also a simplified approach, depending on the number of downconductors installed around the perimeter of the building:
  1 downconductor: k_c = 1
  2 downconductors: k_c = 0.66
  3 or more: k_c = 0.44
• k_m depends on material composition. The air is easy, its k_m is defined to be 1 - but walls are tougher to judge. Inorganic building materials have a lower k_m (e.g. concrete = 0.5), resulting in greater separation required (as k_m is in the denominator). The Dehn Bible mentions some examples, where the aggregate k_m ends up somewhere between 0.4 and 0.6.

Looking at the ballparks of the three k's, we can try estimating the approximate ballpark of the overall coefficient:
10 cm of separation distance per 1 m of downconductor length?
Sounds about right... I've actually seen examples where the number turns out lower, within a decimal order. Those were not examples for tall buildings, exposed radio towers on mountaintops, ships cruising high seas etc.

In the Dehn Bible, you'll find "safe separation" detailed on pages 150 - 156.

I have one other concept that I decided to show in this example: what an "earth termination" often looks like. It typically consists of metal conductors, round or flat at the cross section, buried in the earth. Typically combined (interconnected) with vertical rods rammed deeper in the earth at regular distances. Construction details get determined by a licensed design engineer and are a part of the construction project documentation.
In my practical observation, at least a loop of flat zinc-plated steel conductor (say 30x4 mm) gets buried around a family home, connected to the vertical downcondutors and inner PE.
Stainless steel is also popular - while promising in terms of longevity in the wet earth, it has significantly worse resistivity, and therefore requires a larger cross-section at the backbone of the system, compared to FeZn conductors.
New developments nowadays should have another loop of flat conductor buried in cast concrete in the foundations. This one is not to function as earth termination (concrete is not a good conductor) - rather, it serves/aids the general goal of equalization of potentials throughout the building. Obviously this "steel band in the foundations" also needs to be connected to the central PE busbar (= equipotential bonding).

In the context of the example brick-and-mortar building, the choice of the equipotential bonding interconnection point is hopefully obvious: the node "at the earth termination terminal" will be free of the LPS downconductor's own resistance and inductance (in the path of the lightning current) and will be just the realistic potential where to "equipotentialize" the building as a whole, relative to the background earth potential.

While brick-and-mortar buildings typically have the central PE busbar and equipotential bonding interconnect at the base, other building constructions or industrial structures may use a massive steel skeleton or body as a natural down-conductor with negligible resistance per meter, which turns such a metal body into a near ideal protective earth wherever you need it. But, caveat, you should ground your outside antenna (etc) preferably straight to the massive body - not to dedicated LPS air termination components, or other outside metal structures that can be suspected of having a contact resistance to the building body (and are at risk of a direct hit = reaching outside of the LPZ0b).
Note that this last paragraph about building construction is my own lay man fabulation, you need to verify this on your own. Maybe more importantly, different buildings (or vehicles, or industrial structures) have different constructions, different applicable legislation, different internal safety guidelines, different recommended grounding styles. When approaching a particular location, with an intention to install an antenna, ask around - contact someone in the know or in authority to tell you how things are done and how they shall be done.
Informally, during preparation / a personal survey of the site, look around how others at the site handle lightning protection. Chances are, that they know what they're doing - especially on radio towers or ship masts. Then again, beware that modern-day carrier-grade outdoor radio technologies are transitioning to fiber optical cable for signal transmission. The traditional coax downlink is getting rare. Don't be fooled by absence of arrestors on fiber-optical cables :-)

Some sources suggest, that reinforcement steel in the concrete of modern developments (new buildings) should also be equipotentially interconnected, and some seem to go as far as suggest, that these can be used as a plausible quality natural lightning conductor.
Personally, I am very skeptical about this. As far as I know, for the general case, the meticulously spaced rebar in reinforced concrete is not strictly welded together, by default it is just tied together by snippets of twisted wire, not to collapse or get displaced during casting of the concrete. After the concrete crystalizes ("cures"), structural rigidity / coupling is typically achieved mostly based on the criss-crossing and overlaps of rebar in the concrete monolith. While it is possible to measure resistance at any time, the rebar inside monolithic reinforced concrete is no longer accessible for visual inspection of continuity. How this mixes with the requirement for regular inspections of the LPS, I don't know. How safe a bet it would be, that this electrically loose mesh of wire-wound rebar in cast concrete would work as a reliable natural down-conductor... I don't know. On the contrary, I can imagine how a lightning current that has found a path through the loose rebar mesh can make concrete explode in places, thus putting the very structural integrity of the building in jeopardy.
So unless the building has a solid steel "skeleton" designed that way, and preferably accessible for visual inspection, I would default to treating "monolithic reinforced concrete" as a general "brick and mortar".
It is true that manufacturers such as Dehn make certified fixtures that can be used as "surface terminals" for deterministic access to the natural ground conductor comprised of the interlinked rebar in cast concrete.
I cannot exclude that it's possible to use rebar in monolithic concrete as a natural lightning conductor, provided that the construction is designed that way, that the rebar assembly team is tightly supervised during construction, so that redundant key sweet spots get reliably welded together, and this is documented day by day, node after node, for the purposes of later LPS inspections...
Still, how this fits together with the general goal, to avoid resistive build-up of voltage along the lightning conductor path... To avoid any concerns about Mr. Kirchhoff playing hide and seek in the rebar mesh upon a lightning strike, the mesh would have to comprise a really thorough Faraday cage. Sounds... too good to be true?

A skyscraper with a thorough steel skeleton

A skyscraper - detail

Q: Can I ground the antenna to the outside LPS?
A: Not to the LPS! Do not ground the antenna to anything that serves the primary purpose of attracting and conducting lightning.
If you're absolutely sure, that the building has an inherent and massive natural ground, also serving as a local ad hoc Protective Earth, it is probably safe to use that - but, avoid connecting to outside hardware that is specific to the LPS.
If unsure about the grounding and LPS arrangement of the building, try to keep at least some level of isolation/separation of the antenna from any existing outdoor metal, which is likely connected to the outside LPS.

Suppose that the classic skyscrapers with a welded or riveted steel skeleton can easily conduct lightning strikes through that skeleton without breaking a sweat.
I know for a fact, that getting an antenna placed on the rooftop of such buildings is "difficult to achieve", in terms of getting approval. But suppose that somehow this is not an issue to you, either.
Suppose the building has suitable "earth terminals" on the rooftop, exposing the earth of the humungous steel skeleton of the building. That's where I would dare to earth surge arrestors. I would expect there to be a "building entrance wiring cabinet for signal cabling", where all the surge arrestors could be co-located in a rain-proof environment and properly earthed, to a terminal or busbar prepared for this particular purpose. I've actually seen one such box on one local highrise.
Try to find out (ask around), how inner PE in any possible "datacenter rooms" near the rooftop are created. Where is the equipotential bonding point, relative to the steel skeleton of the building, where the local PE branches off. This bit of information is key to subsequent conclusions about "safe separation distance" about the place.

I'd hazard a guess, that it wouldn't make much sense, if your antenna is on an "antenna mast" a couple (dozen) meters above the roof / top deck, to bring your very own earth conductor all the way to the antenna. At the same time, I would not quite dare to ground the antenna to a mast that also serves as a natural air termination + ownconductor - unless the cross-section of the mast would be reassuring, and it would be preferably welded to the building's steel skeleton. Bolted connections, while mechanically robust enough, may have contact resistance, and these high-up places are very exposed to direct lightning strikes. An antenna mast this high up is a "lightning magnet".
In general, look around, and do as others do. Improperly connected gear won't survive very long in such places.

There is one specific scenario, where antenna masts are a plausible ground: if the mast is "covered" by an isolated air terminator, erected enough above the end of the mechanical mast, and keeping safe separation, by distance of the bare parts and possibly by a layer of insulation/dielectric on the down-conductor cable. Another condition is, that the mast must be grounded to a plausible "inner" PE. Such as, independently of the LPS, to the massive metal skeleton of the building.
For more inspiration, there's another chapter below, trying to focus on various problematic scenarios - its very first example demonstrates this setup, albeit on a small "brick and mortar" house. By geometric dimensions, a small family home is fairly comparable to an antenna mast on a highrise (using the building's masive skeleton as a GND reference).

In general, true highrise buildings tend not to have outside lightning downconductors. Even for mundane buildings such as individual family homes, there are dedicated components to build a downconductor hidden behind the surface of the facade. And, there's probably a way to arrange this inconspicuously using structural components of the outer shell of modern highrise buildings clad in glass. In any case, the outer surfaces of a highrise (above rolling sphere radius) have to be protected by "air termination" of some sort, as the space outside the building is LPZ0a.

While synthesizing this skyscraper chapter ouf ot thin air, I've tried googling a bit (1|2) on the topic. Which has yielded two somewhat interesting finds:

1. a YouTube video, where the speaker explains how safe separation distance is a problem in highrise buildings, if conventional downconductors around the perimeter would be considered = and recommending natural downconductors integral to the building's structure, as a solution. Provides some serious food for thought, about IEC 62305 vs. highrise buildings. (The same video mentions some cute real-world problems faced by the designers in actual customer scenarios, at round 1:00:06.)
2. a conference paper, focusing on the behavior of a glass facade (its metal support structure) upon a lightning strike, depending on the availability of a mesh of natural downconductors in the skeleton of the building.

I haven't found anything about the classic skyscrapers that stand hundreds of meters tall. But, clearly their builders must have their own idea, how to go about lightning downconductors and air termination. Any feedback/insight on this would be warmly welcome.
From the perspective of IEC62305: it is possible to use isolated downconducting paths, using high-volt cables with a thick layer of dielectric. But, making the downconductors separate from the building, with a bonding node at the base, would only exagerrate the safe separation problem. Such a downlink's upper terminal above the rooftop would need dozens of meters of separation, and would not provide cover for the surfaces of the side walls of the building. Noone has ever built a skyscraper wearing a sort of a hat with a funeral veil (mesh) around the top.
I've found several sources claiming that buildings above 60 meters of height (about 20 floors in my small-town circumstances) must have their upper floors protected against direct sideways strikes, which is perfectly consistent with the rolling sphere model (maybe even diluting it a bit).
Actually the k_c constant in the safe separation formula seems to provide a "way of reconciliation" of IEC62305 with tall buildings, and what the practitioners seem to suggest: you need a dense enough mesh protecting the surface of a tall building, and a good quality natural downconductor mesh in the building's skeleton, the two of them interlinked. An imperfect step in this direction would be an outside surface mesh, i.e. with downconductors interlinked by "rings" e.g. at every floor level (also mentioned by some sources). The system needs to provide surface coverage, and relatively very low resistance across the enormous height of the building, and, anti-inductance measures = parallel wiring of downconductors around the perimeter and inside.
The inductance aspect is important. E.g., a single downconductor at the center of the building would not be a very good idea, as it would not provide good cover at the perimeter, and its single path of the pulse current would create a perfect concentration of magnetic field inside the center of the building, where power and signal cabling and pipe networks of all sorts are concentrated, including elevator shafts for instance. A robust mesh, spreading the current, would spread the magnetic field, and would minimize top-to-bottom resistance. Break down Mr. Kirchhoff and Mr. Henry into a pile of equal and small finite elements.

Still, interestingly to me, there are numerous sketches on the web, suggesting a classic setup with multiple downconductors, not even horizontally interlinked, on a highrise, with a single equipotential bonding node at the base - yet the resulting problem with safe separation is not mentioned.
To me, this is another proof that the IEC/EN 62305 can be a pain in many different scenarios, where it deprecates legacy practices :-)

Where I live, just as I'm typing this text, I have a view out of my window, of some rooftops on neighboring buildings:

Note how the LTE "antennas" (outdoor units) are mounted on additional masts. As far as I can tell, only on the tallest building, the masts have an extra "air termination extension" - a piece of rod, directly attached to the mast, the rod reaching about 1 m above the upper end of the antenna "cigars". The LPS air termination and downconductors are unlikely of the isolated/distanced persuasion.
I am told that 4G (LTE) outdoor units use fiber optic for their data link to the base station. Thus, the outdoor unit only needs metallic cabling for power supply, which is relatively easy to protect by arrestors.
I haven't been on those rooftops, I don't know details, all I know is that this particular block of buildings, the tallest in the neighborhood, regularly score a hit during every self-respecting thunderstorm passing across our city.

I've tried to find something about the legacy/original reference solution of LPS on these buildings. There have been several generations during maybe 2 decades... Google finds mostly complaints from people who need to address the LPS during a reconstruction, or when adding something on the roof, only to find that the legacy LPS is either not certifiable to IEC/EN 62305, or just plain broken / defunct even by the previous standards, and difficult to revamp to pass contemporary inspection.

On the outside, I can see that some of buildings of this type are missing external downconductors. I've found notes that "natural" downconductor construction is an option (using rebar, elevator shaft rails and whatnot), that this type of LPS design can be used during a reconstruction (it is one way to satisfy the EN62305), that it may require vertical pipelines in their shafts deep inside the buildings to be refurbed to make them nominally capable of conducting lightning currents...
Either that, or the building may have just one or two legacy external downconductors that I have missed while casually walking around.
As for rebar, these commie-era buildings were assembled on site out of flat prefabricated panels of reinforced concrete, and the panels had rebar eyes for crane hooks and specific "rebar-attached steel interfaces" for welding the panels together on site. I don't have further details, but chances are, that the "faraday cage of rebar" can indeed turn out to be half decent.

And then I've found a reference project in PDF, from a local branch office of Dehn, for this general type of panel buildings. The Dehn design proposes using HV-isolated downconductors around the perimeter, obviously to reduce the "safe separation distance" required - and air termination is only constructed above the roof, safely separated by plastic (fiberglass?) vertical spacers. My impression: this way of tackling the "safe separation distance" on the perimeter walls is obviously also correct, and permitted by the fact, that these buildings normally didn't exceed 40-45 m of height, so that sideways air termination (protection of perimeter walls) is not required.

A tower of steel

Q: Can I ground the antenna to the outside LPS?
A: Not to the LPS! Do not ground the antenna to anything that serves the primary purpose of attracting and conducting lightning, even if it's "equipotentially bonded" a few meters away to the massive steel body.
It is relatively likely, that any massive steel construction in a radio tower will be well grounded, and used to branch off a local PE where needed. While you probably won't be allowed to weld your own nut/terminal to the steel body of the tower at any point of your choice, probably, around antenna masts / mounting places, protective earth terminals should be available, or the local mast itself will be covered against a direct strike by "dedicated air termination". Depending on how well the tower is managed anyway. Typically, antennas tend to sprawl at such places during the years, and the exponential grassroots growth may pose "challenges" to site management...

A tower - detail 1

A tower - detail 2

I've promised some word of mouth... an old practitioner has mentioned to me, decades ago, that at such locations (towers), a single coaxial arrestor was not enough. Two of them in a cascade were allright. One "at the top" near the antenna, another one "at the bottom" = at the boundary/entrance from LPZ0 to LPZ1. Both arrestors were the direct-earthed variety. Where did he ground the upper arrestor? That's probably anyone's guess... but it would be a good spot to ground the antenna, if it has the option.

To close the chapter on a light note, let me add a few photoes of some existing large TV transmitter towers in the region.

All the photoes come from Wikipedia - they're clickable and that's where the links point to.

I haven't tried to make the collection of photoes more diverse, yet I'm sure that the spectrum of sizes, shapes and constructions of radio towers is probably vast.

A ship - from a distance

So much for an overview picture.
Our antenna is comparatively so small, that it doesn't seem fruitful to me, to attempt a simplified sketch at this resolution.
Let's zoom in on the upper decks and the bridge:

A ship - the bridge up close

As you can see, my sketch is still heavily "schematicized" - I don't intend to reconstruct a realistic section through the interior of a bridge or "Computer/DC deck" or whatever its name actually is.
I will zoom in one more time, for those of us whose eyesight is no longer razor sharp (mine is definitely not). I hope you get the idea...

A ship - detail

Q: Can I ground the antenna to the outside LPS?
A: Not to the LPS! Do not ground the antenna to anything that serves the primary purpose of attracting and conducting lightning, even if it's "equipotentially bonded" a few meters away to the massive steel body.
Other than that, if the "massive body of welded steel" is true, you can probably ground your arrestors and your antenna pretty much anywhere suitable. Anywhere where you don't inherit some contact resistances shared with the path of the potential lightning current.

No photoes in this chapter - no suitable objects in my area :-)

I'm wondering if there are any marine electricity/safety norms that would have a say in this scenario. Talkback welcome.

A substation

A substation

Placement "A" is good enough for undemanding applications (NTP and the like). Still the antenna should at least see above the rain gutters, to see a wider angle of the sky above the sloping roof. If there's no better option, placement "A" works half decent even for high-performance timing (PTP and other tech at that level), where placement "B" is generally more appropriate - again with an optimal view of the sky as an optimization criterion.

Placement "C" is with a question mark. How real vs. silly this is, that depends a lot on the particular arrangement of the buildings, pylons, power electric gear etc. about the facility. In the configuration that I've sketched above, and deliberately exagerrated the troublesome points a wee bit to make them clear, placement "C" does not seem very fruitful or safe. Your customer may call it "out of the question" for very particular reasons (norms for substation design and safety). In a substation, the 400+ kV lines can be just a few meters above ground, safe distances are squeezed as close as realistically possible...
In a different scenario, the overall merit may possibly lean in favour of variant "C"... it really depends.

Q: So: can I ground the antenna to the outside LPS?
A: Not to the LPS! Do not ground the antenna to anything that serves the primary purpose of attracting and conducting lightning.
Long story short, the internal PE is your earth of choice for surge arrestors and theoretically also for outside holders and antenna, all in LPZ0b, if distant enough from the outside LPS.
The building in my sketch (and in my reality) is "brick and mortar", typically having just a ground floor and an attic under the sloping roof. At that modest height, "safe separation distance" is not extremely painful, so you probably won't see insulating spacers or some such high end measures as part of the outside LPS. The building is a low-end case of the brick and mortar example above. I also have some troubled cases in a chapter below, relevant to this scenario.

There is one particular aspect, where my sketch above is admittedly unfair / not entirely correct: I have depicted the pylon and the building as each having its own earth termination.
In actual reality, this is just not true. As a rule, substations of any kind have an underground "earth grid" spreading allover the place:

An on-premises substation grounding grid
The picture is actually fake, sketched by me, resembling an actual design.
For real-world examples, try Google images.

An orthogonal grid made of steel bars, each bar several hundred mm² cross section. Across the substation site, the grid varies in density, to satisfy several design criteria. There's a minimum density, and additional links get added around power devices, pylons etc. Around each house (brick and mortar or otherwise), there's a dedicated "ring", in addition to the background spacing of the basic grid. A house needs to be connected to the earth grid by at least two links. The same apparently applies to pylons and smaller support structures. Transformers need to be earthed by four links to the earth grid. Also note the additional ring just outside the perimeter fence.

The primary purpose of this grounding setup is not lightning protection. The point here is, operational stability and safety of the substation under load and during failure events.
In our reality, the 440kV AC high-volt lines normally carry some kiloAmps continuous AC current. During failure events, the fault current can be in the tens of kiloAmps. This is what the substation is designed to handle non-destructively = disconnect such current when a failure is detected. The earth grid is dimensioned to take the fault current without melting. Even in a correctly designed earth grid, buried in the earth, the bars forming "path of least resistance" of an accidental fault current can heat up to a couple hundred °C within seconds of the failure's duration. After that, the protection relays should trip and disconnect the overloaded direction.
Another role of the earth grid is to reduce step (stride) voltage during a failure event, so that human personnel at the substation doesn't get hurt.

Another obvious and desired effect of the earth grid is: minimized resistance against "background earth". Obviously the net result also depends on soil resistivity and the underlying geology. Lowered resistance to background earth translates into a lowered voltage difference and gradient upon a HV failure or a lightning strike. Yet, reportedly, the residual gradient is still harmful to any fauna living in the soil in or around the substation (rodents, worms etc).

All transmission and distribution substations have this uniform earth grid. Only railway traction power substations are a notable exception: reportedly, the railway traction side earth must be separate from the "mains" substation side earth grid. This is to avoid the railway return current from mixing with the mains earth. Probably a factor especially in DC traction, where you want to avoid a "DC bias" in the huge AC transformers.

Reportedly, any group of buildings and structures that comprises an industrial plant or facility, should also have interconnected earth. Not just in the electric energy business - any sort of industry. Arguably, something like a warehouse district with no substantial machinery won't need as much focus on grounding as... say... a heavy industry area hosting a century worth of coke production, iron smelting, steel metallurgy and rolling, stamping and welding...

Does the presence of an outdoor earth grid make any difference as to antenna placement and grounding, as suggested in the "substation sketch" at the top of this chapter?
I suppose it doesn't. Doesn't make "variant C" any more appealing. Voltage gradients occuring upon a lightning strike or HV failure do indeed get diminished, but unfortunately not eradicated completely. Also, loop area matters - will be debated below. If possible, avoid making the coax downlinks too long outside the building, especially in this particular environment.
After all, the people managing the site will probably have an opinion.

Don't despair, all hope is not lost, as long as you can get at least the earth termination sorted = use an existing one, or implement a minimal new earth termination setup. The Dehn Bible on page 292 mentions a few versions of a minimum earth termination, including dimensions
From there, in the minimal variant, you can cater for your modest antenna mast added on the roof and be somehow done with it. Read on for details.

If you ever face a building, that has no LPS and no proper earth termination, and there's no chance of making some proper earth termination of your own, your best option unfortunately is: retreat. Run away. Not worth the responsibility.

Apparently there are a number of people, e.g. among WISP's, who just don't care. Install the outdoor unit, plug in the CAT5e carrying data + PoE, and run. If this is on a roof, the WISP has probably just clamped the ODU to the only existing antenna mast up there, that also doubles as the tallest air termination of the outside LPS. After all, this is how it's been working for decades.

I am deliberately abstracting from scenaria, where you just tuck your antenna outside a window in a deep LPZ0b, maybe ground an indoor arrestor to the PE in a wall socket and go home. That will hopefully work for many applications (in Meinberg parlance, it might as well get NTP started, eventually), and won't require installing cables across several floors in an existing building.
For such cases, you don't need to read this howto.

On to some modest/basic examples:

This setup is promoted by Dehn - see the Dehn Catalogue on page 19, and also the Dehn Bible on page 294, the two pictures at the bottom. It scales to any sort and size of a building, limited only by the density of LPS-connected metal objects on the roof. It presumes that you can find a place, where safe separation of your mast and antenna is achievable.

If you actually do have an existing niche of LPZ0b, where you can place your own mast, safely separated from the LPS - that's an even easier situation: you don't even need to add an additional air termination rod.

Before I get to the point, please note, where the added antenna mast is earthed. That's right: to the inner PE of the buiding. And the conductor doesn't even have to be very thick.
Just to make sure that this point sinks in: as per IEC 62305, you can have metal parts on the roof, that are not linked to the outside LPS. Even more perplexingly, they may be (should be?) earthed to the inner PE of the building. Provided that they are located in a LPZ0b, created by an overhead isolated outside LPS, and that safe separation is maintained.

Q: So: can I ground the antenna to the outside LPS?
A: Not to the LPS!
Q: Allright: can I ground the antenna to my added antenna mast?
A: Yes you can :-) Considering where the mast is grounded... So the antenna holder need not in fact be isolating. Apply your own taste to the issue of a potential ground loop, which can theoretically affect signal transmission in the antenna downlink.

The Dehn Bible seems to suggest this on page 295 (the picture on the right). The original picture features an HV-insulated downconductor (a product of Dehn).
My emphasis: it would likely work with standard (non-isolated) outside LPS downconductor, and a physically separated air termination rod on plastic spacers.
My emphasis: the picture from Dehn does not mention downconductor cross section. I'd suggest a minimum of 16 mm² copper or about 50 mm² galvanized steel, as these tend to be the absolute minima for outside LPS downconductors, as per IEC 62305.

Effectively, the building gets a minimalistic and possibly deficient LPS, where originally it had none.

Note: the system needs an earth! If no existing earth termination is available, one needs to be constructed as part of the project. For inspiration, feel free to check the Dehn Bible on page 292.

As for our fundamental question, for this scenario:
Q: So: can I ground the antenna to the outside LPS?
A: To the minimal separated segment? No! Not to the outside parts, dedicated to conducting lightning.
Q: Allright: can I ground the antenna to the antenna mast?
A: Yes you can :-) The antenna holder actually needn't be isolated. Maybe give some casual thought to potential ground loops.

This setup comes from the Dehn Bible, page 295 (the picture on the left), repeated in a slightly different form in the Dehn Catalog on page 19, the bottom left picture.
Note how the earth system is no longer painted as an LPS in the Dehn docs. Probably because its parameters and "profile" are too deficient.

Note: the system needs an earth! If no existing earth termination is available, one needs to be constructed as part of the project. For inspiration, feel free to check the Dehn Bible on page 292.

As for our fundamental question, for this scenario:
Q: So: can I ground the antenna to the antenna mast?
A: Yes you can :-) The antenna holder actually needn't be isolated. Maybe give some casual thought to potential ground loops.

This is merely a relatively small variation of the previous solution #2.

In this example, the antenna installation team faces a building with no outside LPS.

And the suggested solution is, to run an inner Protective Earth, worth 16 mm² of copper, inside the building. The route should be straight, with no loops or even unnecessary meanders and bends.

No LPS, solution #3

This setup comes from the Dehn Catalog on page 19, the bottom right picture.
Note how the earth system is no longer painted as an LPS in the Dehn docs. Probably because its parameters and "profile" are too deficient.

Note: the system needs an earth! If no existing earth termination is available, one needs to be constructed as part of the project. For inspiration, feel free to check the Dehn Bible on page 292.

As for our fundamental question, for this scenario:
Q: So: can I ground the antenna to the antenna mast?
A: Yes you can :-) The antenna holder actually needn't be isolated. Maybe give some casual thought to potential ground loops.

Multiple stage protection in a building

Using two arrestors in a cascade improves protection = safety.
The first one sustains the (fraction of) raw lightning energy, possibly coming down the coax downlink, when a lightning hits near by. It may also help protect the active antenna's output.
The second one helps keep the tail end of the cable in a sane ballpark of voltage, especially against EM-coupled (inductive) effects of a nearby lightning strike. The arrestor clamps the resulting voltage to a level, that hopefully doesn't set the receiver on fire, doesn't blow through the receiver box and into Ethernet or other signal outputs, and if the gods are merciful, hopefully allows the sensitive antenna input to survive without damage.
Note that the primary purpose of the outside LPS and the signal-level arrestors is still to protect health and property against massive damage. A blown antenna input is comparably minor collateral damage that cannot be completely avoided.
That said, in my practice, coax arrestors typically succeed in protecting even the antenna input.

Let's take a look at the signal chain in a little bit more detail:

Antenna downlink signal chain / protection cascade, in detail

The issue of ground loops doesn't seem very painful. If in doubt, it's nice to try the second arrestor direct earthed vs. isolated, compare RX quality figures, see if there's a difference... Don't expect to find much.

In general:

for the 1.6 GHz band (and 1.2 as well), the wavelength is about 185 / 250 mm in vacuum, times 66%-85% in a coax cable. At high multiples of the wavelength, do not expect a loop to work as an efficient antenna. Also the attenuation of the useful signal is such, that any impedance mismatch effects (reflections, impedance transformation) won't work around loops spanning many dozen meters. Thus, at these high bands, the ground loop effects are unlikely to present a problem. Just use two direct-earthed arrestors in a cascade, if you need to, for safety reasons. This is also convenient in combination with receivers that don't have galvanically isolated input.

Speaking of the Meinberg 35 MHz band (35/10 MHz actually), that's where the length of antenna downlinks might play quarter-wave tricks with an external ground loop. This is also where the earth-isolated arrestors have some merit, given their often more limited bandwidth. If unsure, in the context of a particular trouble case (poor RX quality), feel free to try different arrestor setups. Don't expect to find too much of a difference.

It makes no sense to use and earth-isolated arrestor just before an antenna input on a radio that does not have input isolation = where coax shield is connected to chassis ground. If some energy comes down the antenna downlink's coax shield, it ends up finding its way through the radio, instead of getting guided safely away by a prepended arrestor.
A combination of earth-isolated second arrestor + isolated input on the radio has optimal chance of protecting the sensitive radio input. For radioes without input isolation, prepend a direct-earthed (second stage) arrestor.

Still, no matter how tightly you manage to protect the input, it is nearly impossible to protect against in-band RF energy. The arcing of a lightning strike produces lots of broadband RF AC noise (power), some of it in the band passed by isolators and even passband filters... this is nearly impossible to limit, without preventing reception or demodulation of the desired useful signal.

Some vendors produce "combined" arrestors with multiple stages in one package, for various types of signal. Unfortunately, protection factor with the finer arrestors often contradicts bandwidth.
To learn some practical internal schematics, check with the various vendors of signal-protection surge arrestors: Dehn, Phoenix, Saltek, ...

A spark gap glowing, during a continuity test using a few mA of current

A surge arrestor under test, using a high-current test pulse.
Click for a video (with audio).

The field "concentrates" around the point charge / small sphere.
And no, I don't mean "concentric arrangement of the linear scale". (Although that's what my Inkscape gradients actually depict. Well at least more of the scale is actually visible. For an alternative picture, check out the Dehn bible on page 20.)
For a more mathematically correct curve, behold the charts below. Generated in Maxima/Gnuplot and manually polished.

Votage (potential) and field intensity (gradient) in an X/Y plot
Horizontal axis: distance from charge center (spherical radius)
Vertical axis: blue: Voltage (potential), Red: intensity (gradient)
The sign (polarity) is subject to a further debate...

Around a point or spherical charge, the scale of potential (Voltage) actually becomes hyperbolic: 1/r (times a constant). Where "r" is a radius, a spherical coordinate, starting from 0, but practically bounded by the outer spherical surface of the electrode. In a spherical electrode with a non-zero radius of its own, the hyperbolic curve "virtually" starts descending from the ideal center, but only actually materializes starting from the surface of the electrode (outward). Thus, other conditions equal (the same Q = charge), a larger spherical electrode produces a lower surface Voltage. But the rest of the hyperbolic curve = potential fading out into 3D space is the same. Which also means that the E = field intensity = gradient, slope of voltage (ΔV/Δr), starts at a lower value, around a larger object.

I may later try to infer some reasons for the hyperbolic curve, but for the moment, let me focus on some interesting consequences:
The "gradient" AKA field intensity, labeled capital E, being the slope of potential (voltage), becomes even steeper 1/r^2.
And, because neither the hyperbola, nor its quadratic 1st derivative, are defined for a distance of 0, an ideally dimensionless point charge is really not possible. Some sources of wisdom actually use a single subatomic particle as a minimal example = where our macro world meets quantum mechanics.
Also, "the other electrode" or "background" seems to be where the V = 1/r hyperbola reaches a V=0, which happens asymptotically at r = infinity.

Paradoxes of infinities aside, the effect of the field concentrating around small charged objects has interesting practical consequences.

The more energetic experimenters may prefer Tesla transformers. For maximum show, these devices tend to feature spiky electrodes, giving mighty visible coronas... or long jagged sparks.

Dangerous toys...

This is also why lightning collector rods ("air termination" in modern newspeak) often have a sharp tip. This turns them into nature-favoured candidates for a grounding point for any lightning looking for a spot to hit. The precise mechanism is, that as the overall gradient from the sky intensifies (while the downward leader is getting closer), the tallest and spikiest objects attached to ground are the first to surround themselves with the sort of gradient to break the air's isolation strength, and therefore have the best chance of starting a corona, eventually overgrowing into an ionized upward-growing "welcome channel", which effectively extends the spike-tipped air termination rod further up.
In that sense, apologies for drawing my "air termination rods" with a small cartoonish ball at the tip. "How large is still small" is relative :-) It is just an illustration.

The math that can be used to describe and understand these phenomena turns out to be surprisingly simple and straightforward, combatible using high-school level knowledge.
Don't be intimidated by the number of symbols in the formulas below, it really boils down to just a few variables, a handful of constants, and a wee bit of extra complexity to account for non-ideal geometry in real life.
To give credit where credit is due, AFAICT, the formulas come from publications by gentlemen Rosa and Grover.

Essentially, even a section of straight wire has inductance. It may be difficult to independently measure, as by attaching probe wires, you form a loop - but it's probably safe to believe the wise men who have coined the formulas for us...
So: a straight wire has inductance.
Two straight wires in parallel therefore share a part of their surrounding magnetic field, thus comprising a transformer. Albeit a non-ideal one. The point of this chapter is, to put our finger on what "non-ideal" may practically mean, and the ballpark of what voltage can result at the secondary side.

Let's get to the first formula. Let's start with coupling between two parallel straight wires (AKA filaments, in the source literature).

Mutual inductance of parallel wires

The wires in the formula are considered ideally thin = wire diameter is not reflected.
The two input variables are:
l = length of either wire, they're both the same length
d = the spacing between the wires.
As for units, both inputs are expected in meters.
The output that we get is an inductance, in units of Henry. A so-called mutual inductance, between the two "windings" (wires) of our transformer. Mutual, hence the letter M.

μ₀ is the permitivity of vacuum (air has almost the same) = constant, the π is a constant too. The point so far should probably be, that a large ratio of l/d results in a high mutual inductance.

Yeah right... inductance between two coils... where are we going with this?

So the next step is, that the mutual inductance plugs into a formula for a so-called "coupling coefficient" between two inductors:

And if the two inductors are the same, we get:

The coupling coefficient k is a unitless ratio on a scale of 0 < k < 1. And indeed it seems to translate approximately, into how much voltage (or current?) you get on the output of a non-ideal transformer, with a transformation ratio of 1:1 (turns ratio). Except I've never seen its purpose defined that way - we'll get back to that.

Oh wait... where do we get the own inductance L of a single straight wire?
That's simple: there's another formula from gentlemen Rosa and Grover.
If this gives you a deja vu, you are probably right. In their publications, the two formulas are "on the same page" (or thereabouts).

Self-inductance of a straight wire

The two input variables are:
l = length of the straight wire
ρ = radius of the wire
As for units, both inputs are expected in meters.
The output that we get is a plain old inductance, in units of Henry.

In practical terms, 1 meter of a wire can have roughly 15-20 microHenry of own inductance (depending on how thick) and two such wires spaced 10 cm apart will have about 8 microHenry of mutual inductance.
All of that combined results in a k of about 50% .
And because it's l/d that matters most, you get a similar result e.g. for length = 10m and spacing = 1 m.

Here you are an Excel table for some "back of an envelope" calculations...

50 per cent... sounds spooky or what? Where does frequency or slew rate come in the game? How do we get to some voltages, finally?

I've ended up simulating the behavior of a lightning down-conductor in Qucs Studio, using its "file-based current source" element.

To us near the ground, lightning behaves a lot like a current source. Typically not a constant current, but given. The difference of potentials between GND and "somewhere up in the clouds" can be a couple hundred million Volts. Once the arc strikes, having found a path through a couple hundred meters of air, that it had to ionize first, resistances in the LPS in the units of Ohms (or thereabouts) don't make a difference to the current flowing our way from the accumulated charge up above, possibly draining additional nearby clouds of charge available up there. Our earthly resistive and inductive effects therefore transpose directly into voltage values.

After an initial tuning of the simulation setup and seeing the first results, I've sketched the following explanation of what's actually going on, as some of the details are not obvious from the QucsStudio output (e.g. the current waveform is not in the raw sim charts).
Only in the later stages of redacting this howto, I've found this same picture in The Dehn Bible on page 21. Speak of reinventing the wheel, sheesh... well at least I know I've done the maths right.

An explanation to the following sims. (Note: the colours here have different meanings.)

The raw content of the input CSV file (current waveform) looks like this:

0;0
5e-6;0
1e-5;0
1.5e-5;5e+4
2e-5;1e+5
3.7e-4;5e+4
7.2e-4;2.5e+4
1.16e-3;1.25e+4
1.51e-3;6.25e+3
1.86e-3;3.125e+3
2.21e-3;1.5625e+3
      

To have the simulation produce "nice" output, I specified L1 = L2 = 10 uH and a coupling coefficiet k = 0.4 - as can be seen in the schematic screenshots.

Simulation #1 schematic: inductive only (the downconductor has 0 ohms resistance)

Simulation #1 result plot: inductive only (the downconductor has 0 ohms resistance)
Blue: voltage at the primary side hot end (LPS air termination)
Red: voltage at the secondary side open ended
Timescale: 1 ms (upper chart), 50 μs (lower chart)
Unit of vertical axis: Volt

Simulation #2 schematic: inductive with resistance in series

Simulation #2 result plot: inductive with resistance in series
Blue: voltage at the primary side hot end (LPS air termination)
Red: voltage at the secondary side open ended
Timescale: 1 ms (upper chart), 50 μs (lower chart)
Unit of vertical axis: Volt

The Dehn Bible actually mentions this scenario on page 21. It also quotes a conveniently simple and straightforward formula, making direct use of the "mutual inductance" (M):

Arguably, it can hardly get any simpler than that :-) Probably the best clarification of what the mutual inductance is good for.

On the same page 21 with the formula, the Dehn Bible has a convenient nomogram, giving you the values of M for various geometrical arrangements of the LPS downconductor (straight wire) and an arbitrarily placed wire loop.

In various low-profile websites I have observed a corresponding formula along these lines:

That seems even simpler than Rosa+Grover.

All the formulas in this chapter are in SI units, BTW = meters, Henrys, Volts, Ampers, seconds.

A secondary loop taking energy from a primary wire has one interesting property: the turns ratio is greater than one. This setup transforms voltage up.
The Dehn Bible on page 21 also has an example calculation, where the voltage levels seem to come out correspondingly higher than my guesstimate above for parallel wires.

The Lightning Protection Guide by Dehn.
Should the link drop dead, here you are a local copy for historical reference.
The book, currently at 3rd edition, is almost 500 pages long, and deserves a list of references to particular pages. Straight from my scrapbook:

Page	topic
15	Chapter 2: what is lightning
20	Gradient of voltage in earth, depending on distance from the point of lightning strike
21	Induced voltage in conductors (loops) in the vicinity of a lightning path
34	Flash density stats in Germany (a map)
54	Kirchhoff's Law, demonstrated on the outside lightning downconductor network (mesh)
64	LPS architecture (the Parthenon picture)
64-68	Rolling sphere (dimensioning criteria on page 25 and 90 too, including mesh size)
69-71	Cone model
73	Sheet metal thickness preventing puncture
75	Isolated (separated) air termination rod
95	Downconductors - spacing
97	Downconductors - maximum temperature rise, based on material and cross-section
104	High-volt isolated downconductors
119	Step/stride voltage gradient in earth
122	Resistivity values for different soil types / geology
128	Earth resistance examples based on soil types and termination length
122-129	Earth resistance and resistivity, in general
149	Dimensioning of earth electrodes
150-156	Separation distance (the reference on page 102 is related to HVI conductors)
178	Equipotential bonding at the base of the building
187+	Protection of electronic systems, LPZ, 62305-4: chapter 7 starting on page 187
199	Avoiding GND loops between buildings
292	Minimal parameters and practical construction of earth electrodes
293-295	Example: Antenna on a roof, with an isolated/separated "air termination", and arrestors grounded inside
345-349	Example: LPZones on a wind turbine
358	Example: LTE radio tower
371	Rolling sphere method versus protective angle method for determining the protected volume (the bottom picture)
452+	Yachts

The page numbers refer to PDF file page numbering. The numbers in print are off by one.

The Dehn Catalogue of Lightning Protection / Earthing
Should the link drop dead, here you are a local copy for historical reference.

Kniska is a publication in Czech language by Jan Hajek of Dehn CZ and Dalibor Salansky of LUMA Plus s.r.o.
Written in casual style, but thorough, I hardly dare to call this an introduction.
Obviously a promotional material, but nice. Contains some interesting pictures/examples that I haven't seen elsewhere.

The formulas on conductor self-inductance and mutual inductance of two straight wires come from a somewhat ancient source:
A book by Frederick W. Grover, called Inductance Calculations: Working Formulas and Tables.
It has been re-printed several times since its initial publication in 1946.
Apparently, there are prints in the public domain that predate the book: bulettins of the Bureau of Standards from 1908 and 1916, co-authored by Frederick W. Grover and Edward B. Rosa. They were colleagues and collaborators, and F.Grover took over the torch after E.Rosa died in 1921.
The formulas as published in those original prints did not pay much attention to mentioning the physical units used for input and output - apparently, centimeters and nanohenries were a popular choice. The formulas as quoted in this howto have been scaled to SI units (meters and Henries). It is not surprising that Grover and Rosa originally did not stick to SI units in their day and age, as the SI system has only been standardized in 1960.

Dimensioning of earthing system in HV switchgear
-- a master's thesis by Roman Bursik. The paper is in Czech (unfortunately for the global audience).
Contains a neat example of a substation earthing grid on the very last page, and e.g. a table of resistivities for various types of earth.

Regarding the substation grounding grid, I've been pointed to this by a friendly commentard in a benign forum on... system administration :-)
Apologies to my global audience, the linked text is in Czech.
The nick M D is not unknown to me in real life - a seasoned practitioner in substation automation, well versed in the High-Volt side of things and in industrial IT+networking. In that IT forum, upon my off-topic troll prompt ;-) he didn't hesitate to initiate me and the rest of the audience. He started by explaining various things relatively on topic, quoting from the IEC\EN 62305, and upon my prompt, went on to refer me to some intra-corporate norms of our domestic utility companies in the high-volt business...

Etc.

I recall several other fleeting conversations with people I met on random occasions during the years:
Jiri Janda sr. of JJJ-sat, who used to sell and install TV+SAT gear back during the nineties...
Several people in the electric power transmission and distribution companies (our customers at FCCPS)...
Electricity inspection engineers who come regularly to give us training...
Etc.

This scribble by: Frank Rysanek (rysanek [AT] fccps [dot] cz) (8/2023)