Estimating the Effects of Lightning on Antennas
Parameters can be used to model a typical strike in order to estimate the coupling and illustrate effects.
KEN RAINA,
G. M. KAUFFMAN, Co
Introduction
It is important to estimate the effect of lightning on a typical antenna system in order to determine risk of damage, and estimate the requirements of a suppressor capable of meeting that threat. What is presented here is a simplified method for sizing the risk, and a method for determining the appropriate parameters for a surge suppressor. While this is to show typical effects, it should be noted that it is common practice to select a suppressor with approximately ten fold safety margin, due to inaccuracies in modeling these types of events. Also, since the model presented here does not include direct column or branch attachment effects, this does not show worst-case conditions, but rather reasonable design levels useful where safety is not involved.
The effects of lightning on modern antenna systems originates from two primary sources:
1.
E field coupling into the exposed antenna.
2.
Current injection into ground, including man-made structures such as towers.
Table 1.
Parameter |
Magnitude |
E Field |
500 kV/m |
Peak Current |
90 kA |
Pulse Width |
20 us |
Voltage Risetime |
1 us |
Current Risetime |
<5 us |
Lightning Characteristics at 100m
In order to model these two effects, the threat parameters must first be characterized. Despite the fact that there can be variations in lightning in nature, parameters can be used to model the typical strike, for the purposes of estimating the coupling and illustrating effects. (Table 1)
Antenna Coupling
Estimates of the open circuit voltage, short circuit current, and the maximum energy coupled into a mono-pole antenna yield:
V_{oc} = H_{eff} x E (1)
where
H_{eff} = the effective antenna height,
or about one half the physical height, and
E = the electrical field strength in V/m.
The short circuit current of the antenna is approximately:
I_{sc} = c x d (V_{oc}(t)) /dt,
or for the initial risetime
I_{sc} = c x V_{oc} / t_{r} (2a and 2b)
where
c = the antenna capacitance in pF,
and t_{r} = the pulse rise time in seconds.
To estimate the antenna capacitance, the following relationship provides close approximation for a wide range of geometries:
c = 19 x h
Where
c = the antenna capacitance in pF, and
h = the physical antenna height in meters.
The estimates of the voltage and current, and derived information such as the coupled energy, are given for a range of antennas lengths (Table 2).
Table 2.
Mono-pole antenna length (m) |
Antenna V_{oc} in kilo-Volts |
Antenna I_{sc} in Amperes |
Maximum Energy in J |
0.25 |
63 |
0.03 |
0.02 |
0.5 |
125 |
0.11 |
0.14 |
1 |
250 |
0.44 |
1.1 |
2 |
500 |
1.77 |
8.8 |
5 |
1250 |
11.05 |
138 |
10 |
2500 |
44.20 |
1105 |
Antenna Voltage Pick-up
To protect and last an acceptable lifetime, a protector would need the current capacity for a time duration of the rise time of the pulse, on the order of 10 times or more than the current listed in Table 2.
Current Injection Coupling
The direct effects of the lightning current into the earth and man-made structures is to produce voltage potentials and currents across resistive and inductive impedances. These voltages are estimated respectively by:
V = i(t) (p / (2 * pi )) / (1/r_{1} - 1/r_{2}) (3)
and
V = L (di/dt) (4)
where
i = the lightning current,
r_{1} = distance from the lightning injection point to the nearest end of the shielded cable,
r_{2} = the distance from the lightning injection point to the far end of the cable,
p = the soil resistivity, and
L = the inductance of any lightning current path in the direction of the cable.
The inductance is usually 5 to 100 nH per meter of length for most structures and towers. Typical soil resistivities are 25 to several hundred ohm-m.
Note that the current limit or i_{sc} for the shield to ground is nearly unlimited, and can approach a large portion of the value of the lightning current, while the differential or normal mode current is limited by the voltage divided by the source and load impedances. Also note that these voltages are orthogonal
phase vectors, which are not directly additive.
An example is the voltage for a 200 meter RG-402 cable run, 100 meters along the ground and 100 meters up a building and tower (Figure 1). For the lightning parameters listed in Table 1 and for the site parameters listed in Table 3 the values in Table 4 result.
Figure 1:
Typical Antenna Configuration
Table 3.
Antenna Wiring Inductance |
Soil Resistivity |
Source / Load Impedance |
Distance (r_{1}) |
Length (r_{2}-r_{1}) |
0.5 mH |
150 omega-m |
50 Ohms |
100 m |
100 m |
Example Site Parameters
Table 4.
Current (kA) |
Resistive Voltage |
Inductive Voltage |
Total Voltage |
50 Ohm Differential Current (A) |
Shorted Differential Current (A) |
Energy (J) |
90 |
10748 |
4500 |
11652 |
117 |
2200 |
3.1 |
Current Injection Energy
Thus, the electrical energy is again significant, with an even higher current than antenna coupling into the source/load of 50 ohms. Actually, the current through a shorting type suppressor can be considerably higher, as a shorting device will provide much less than 50 ohms of impedance. In this case the current is limited by the resistance and impedance of the centre coaxial conductor, or about 5.3 ohms.
Conclusion
It can be seen that the physical layout of antennas alone provide considerable energy pick-up, and the cable run itself can provide significant energy coupling, even if the cable provides full shielding of the centre conductor. This effect is highly influenced by the intentional and unintentional grounding of the
shield including parasitic capacitance and inductive coupling; and the geometry of the installation.
If suppressors are required for preventing hazards to humans, or if maintaining equipment operation has critical economic or safety applications, usually one or more of the following is required: a more detailed estimate of threats, redundant systems for failure resistance, or multiple levels of protection with testing and maintenance programs.
About the authors:
KEN RAINA received a BSEE from the University of Massachusetts and an MSEE in Communication Engineering from Northeastern University. He has over 20 years of analogue and digital design experience in areas that include communication, power supply and computer system applications.
G. M. KAUFFMAN received a BSME and a Masters in Engineering Management from the University of Massachusetts. He has been in EMC for seventeen years, and holds three patents in the field. He is a consulting engineer.