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Electrically Initiated Blasting and Electromagnetic Fields. I.M.E. Fall Meeting 2004 Technical Committee 19 October 2004. Outline of Topics. The physics of the field around a current-carrying conductor Background of electric, magnetic and electromagnetic fields

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Electrically initiated blasting and electromagnetic fields

Electrically Initiated Blasting and Electromagnetic Fields

I.M.E. Fall Meeting 2004

Technical Committee

19 October 2004


Outline of topics
Outline of Topics

  • The physics of the field around a current-carrying conductor

    • Background of electric, magnetic and electromagnetic fields

    • James Clerk Maxwell's equations of waves in free space

    • The wave equation and wave propagation

    • Radiating and non-radiating fields

    • Near Field and Far Field, (Fraunhofer) Effects

  • High current, low frequency power transmission lines

    • The reactive near-field

  • Transmitting and receiving antennas

    • Definitions

    • Units

    • Antenna Configurations

    • Blasting circuits as receiving antennas

    • Safe Distance equations and parameters affecting safe distance


The physics of the fields around a current carrying conductor
The Physics of the Fields around a Current-Carrying Conductor

  • Background

    • The term field refers to the mathematical description of the forces created between charges. There are three fields of interest from DC to microwave, electric, magnetic and electromagnetic (radiation) force fields. Fields are not physical things but mathematical descriptions of influences that fields have over free space that occur over a distance.

      • The Electric, (Coulomb), field results from uneven charge distribution. The charge distributions may be static or dynamic. Electric fields go hand-in-hand with voltage difference between two physical points.

      • The Magnetic field results from moving charge, for example, current flow in a conductor.

      • The Electromagnetic field, (radiation), results from accelerating charge, i.e., when charge changes speed or direction.

    • Antennas have all three fields associated with them.

    • The stationary, moving or accelerating charge of concern is the mass of free electrons in the current carrying elements of an antenna.


Definitions of terms
Definitions of Terms Conductor

Term Definition Units (MKS)

E Electric Field (Electric Force per unit Volts/Meter

Charge)

B Magnetic Field (Field of Influence Tesla (1 Tesla=104 Gauss in cgs units)

as a result of charge in motion)

H Magnetic Field Strength Amperes/Meter

c Speed of Light 3x10+8 Meter/Second

ε0 permittivity of free space (how a medium 8.8542 x10-12 Coulomb2/Newton Meter2 changes to absorb energy in an EM field)

μ0 permeability of free space (response of a 4x10-07 Newtons/Ampere2

medium to a magnetic field)

J current density Ampere/Meter2

 charge density Coulomb/Meter2


Maxwell s equations
Maxwell's Equations Conductor

  • James Clerk Maxwell's Equations in differential form:

    • Gauss' Law for Electricity

      • The electric flux out of any closed surface is proportional to the total charge enclosed within that surface

         E = /ε0 = 4 k  where k=1/4ε0or Coulomb's Constant

    • Gauss' Law for Magnetism

      • The net magnetic flux out of any closed surface is zero

          B = 0

    • Faraday's Law of Induction

      • The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop or is equal to the generated voltage in the loop.

         x E = - ∂B/∂t

    • Ampere's Law

      • In the case of a static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop.

         x B = μ0J + (1/c2) ∂E/∂t where c2 = 1/μ0ε0


The wave equation and wave propagation in free space
The Wave Equation and Wave Propagation in Free Space Conductor

  • From the third of the previous four equations we take the curl of both sides of the equation:

     x ( x E ) = - (∂/∂t) (x B)

  • From substituting equation four of the previous four equations where J = 0 into the above and solving:

    2E = -μ0ε0 ∂2E/∂t2 where c = (1/μ0ε0)½

  • The solution of the equation is the simple wave equation showing that the propagation of electromagnetic radiation is transverse, (TEM), and the electric, (and also magnetic), fields oscillate in a plane perpendicular to the direction of propagation, (and are perpendicular to each other).


Radiating and non radiating fields
Radiating and Non-Radiating Fields Conductor

  • Field Regions

    • The volume of space surrounding an antenna consists of two or three distinct regions depending on the nature of the electromagnetic field produced by the antenna.

  • Far Field or Fraunhoffer Region

    • The far field region of a radiating antenna is the region far enough from the source that only the radiating field components are significant. The electric and magnetic fields decay inversely with distance from the source, the energy is equally distributed between the electric and magnetic fields and the field components are orthogonal. Power density decays with the inverse square of the distance from the source. Angular field distribution is independent of distance from the antenna.

  • Radiating Near Field or Fresnel Region

    • The radiating field predominates, but the non-radiating fields are not insignificant. The outer boundary is approximated by R ~ 2D2/, where D is the largest dimension of the antenna. Interference between different parts the antenna is significant. The angular field distribution is dependent on distance from the antenna.

  • Reactive Near Field

    • The non-radiating electric and magnetic fields dominate. For electrically small antennas, the region is either predominately electric or predominately magnetic. R ~ /2.


Antenna basics
Antenna Basics Conductor

  • Any conductor will radiate at any frequency. The purpose for the variety of different antenna shapes is to control the radiation pattern.

  • Insulators can also radiate electromagnetic energy.

  • Antenna Gain

    • The radiated power of any antenna attached to a transmitter of constant power output is constant. An isotropic antenna radiates uniformly in all directions or has a gain of unity. By changing the shape of the radiation pattern, the radiation can be concentrated in preferred directions, hence achieve antenna gains larger than unity.

  • Antenna Aperture

    • The portion of a plane surface normal to the direction of propagation near a radiating antenna through which most of the radiation passes.

  • Effective Radiated Power

    • ERP = Power Input to Antenna X Antenna Gain


High current low frequency power transmission and distribution lines
High Current, Low Frequency Power Transmission and Distribution Lines

  • Fields surrounding 60 Hertz power transmission lines

    • The frequency of the alternating current sent through transmission and distribution lines is 50-60 Hertz, thus the wavelength is greater than 5000 kilometers, (c = f ), making the power line a poor transmitter of radiation. The near field extends out very far and the non-radiant electric and magnetic fields decay rapidly with distance from the power lines.

    • The significant fields are the non-radiating electric and magnetic fields

      Transmission Voltage E Field @ 30 meters B Field @ 30 meters

      (volts) (Volts/Meter) (milliGauss) (1μT = 10 mG)

      115,000 0.07 1.7

      230,000 0.30 7.1

      500,000 1.0 12.6

    • Since power lines have opposing, separated currents, EM fields are produced that diminish with the inverse square of distance.

    • The radiative component is so small, a 500 Megawatt power line will radiate approximately 1 milliwatt per 10 kilometer length @ 60 Hertz.


Transmitting and receiving antennas
Transmitting and Receiving Antennas Distribution Lines

  • Antenna Polarization

    • Also referred to as wave polarization, it is the orientation of the electric flux lines, (not the magnetic flux), in an electric field. The best transmission of RF occurs when both the receiving and transmitting antennas have the same polarization. When the receiving and transmitting antennas are at right angles to each other, the least efficient coupling is the result. Some antenna systems use circular or elliptical polarization where the electric flux lines rotate either in a clockwise or counterclockwise orientation with each wave cycle. These antennas are commonly used for satellite uplink or downlink communications. The antennas look like a "coil spring" with a back reflector.

  • The Antenna as a Reciprocal Device

    • Antennas receive as well as transmit electromagnetic energy. They work both ways with equal validity.


Units pertaining to rf transmission
Units pertaining to RF Transmission Distribution Lines

ParameterUnits

Antenna Power or watts or milliwatts (mw)

Effective Radiated Power

Antenna Gain dimensionless or dBm (reference 1 mw) or

dBi (reference isotropic antenna, (Gain=1)

Beamwidth The angle to the direction of the main lobe of the antenna where the power is -3 dB down. A measure of the antenna's directivity.

Bandwidth The measure of how the frequency to the antenna can be varied and obtain acceptable performance


Antenna configurations
Antenna Configurations Distribution Lines

  • Reference Antenna

    • Radiation pattern is isotropic, radiates equally in all directions, Gain = 1, it is a reference for all other antenna types with a gain of dBi = 0. It is a theoretical model only and does not exist other than as a mathematical baseline.

  • Dipole

    • A horizontal long wire of length of some multiple of /2, generally center fed, with a gain of 2.14 dBi. The antenna is horizontally polarized. An EED with its legwires separated is a dipole receiving antenna.

  • Monopole with Ground Plane Reflector

    • A center-fed dipole that is vertically mounted with the lower half removed and a ground plane reflector substituted in its place. Physically, the antenna is a vertical mast perpendicular to the ground with the direction of polarization being vertical. It is the common mobile transmitting antenna configuration and the common mobile vehicular-mounted receiving antenna. Gain for a (1/4) is 5.16 dBi. The AM broadcast band transmitting antennas are of such a configuration with the antenna height being 75 meters tall for AM transmission.


Antenna configurations cont d
Antenna Configurations (cont'd) Distribution Lines

  • Small circular loop

    • When the loop is oriented so that the loop is parallel with the ground the polarization is horizontal with a gain from -2 to +2 dBi

  • Parabolic Dish

    • Has the same polarization as the antenna feedline. Gain is 20 to 30 dBi. Highly directional, used for a variety of applications at frequencies from 400 MHz to 13+ GHz.

  • Yagi

    • Commonly used as an outside antenna for TV and FM reception. Consists of a reflector and one or more directors, the Yagi is highly directional with a gain of 5 to 15 dBi. Frequency ranges from 50 MHz to 2 GHz.

  • Horn

    • A high gain antenna used on cellular telephone repeater towers and microwave relays, frequency range is commonly 40 GHz to 50 GHz. Gain is 5 to 20 dBi.


Blasting circuits as receiving antennas
Blasting Circuits as Receiving Antennas Distribution Lines

  • Detonator "no-fire" power level

    • Sensitivity to induced voltages can vary greatly with the detonator geometry, materials, and the presence of elements which will dissipate energy. This data is obtained by testing the device using a statistical test method such as a Bruceton "up-down" test. Since RF power is not as efficient in heating a bridgewire than direct application of DC to the legwires, the DC "no-fire" data is a conservative approach to predicting safe levels of RF energy.

  • "Worst Case" Analysis

    • Franklin Applied Physics models the receiving antenna, (blasting circuit), as the most effective antenna possible. That would be a shot line geometry if a vertically polarized transmitter is nearest the "hellbox or blasting machine" and a person picks up one leg of the shot line five feet above ground forming an isosceles triangle with the legwire of 7.35E+02 cm perimeter and 2.32E+04 cm2 loop area.

    • From prior studies, a 40 milliwatt "no-fire" power level was used to represent the typical 1 ohm, 1 amp, 1 watt "all-fire" detonator. This was and still is the basis for the tables in IME SLP-20. If some other value may be the case, it is the responsibility of the detonator's manufacturer to determine the electrical characteristics of the device.

  • Nearby Reflective Surfaces

    • A blasting circuit may be located in the vicinity of a large flat metal reflective surface. A reflection coefficient on one is assumed for a conservative calculation.


Safe distance equations from rf sources to blasting circuits the associated parameters
Safe Distance Equations Distribution Lines from RF Sources to Blasting Circuits & the Associated Parameters

  • The detonator circuit is modeled as a receiving antenna, (recalling the reciprocal nature of antennas), with the receiving antenna pattern pointed toward the RF source. The receiving antenna is located in such a way that the maximum amount of power is dissipated in the load, (detonator).

  • In the case of AM broadcast band transmission, , (0.54 MHz to 1.6 MHz),

    • The receiving antenna is a "small loop", (small electrical size compared to the wavelength of the transmission). The worst case is used where someone picks up one leg of the shotline to an elevation of five feet above the ground. Using 20 AWG shotline and the usual constants for the wire and a 40 milliwatt 'no-fire" current for the detonator, Table 1 values in SLP-20 are computed. Since the safe distance increases with frequency, the high end frequency of 1.6 MHz is used. An antenna gain of 10 is assumed. (Refer to Equation 1.)


Safe distance equations from rf sources to blasting circuits the associated parameters cont d
Safe Distance Equations Distribution Linesfrom RF Sources to Blasting Circuits & the Associated Parameters (cont'd)

  • The case of Medium to High Frequency Fixed Vertical Transmitters up to 50 MHz other than AM Broadcast Band Transmitters

    • The same equation is used that was used for AM sources for transmitters up to 50 MHz with an antenna gain of 10. This simulates an operation in the vicinity of a shortwave broadcasting antenna or medium wave amateur operations, (80, 40, 20 meter bands). The worst case frequency is approximately 22.8 MHz. Corresponds to Table 2 in IME SLP-20. (Refer to Equation 1.)

  • The case of low-end Medium Frequency Mobile Transmitters from 1.7 MHz to 3.4 MHz

    • A frequency of 3.0 MHz with an antenna gain of 1.6 is assumed. The transmitting antenna is a whip antenna as commonly found on mobile transmitters in vehicles. A reflection coefficient of unity is assumed in the event that the blasting circuit is located near a perfect reflecting surface. Corresponds to IME SLP-20 Table 3,Column 2. (Refer to Equation 2.)


Safe distance equations from rf sources to blasting circuits the associated parameters cont d1
Safe Distance Equations Distribution Linesfrom RF Sources to Blasting Circuits & the Associated Parameters, (cont'd)

  • The case of High Frequency through UHF, (28 MHz and above)

    • For this case, the electrical dimensions of the receiving antenna, (blasting circuit), are large in comparison to wavelength of the RF transmission. This is the basis for IME SLP-20 Table 3, Columns 3 through 6. This service includes amateur, marine, public service, railroad and aircraft communication. (Refer to Equation 3.)

  • The case of VHF TV, UHF TV, and FM Broadcasting

    • This case applies to transmitters with horizontally polarized radiation through a mast antenna of known height. This is the basis for the safe distance Table 4, column 2 (Channels 2 to 6), column 3 (FM Radio), and column 4 (Channels 7 to 13), and Table 5 (UHF TV Channels 14 to 69, maximum ERP is 5,000,000 watts), in SLP-20. A mast height of 2000 feet, (610 meters), is assumed with an antenna gain of 1. (Refer to Equation 4.)


The safe distance equations
The Safe Distance Equations* Distribution Lines


Bibliography
Bibliography Distribution Lines

  • "Safety Guide for the Prevention of Radio Frequency Hazards in the Use of Commercial Electric Detonators", Institute of Makers of Explosives, SLP 20, July 2001.

  • Stutzman, W. L., Thiele, G. A., "Antenna Theory and Design", 2nd edition, Wiley, 1998.

  • "Electromagnetic Radiation Theory", Franklin Applied Physics, April 2001.

  • "IEEE Recommended Practice for Determining Safe Distances from Radio Frequency Transmitting Antennas When using Electric Blasting Caps during Explosive Operations", IEEE Std C95.4-2002.


That concludes this broadcast
That Concludes this Broadcast Distribution Lines


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