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Field Tools

Click on the following bookmarks for further details of a Field Tool:

Common Mode Field Coupling
Helmholtz Coils
Electromagnetic Field Formulae
Magnetic Field due to a Current in a Wire


Common Mode Field Coupling

    Common mode field coupling occurs when cables connected to an item of equipment are subjected to an external field, as shown below.

910_1.bmp (131634 bytes)

    A loop is formed between the cabling, the equipments and a ground path, the induced loop voltage driving currents in the same direction along the cabling. The loop may often be hard to define in physical terms, depending on a cabling layout which may be variable, and a ground path which is also ill-defined. In addition, the coupling to the ground path, often capacitive, may also not be easily defined.

    The Common Mode Field Coupling Tool provides several facilities to investigate the effects on a circuit of this arrangement. With the comments of the previous paragraph in mind, it must be understood that modelling common mode coupling is affected by many variables, and is unlikely to accurately reflect a real situation. Nonetheless, an understanding of the mechanism is vital in mitigating a widely encountered means of coupling interference currents into an equipment. The effects of circuit grounding, and the use of unblanced and balanced inputs are also clearly contrasted.

    The Balanced circuit model is shown below: Note how the circuitry, and the equipment boxes can be grounded or capacitively coupled, which has a major effect on Common Mode Rejection Ratio (CMRR).

910_5.bmp (171054 bytes)

    Spot analyses and swept frequency graphs can be made for the basic common mode loop, and for unbalanced and balanced circuits. Load voltage and CMRR can be calculated and plotted.


Helmholtz Coils

    The magnetic field B on the axis of a coil falls with distance x from the coil according to the relation:

B = uo N I r2 / ( 2 ( r2 + x2 ) 1.5 Tesla

    Where N is the number of turns, I is the current in the coil, and r is the coil radius. By differentiating B to find dB/dx, and differentiating again to find d2B/dx2, a point of inflexion at x = r/2 is found by equating the result to zero.

    If a second coil is placed at distance r from the first coil, a near uniform field is produced in the central region between the coils. For example, two coils of 1m radius, placed 1m apart, produces a field which is uniform to 0.1% of peak field over a distance of 346mm. The Helmholtz Coils Tool allows the field on the axis of two coils to be calculated, plotted and tabulated, and is shown below:

900_1.bmp (599094 bytes)

    The coils can be placed any distance apart, although for optimum uniformity the Helmholtz condition must be applied, where the distance between the coils equals the coil radius. The Plot button produces the separate fields due to each coil, as well as the total field.

    The Analyse button calculates the fields at any point between the coils, whilst the Tabulation button produces a list at the desired distance interval. The Export button shows a filename box; when a filename is provided, the tabulation figures are stored in a comma separated value (CSV) file, which can be opened by spreadsheet applications. Both the plotted graph and the tabulation can be printed.


Electromagnetic Field Formulae

    The field formulae tool contains a number of basic calculations and conversions concerning electromagnetic fields, described as follows.

1) Near Field to Far Field transition point.
    When the distance from the source exceeds the (wavelength / 2 * Pi), the ratio of the E-field to the H-field, which is the wave impedance, is constant at 377 ohms in free space. This is known as the far field.
    When the distance is less, the point of observation is said to be in the near field. The wave impedance in the near field may be more or less than 377 ohms, depending respectively whether the electric or magnetic field predominates. A knowledge of whether near or far field conditions apply is useful in shielding effectiveness calculations, where shielding level depends on the wave impedance.
    The tool calculates the transition distance from near to far field for a given frequency, and takes the user's distance figure, and indicates whether it is in the near or far field, or in fact in the transition region between the two.

2) Wave Impedances in a Dielectric
    This tool calculates wave impedance in free space or a dielectric, in the near field or far field. A constant impedance in the far field is produced by the ratio of (permeability / permittivity)0.5. The tool allows both relative permittivity and relative permeability to be specified, although apart from the specialised application of waves launched in a dielectric waveguide, this will rarely be needed, and is included for completeness.

    The electric wave impedance due to an electric dipole is given by
(2 * Pi * f * E * d)-1 , where f is frequency, E is permittivity and d is distance.

    The magnetic wave impedance due to a current loop is given by (2 * Pi * f * mu *d ), where mu is the permeability.

3) Power to Field Conversion in the far field.
    This tool will take a field strength E in V/m, and convert it to a power density P in mW/sq.cm. The reverse calculation can also be made, by entering a number in the power box.     The calculation is: P = E2 / 1200 * Pi

4) Power Density and Field at a distance from an isotropic transmitter.
    This calculates power density Pd in W/sq.m and field strength E in V/m, for a given transmitter power Pt.
    The formulae are:
P = Pd / (4 * Pi * R2n) and E = ((30 * Pt) 0.5 ) / Rn
    n is a correction factor for ground attenuation, which causes faster attenuation than 1/R. It varies between 1.3 (open country) and 2.8 (buildings), betweem 30 and 300MHz and distances > 30m. The default setting for n is 1.

5) Magnetic Field Unit Conversions
    This provides conversion between Gauss, Amps/metre and Tesla. A figure entered in any one box clears data in the other two, until the 'convert' button is pressed.

The field formulae form is shown below:

Fields Form.gif (10926 bytes)


Magnetic Field due to a Current in a Wire

This tool calculates the magnetic field produced near a wire carrying a current, for the two situations of short wire and long wire. The field B due to a short length of wire, carrying current I, at perpendicular distance r from the wire is given by:

            Bsw = mI (cos(b) – cos(a)) / (4 * Pi * r) Tesla

The field is directed into the the plane of the diagram, as shown below on the Short Wire tab..

920_1.bmp (337174 bytes)

For an infinite wire, angle a = 180 degrees and angle b = 0, and the long wire result is found:

        Blw = mI / ( 2 * Pi * r) Tesla

The long wire tab is shown below:

920_2.bmp (337174 bytes)

Both analyses express the field in microTeslas.


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