In Expert MININEC Series the solution for currents is based on the numerical solution of an integral equation representation of the electric fields. The process of solution begins with several assumptions which are valid for thin wires
The wires radius is very small with respect to the wavelength and the wire length.
The wire must be subdivided into short segments so the radius is assumed small with respect to segment lengths. Thus the currents can be assumed to be axially directed (i.e., no circumferential currents on the wires).
The electric field is formulated in terms of its scalar and vector sources. These sources are the vector magnetic potential and the scalar electric potential. The two potentials are calculated from potential integrals, which are solutions of the Helmholtz vector and scalar wave equations. In the potential integrals, the integrands are the wire current and wire charge distributions, which are assumed to be known. The current and charge are linked via the equation of continuity. Expert MININEC makes use of the boundary condition on tangential electric field at the surface of a perfect conductor, namely that the electric field must be zero. Since the wires are assumed to be thin, this forces the total axial electric field on the wire to zero. The three sources of the tangential electric field on the wire are
currents and charges on the wires and on nearby wires,
incoming waves from distance or nearby radiators and
local sources of electric field on the wire.
The local sources are usually in the form of voltage sources, current sources, or transmission lines that connect to the wires. By summing the tangential electric field components at each segment on the wire antenna and enforcing the zero total value, an integral representation for the currents and charges is obtained.
The method of moments solution in the Expert MININEC Series is a numerical procedure for solving the electric field integral equation. Basis functions are chosen to represent the unknown currents (i.e., triangular basis functions). Testing functions are chosen to enforce the integral equation on the surface of the wires. With the choice of basis and testing functions, a matrix approximating the integral equation is derived. If this matrix is inverted and multiplied by the local sources of electric field, the complex magnitudes of the current basis functions are derived. All antenna performance parameters can be determined from the derived current distribution.
Ground planes are accommodated by the method of images. Where a wire attaches to the ground plane, a current basis function is automatically added to the wire end point connection to ground. Current continuity is maintained. Real grounds can also be considered using the Reflection Coefficient Approximation.
Lumped parameter impedance loading is added when requested by the user to selected junctions between connecting segments. The load impedance is added to the self term of the solution matrix for the corresponding matrix element.
Near electric fields are calculated at a given point in the vicinity of a wire structure by placing a small virtual dipole at the observation point and calculating the open-circuit voltage from a knowledge of the structure current distribution and the mutual impedance between the virtual dipole and the antenna. For the magnetic near field, the current distribution and the difference between the appropriate components of the vector magnetic potential are used. In calculating near electric fields real ground can also be considered using the Reflection Coefficient Approximation.
Radiation patterns are calculated from the electric field in terms of the structure currents, in the classical closed-form solution. Finite grounds can also be considered using the Reflection Coefficient Approximation.
Real ground includes the following features
In computing the radiated field in a given direction, the given ground media is determined where the ray from each current node reflects. The reflected ray is computed using the appropriate ground parameters and height of the ground associated with the given ground media.
Diffraction from the cliff edge is not included.
The Reflection Coefficient Approximation (RCA) method is used to compute the effect of a real ground. The RCA solution evaluates the field of the image multiplied by the Fresnel plane wave reflection coefficients, and can only be used with currents nodes that are sufficiently far from the ground. The RCA method should not be used for currents nodes that are close to the ground surface. Reasonable engineering estimates are obtained when a current node is greater than .1 to .2 wavelengths from the ground.
The radial wire ground screen approximation is based on a modified reflection coefficient. The reflection coefficient at each point on the ground is computed from the surface impedance. The surface impedance is a parallel combination of the radial wire screen and the ground impedance.
The connection of a wire to ground is assumed to be perfect ground. The solution for a vertical monopole on a real ground will be the same as for the monopole on a perfectly conducting ground.