Re: NEC-LIST: How does NEC4 work?

Jason Cooke wrote:
>
> Given that a wire segment is defined in NEC4 and excited by an
> incident plane wave of magnitude 1 V/m at frequency f. Is it correct
> to say that the current NEC4 calculates on the wire segment is simply
> the time-domain response of the system to a unit complex exponential
> at frequency f?

Not really. NEC and related codes calculate the steady-state
solution, not the transient response. They do so by reducing an
integral equation of the form

               Int I(z') K(z,z') dz' = -Ei(z) (1)

to a system of simultaneous linear algebraic equations in terms of the
unknown current I(z').

                    [Zmn] [In] = [Em] (2)

In (1), I(z) is the unknown current distribution, E(z) is the
incident electric field, and K is the kernel function. The integral
equation is referred to as an "integral equation of the first kind"
because the unknown I(z') appears only under the integral.

In (2), Z(m,n) is the impedance matrix defined by the kernel function
and is strictly a function of the geometry of the wires, plates, etc.
I(n) and E(m) are the current and (incident) voltage distributions
corresponding to I(z') and Ei(z).

In the general case, K is rather complicated. In Pocklington's
integral equation (and a related form referred to as Hallen's integral
equation), K is simplified by assuming thin wires (so the currents are
always directed along the length of the wire) and a particular model,
say a delta-gap voltage source or a magnetic frill, for the excitation
field.

The first step in solving a scattering or radiation problem using the
MoM is to set up the impedance matrix for the problem geometry being
considered. The solution to (2) is then given by

                   [In] = [Zmn]^-1 [Vm] (3)

Since the size of matrix is often quite large, the second step is the
most time-consuming. See, for example, section 7.8.1 of Stutzman and
Theile (1981).

More detailed descriptions of the method can be found in:

      W.L. Stutzman and G.A. Thiele, "Antenna Theory and Design."
      Wiley, 1981, pp. 306-374.

      C.A. Balanis, "Antenna Theory: Analysis and Design."
      Harper & Row, 1982, pp. pp. 283-321.

      R.E. Collin, "Antennas and Radiowave Propagation."
      McGraw-Hill, 1985, pp. 46-86.

as well as the NEC documentation produced by LLNL.

I hope this helps.

-- 
Dave Michelson                                  AT&T Wireless Services
davem_at_ee.ubc.ca                               Strategic Technology Group