Figure 1. Conductance versus unknowns for a short dipole.
Figure 2. Susceptance versus unknowns for a short dipole.
The accuracy of the results from using any numerical modeling code depends both on the user as well as on the code. The old adage "garbage in, garbage out" applies all too well. Given that a knowledgeable user has defined the antenna model within the modeling constraints, what kind of accuracy can be expected? How does the latest versions in the Expert MININEC Series of codes compare to the latest version of NEC [Burke and Poggio, 1981]? The following examples should give the reader an indication of what to expect. The results of the Expert MININEC Series of codes are compared with Version 4 of NEC.
Any evaluation of a wire antenna modeling code will begin with the evaluation of a dipole antenna. Figures 1 and 2 show a comparison of the new MININEC to NEC in a typical convergence test for a short dipole in free space. In a convergence test the accuracy is determined as a function of the number of unknowns. A convergence test provides the rationale for selection of segment density for a desired accuracy. It also demonstrates the stability of the analysis. The dipole half length is 0.159155 meters and radius is 0.001588 meters. Figure 1 shows the conductance versus the number of unknowns and Figure 2 shows the susceptance versus the number of unknowns. R.W.P. King [King, 1971] reports an admittance (conductance + j susceptance) of 0.25 + j 3.87 mmhos. These figures show that as the number of segments (unknowns) is increased, the admittance of both codes converges towards approximately the same asymptotic values.
Figure 1. Conductance versus unknowns for a short dipole.
Figure 2. Susceptance versus unknowns for a short dipole.
Figures 3 and 4 show the admittance results of MININEC compared to NEC for a short dipole over a range of frequencies. Figures 3 and 4 show conductance and susceptance versus frequency. Also shown are values from R.W.P. King [King, 1971]. The dipole has a half length of 0.25 meters and a radius of 0.00351 meters. The length to radius ratio is 142. A segmentation scheme was used that provided 29 unknowns over the frequency band. Both codes perform very well.
Figure 3. Dipole conductance vs. frequency (29 unknowns).
Figure 4. Dipole susceptance vs. frequency (29 unknowns).
A second step in an evaluation is calculation of a multiple wire antenna. Figures 5 and 6 display MININEC and NEC conductance and admittance calculations for a TEE Antenna described by King [Prasad and King, 1961]. The specific antenna has KH=.2, where K = 2p/l, where l is the wavelength and H is the height in wavelengths. King reports an admittance for this antenna of 29.6 - j102.6 mmhos.
Figure 5. KH=.2 TEE antenna conductance vs. unknowns.
Figure 6. KH=.2 TEE antenna susceptance vs. unknowns.
Figures 7 and 8 show the impedance computed by MININEC compared to the impedance computed by NEC for a dipole over real ground. The antenna is a 0.5 meter center fed dipole with 0.0005 meter radius at 0.1 meters above an average ground. The dielectric constant of the ground is 15, and the conductivity is 27.8 mmhos. Figure 7 shows the dipole resistance versus frequency and Figure 8 the dipole reactance versus frequency. Two sets of calculations are shown for NEC. One set of calculations is for the solution using the Fresnel reflection coefficient method, and the other set is for the Sommerfeld solution. These results have been obtained after checking the solutions of both codes for convergence. The Fresnel reflection coefficient method is shown to be a good approximation to more general, exact Sommerfeld solution.
Figure 7. Dipole resistance of a dipole over average ground.
Figure 8. Dipole reactance of a dipole over average ground.
Figures 9 and 10 show the Yagi radiation patterns computed by MININEC compared to the radiation patterns of NEC. Figure 9 is the pattern for a three element Yagi, and Figure 10 is the pattern for a five element Yagi. The Yagi dimensions in meters are shown in the following table.
Table 1. Dimensions of 3 and 5 element Yagi antennas.
| Yagi | 3 element | 5 element |
| Reflector length | 0.482 | 0.482 |
| Driven element length | 0.25 | 0.25 |
| 1st director length | 0.442 | 0.428 |
| 2nd director length | 0.424 | |
| 3rd director length | 0.428 | |
| director spacing | 0.2 | 0.2 |
Figure 9. Radiation pattern of a 3 element Yagi.
Figure 10. Radiation pattern of a 5 element Yagi.
It has been shown from the selected examples that MININEC gives comparable results to NEC. This is not a complete picture of the comparison of these codes, but it gives the reader a glimpse of the results to be expected. A more thorough analysis of MININEC is presented in References [Rockway and Logan, 1995] and [Rockway and Logan, 1996]. In this analysis is shown that for a wide variety of problems MININEC and NEC provide comparable results.
