FCC Part 15 rules for the industrial, scientific, and medical band at 13.56 MHz include radiation limits. Maximum field strength from 13.553 to 13.567 MHz is 15,848 µV/m (84 dBµV/m) at a distance of 30 meters. Experimenters exploit this limit to see how far tiny signals can propagate. I used NEC-2 to calculate maximum input power for legal field strength for several antennas over three types of ground.
Radiation patterns are for average ground quality. Conductors are #14 bare copper wire. The models do not include insulator end effects. I calculated the electric field 30 meters from the origin and 1 meter above ground.
The wire is 425˝″ long and 30 feet above ground. The red dot marks the feedpoint.
Ground Legal Power Impedance Very good 112 mW 83.7−j2.8 Ω Average 89 81.8+j0.7 Very poor 52 79.2+j4.3
The apex is at 30 feet. Each wire slopes 45° and is 216″ long.
Ground Legal Power Impedance Very good 49 mW 55.2−j1.5 Ω Average 115 52.2−j0.7 Very poor 72 48.8−j0.2
Base height is 10 feet. The radials slope 10° with ends 82˝″ high. Each wire is 216″ long.
Ground Legal Power Impedance Very good 2.8 mW 36.3−j1.2 Ω Average 4.4 34.7−j0.3 Very poor 6.6 32.9+j0.9
Ground Legal Power Impedance Very good 473 mW 53.6+j9.0 Ω Average 412 58.7−j0.2 Very poor 228 65.2−j8.0
Lowering a horizontal antenna reduces low-angle radiation, but it also decreases the field strength near ground, which allows higher input power. The plots show relative patterns for dipoles at 10 and 30 feet with each fed legal power. Radiation is similar at low angles, but total radiated power is much greater for the low antenna, which is also less directional. The disadvantage of a low antenna is that ground more strongly affects its impedance. But if you can measure it, you can turn this to your advantage by using the value to calculate ground characteristics and legal power.
The dipole is 417˝″ from end to end and 120″ above ground. Support the feedpoint to keep the wire straight. The antenna should be in the clear with no structures, large objects, or other conductors nearby. The antenna model does not account for wire loops at insulators. Use tiny loops, knots, or insulated clamps, or tie-wrap the entire wire to dacron line. Place a connector at the center compatible with your vector network analyzer.
Measure the antenna impedance at 13.56 MHz with the VNA. Attach it to the antenna feedpoint with a short coax jumper. Calibrate the VNA at the end of the jumper. Use a ladder or Bluetooth to read the impedance. To use the VNA at ground level, attach feedline with a common-mode choke. Calibrate the VNA at the antenna end.
Enter measured R and X values in pwr.exe to calculate ground permittivity, conductivity, and legal antenna input power. The program interpolates results for 100 antenna models that cover a wide range of permittivity and conductivity values.
Ground characteristics vary with moisture content and temperature. You may want to remeasure at different seasons.
5° 10° 20° 30° 45°
Low Dipole 0.0 0.0 0.0 0.0 0.0 dB
Dipole +0.8 +0.6 −0.3 −1.5 −4.3
Inverted V −0.4 −0.5 −1.2 −2.0 −3.9
Ground-plane −12.2 −14.3 −17.9 −21.3 −32.0
This table shows radiated signal level at peak azimuth relative to that of a low dipole for five elevation angles, legal power, and average ground.
Permittivity Conductivity
Very good 20 30 mS/m Pastoral, low hills, rich soil
Average 13 5 Pastoral, medium hills and forestation, heavy clay soil
Very poor 5 1 Cities, industrial areas
Local permittivity and conductivity can differ greatly from these nominal values. They also vary with frequency. For antennas other than a low dipole, use a ground probe, VNA, and this program to measure permittivity and conductivity at 13.56 MHz. Then interpolate legal power results to estimate the limit for your local ground.
If you can, measure the feedline loss and the impedance at the transmitter end of the feedline. Otherwise, calculate these values as described below. Increase legal power by the feedline loss and use a calibrated, wideband oscilloscope with low-capacitance probe to set the resulting RF voltage at the transmitter.
Let's say you install a dipole 10 feet over average ground and feed it with 100 feet of Belden RG-58C/U. In this calculator enter 58.7 for load R, −0.2 for load X, 13.56 for frequency, 100 feet for length, and Belden 8262 for cable type. Click calculate. Total loss is 1.6 dB (substitute measured value), which is a power ratio of 100.16 = 1.45. Legal transmitter power is 1.45 × 412 = 597 mW. Impedance through the feedline is 51.2−j5.8Ω (substitute measured value) so the legal transmitter RF voltage is √(0.597(51.2˛+5.8˛) ∕ 51.2) = 5.56 V RMS = 15.7 V P-P.
Use a common-mode choke to inhibit feedline radiation. You can make a very effective choke by coiling about 12 feet of coax into a 1-foot diameter solenoid with roughly four turns. Tape the coil so that adjacent turns never overlap and everywhere touch. Connect the shields of the coil leads to the two ports of a VNA. Vary the fractional number of turns until self-resonance occurs at 13.56 MHz (maximum port-to-port attenuation). Use appropriate lead dress. Add connectors and insert the choke at the antenna feedpoint, or duplicate it by coiling identical feedline in the same way. Mount the coil perpendicular to the antenna wires and away from anything metallic.
§ 15.23 Home-built devices.
(a) Equipment authorization is not required for devices that are not marketed, are not constructed from a kit, and are built in quantities of five or less for personal use.
(b) It is recognized that the individual builder of home-built equipment may not possess the means to perform the measurements for determining compliance with the regulations. In this case, the builder is expected to employ good engineering practices to meet the specified technical standards to the greatest extent practicable. The provisions of § 15.5 apply to this equipment.
88–108 MHz