13.56 MHz Antennas

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 V/m (84 dBV/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.

Part 15 incorporates ANSI C63.10, which contains a technical error. It says to measure the magnetic field and multiply by 377 to get the electric field. But since the field strength ratio near ground varies widely from this free-space value, the result is invalid. I list maximum legal power for both correct and flawed electric field measures.

Radiation patterns are for average ground quality. Conductors are #14 bare copper wire and the models do not account for insulator end effects. I used Sommerfeld-Norton ground and calculated the field 30 meters from the origin and 1 meter above ground per C63.10.

Dipole

Height is 30 feet. The wire is 212″ long each side of center. The red dot marks the feedpoint.

                  Legal Power mW    Impedance
E-field measure   Correct Flawed        Ω
Very good ground    111.6   18.2    83.7−j2.8
Average ground       89.0   17.5    81.8+j0.7
Very poor ground     51.9   16.3    79.2+j4.3

Inverted V

The apex is at 30 feet. Each wire slopes 45 and is 216″ long.

                  Legal Power mW    Impedance
E-field measure   Correct Flawed        Ω
Very good ground    171.5   24.2    55.2−j1.5
Average ground      130.0   24.1    52.2−j0.7
Very poor ground     71.8   22.1    48.8−j0.2

Lowering an antenna reduces low-angle radiation, but it also decreases the field strength near ground, which allows higher input power. The patterns below show relative radiation for inverted Vs at 10 and 30 feet when each is fed legal power. Radiation is the same at low angles while total radiated power is much greater for the low antenna. The disadvantage of a low antenna is that ground quality more strongly affects impedance. But if you can measure it, you can turn this to your advantage by using the value to estimate ground quality.

The apex is at 10 feet. Each wire slopes 10 and is 208″ long. The ends are 83″ above ground.

Relative end-fire response for the low antenna is smallest at a wave angle of 24 where it is down 5.1 dB.

                  Legal Power mW    Impedance
E-field measure   Correct Flawed        Ω
Very good ground    536.8   94.3    50.2+j10.5
Average ground      484.5  103.1    57.1+j0.5
Very poor ground    262.6   98.8    64.6−j7.1

Inverted V Turnstile

The apex is at 30 feet and each wire slopes 45. The inverted V currents are in phase-quadrature.

This overhead view of the offset antenna shows one V with 209″ wires and the other with 224″.

A 2″ jumper (perhaps just coax leads) fed at the center joins wire pairs of unequal length.

                  Legal Power mW    Impedance
E-field measure   Correct Flawed        Ω
Very good ground     26.5   23.6    52.0+j3.4
Average ground       44.7   28.8    51.9+j3.5
Very poor ground     64.7   31.1    52.0+j3.5

Ground-plane

Base height is 10 feet. Two radials slope 10 with the ends 82⅜″ above ground. All wires are 216″ long.

                  Legal Power mW    Impedance
E-field measure   Correct Flawed        Ω
Very good ground      2.6    5.5    37.3−j0.8
Average ground        4.4    9.6    36.1+j0.0
Very poor ground      7.0   16.0    34.6+j1.2

Transmitter RF Voltage

If you can, measure the feedline loss and the antenna impedance through the feedline. Otherwise, calculate these values as described below. Increase legal power by the feedline loss and use a calibrated oscilloscope with low-capacitance probe to set the resulting RF voltage at the transmitter.

Let's say you install an inverted V 10 feet over average ground and feed it with 100 feet of Belden RG-58C/U. In this calculator enter 57.1 for load R, 0.5 for load X, 13.56 for frequency, 100 feet for length, and Belden 8262 for cable type. Click calculate. Total loss is 1.59 dB, which is a power ratio of 100.159 = 1.44. Legal transmitter power is 1.44 × 484.5 = 699 mW. Impedance through the feedline is 51.6−j4.8Ω so the legal transmitter RF voltage is √(0.699(51.6+4.8) ∕ 51.6) = 6.03 V RMS (17.1 V P-P).

Ground Quality

          Dielectric  Conductivity
           Constant       mS/m
Very good     20           30       Pastoral, low hills, rich soil (Dallas TX to Lincoln NE)
Average       13            5       Pastoral, medium hills and forestation, heavy clay soil (central VA)
Very poor      5            1       Cities, industrial areas

FCC Part 15 Excerpt

15.23Home-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.


July 29, 202188108 MHz