# Magnetic Loop RF Exposure Calculator

This JavaScript RF Hazard Calculator is a practical web-based application proving the user with estimated distances that are credible using FCC safety compliant methods. The calculator estimates field strengths using FCC equations from FCC, OET Bulletin 65. Each case assumes maximum or peak conditions as a simplified static case. JavaScript programming language was selected as the best way to deliver a client-side interactive web page and is simply the best way to get an online calculator built. JavaScript is similar to a spreadsheet for math capability. It is not a good language to solve differential equations or a complex numerical problem. In this case the JavaScript application meets the need. When an algorithm was too complex it was simplified and these equations were replaced with brute force loops that run until a solution is within a range specified. All cases requiring a constant were given a worst-case boundary or split into multiple single worst cases that each determined the maximum distance required for safety and reports the maximum result. This simplification process is commonly used in engineering to quickly identify issues and is one of the FCC compliant method to determine human exposure to radiofrequency (RF) electromagnetic fields. It is not used to determined how well an antenna will work like the EZNEC or 4NEC2 finite element method programs.

# Source: FCC, OET Bulletin 65 Sup B (1997) p 15

Commission's limits on human exposure to radiofrequency (RF) electromagnetic fields. Amateurs can select from a number of technically valid methods that can be useful in performing the required station evaluations. In general, it will be appropriate to use one of the following methods:

• Estimated compliance distances using tables developed from field-strength equations

• Estimated compliance distances using tables derived from antenna modeling

• Estimated compliance distances using antenna modeling (NEC, MININEC, etc.)

• Estimated compliance distances using field-strength equations

• Estimated compliance distances using software developed from field-strength equations

• Estimated compliance distances using calibrated field-strength measurements

# Source: FCC, OET Bulletin 65 (1997) p 67 # Assumptions and mathematical determination

The process for estimating compliance distances using field-strength equations to find the minimum safe distance is a twenty plus step process as loop current must be determined to estimated field strength;

1. Determine loop current from User inputs, used for H Field determination

2. Determine EIRP from User inputs, used for E Field determination

3. Determine MPE from Table 1 Limits for Maximum Permissible Exposure, FCC, OET Bulletin 65 (1997) p 67, calculated from the frequency input by the user.

4. Rearrange the magnetic field = µo I R^2 / [ 2 (Distance^2 + R^2)^3/2, Biot-Savart Law, magnetic field of solenoids to determine H Field Strength for distance (R).

5. Rearrange the power density and field strength equations, S = EIRP / 4∏R^2 = E2 / 3770 = 37.7 H^2 from FCC, OET Bulletin 65 (1997) pp 9, 19-21 to solve for E Field Strength for distance (R).

6. Utilizing the repetition of a sequence of operations calculate H and E Fields at 1 cm intervals moving outward from the antenna until both fields are less than their respective MPE.

7. Repeated for controlled and uncontrolled. Assumptions:

• Always include 4.1 dB (2.56) for ground reflection factor based on FCC, OET Bulletin 65 (1997) pp 20-21 and let the user increase losses should they desire a free space solution.

• Duty Cycle is a direct percentage of power.

• Minimum power of 5 W limit was subjective.

• Maximum power of 1500 W limit is the highest allowed by FCC Part 97.

• Minimum frequency of 3 MHz limit is MPE break point.

• Maximum frequency of 30 MHz limit is MPE break point.

• Loop Circumference are most common sizes used by HAMs, 5 – 25 is approximately 0.5 M to 2 M diameter loops.

• Cable losses of 0 to -10 dB was subjective.

• Worst case used for Radiation Loss as it does not include DC resistance or capacitor losses.

• The gain or loss of a magnetic loop antenna is a debated topic as the answer depends on a dozen variables. Worst case maximum value was used, 2.15 dBi (gain of dipole) as a loop is an infinitely small dipole. Modeling does show low angle 2.1 dbi gain is possible when the loop approaches /3 at 2 M height above ground, P. DeNeef, AE7PD, “Effects Due to Ground For Small Transmitting Loop Antennas.” QEX, July/August 2018, pp 15-17.