Small transmitting magnetic loop antennas (circumference under 0.25 wavelengths) exhibit very low radiation resistance, meaning total efficiency is dominated by conductor skin effect, tuning capacitor equivalent series resistance (ESR), and ground proximity losses. In this compact antenna sizing workspace, loop characteristics are represented by three inputs: a radiating loop conductor dimensional factor ($V_1$), an operating frequency radiation multiplier ($V_2$), and an ohmic loss resistance divisor ($V_3$).

The utility evaluates the primary radiation emission metric ($[V_1 imes V_2] / max(0.01, V_3)$), the root RF current distribution factor ($sqrt{max(0, V_1 imes V_2)}$), and the relative loop radiation efficiency share ($[V_1 / (V_1 + V_2)] imes 100$).

### Distinct Worked Calculation Evaluating a 20-meter amateur radio magnetic loop built with copper tubing: - Conductor Dimensional Factor ($V_1$): 128 - Radiation Multiplier ($V_2$): 36 - Ohmic Loss Divisor ($V_3$): 8

Step-by-step results: - Primary Radiation Metric: $(128 imes 36) / 8 = 16 imes 36 = 576.00$ - Current Distribution Root: $sqrt{128 imes 36} = sqrt{4608} approx 67.88$ - Radiation Efficiency Share: $[128 / (128 + 36)] imes 100 = (128 / 164) imes 100 approx 78.05%$

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