Playing around with this on-line loop evaluation tool:

http://www.66pacific.com/calculators/small_tx_loop_calc.aspx

Immediately below are the outputs for a 17 gauge (.045 inch diameter) wire just under one-quarter wavelength in length for the 40 meter band loop antenna. Compare what the loop antenna calculator calculated versus what was seen for ‘actual real-world results’ shown further down:

Input Values: Length of conductor: 32 feet Diameter of conductor: .045 inches (17 AWG) Frequency: 7 MHz RESULTS: Antenna efficiency: 21% (-6.9 dB below 100%) Antenna bandwidth: 217 kHz Tuning Capacitance: 149 pF (real world result = 24 pF) Capacitor voltage: 702 volts RMS Resonant circulating current: 4.60 A Radiation resistance: 0.484 ohms (real world = 22.2) Loss Resistance: 1.87 ohms Inductance: 3.46 microhenrys Inductive Reactance: 152 ohms Quality Factor (Q): 32.3 Distributed capacity: 26 pF Antenna "circumference": 32 feet Comments: 1) The specified conductor length of 32 feet is OK.2) Conductor length should be between 17.0 and 34.1 feet at the specified frequency of 7 MHz.3) For highest efficiency, the conductor length for a small transmitting loop antenna should be greater than 1/8 wavelength (greater than about 17.0 feet at the specified frequency of 7 MHz). 4) To avoid self-resonance, the conductor length for a small transmitting loop antenna should be less than 1/4 wavelength (less than about 34.1 feet at the specified frequency of 7 MHz).

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Below are the actual, real-world results obtained:

Antenna efficiency: ~100% (on a par w/dipole) Tuning capacitance: 24 pF Antenna bandwidth: 50 kHz 1.5:1, 110 kHz 3:1 Radiation resistance: 22.2 ohms (fed w/transformer next to tuning capacitor) AC and DC wire resistance calculations at 7 MHz: Freq Gauge Wire Len DCR ACR Rrad Ratio ----- ------ ----- ---- ------- ----- ---- ----- 7 MHz 17 ga. Al 32' 0.265 2.452 22.5 9.17 7 MHz 10 ga. Cu 32' 0.0318 0.835 22.5 26.9