vk3cpu/magloop_equations.html

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<title>VK3CPU Magloop Antenna Calculator Equations</title>
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<header><b><a href="mailto:vk3cpu@gmail.com">VK3CPU</a> - <a href="./magloop.html">Magloop Antenna Calculator</a> Equations:</b></header>
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<b>For single-turn circular loop inductance:</b><br>
<img src="MagloopSingleTurnInductance.png" alt="magloop single-turn loop antenna inductance"><br>
<i>[r_loop - loop radius in meters; r_conductor - conductor radius in meters]</i><br><br>
<b>For multi-turn circular loop inductance:</b><br>
<img src="MagloopMultiTurnInductance.png" alt="magloop multi-turn loop antenna inductance"><br>
<i>[k_nagaoka - Nagaoka coefficient; l_coil - length of the coil in meters; r_loop - radius of the loop in meters]</i><br><br>
<b>For octagonal loop antenna inductance:[F W Grover]</b><br>
<img src="L_oct.png" alt="octagonal magloop antenna inductance"><br>
<i>[L - microhenries; N - turns; s - section side length cm; r - loop circumradius in cm; b - coil length in cm]</i><br><br>
<b>For hexagonal loop antenna inductance:[F W Grover]</b><br>
<img src="L_hex.png" alt="hexagonal magloop antenna inductance"><br>
<i>[L - microhenries; N - turns; s - section side length cm; r - loop circumradius in cm; b - coil length in cm]</i><br><br>
<b>For square loop antenna inductance:[F W Grover]</b><br>
<img src="L_sqr.png" alt="square magloop antenna inductance"><br>
<i>[L - microhenries; N - turns; s - section side length cm; r - loop circumradius in cm; b - coil length in cm]</i><br><br>
<b>Loss resistance:</b><br>
<img src="MagloopLossResistance.png" alt="magloop multi-turn loss resistance"><br><br>
<b>Surface resistance:</b><br>
<img src="MagloopSurfaceResistance.png" alt="magloop surface resistance of conductor"><br><br>
<b>Radiation resistance for circular loop:</b><br>
<img src="MagloopRadiationResistance.png" alt="multi-turn magloop radiation resistance"><br><br>
<b>Radiation resistance for octagon, hexagon and square loop:</b><br>
<img src="MagloopRadiationResistanceGrover.png" alt="multi-turn magloop radiation resistance"><br><br>
<b>Radiation efficiency:</b><br>
<img src="MagloopEfficiency.png" alt="magloop antenna efficiency"><br><br>
<b>Q factor:</b><br>
<img src="MagloopQ.png" alt="magloop antenna Q factor"><br><br>
<b>Capacitor voltage:</b><br>
<img src="Vcap.png" alt="magloop antenna capacitor voltage"><br><br>
<b>Loop current:</b><br>
<img src="I_loop.png" alt="magloop antenna loop current"><br><br>
<b>Bandwidth:</b><br>
<img src="BW.png" alt="magloop antenna bandwidth"><br><br>
<b>Single-loop capacitance:</b><br>
<img src="C_loop.png" alt="magloop antenna multi-turn loop capacitance"><br>
<i>[l_perimeter - conductor perimeter length in meters]</i><br><br>
<b>Multi-turn loop capacitance:</b><br>
<img src="MultiloopCapacitance.png" alt="magloop antenna multi-turn loop capacitance"><br>
<i>[Based on David W Knight's (G3YNH) paper "The self-resonance and self-capacitance of solenoid coils: applicable theory, models and calculation methods"]</i><br>
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