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  • L : Inductance in microhenries.
  • A : Loop area in square meters or square feet.
    • -
  • C : Effective capacitance for multi-turn loops in picofarads.
    • +
  • C : Effective capacitance of the loop in picofarads.
  • peri : Perimeter of the main loop in meters or feet.
  • c : Distance between windings, measured from the conductor centers in mm or inches.
  • cond : Total required conductor length in meters or feet.
    • @@ -108,6 +108,8 @@

Change history:
+ [21-Sep-21]
+ * Added distributed capacitance calculation and display for the single turn loop.
[19-Sep-21]
* Increased supported conductor diameter to 80 mm. (3.15 inches)
[18-Sep-21]
@@ -157,7 +159,8 @@ var inductance = 0.0; var area = 0.0; // Loop area in square meters. var perimeter = 0.0; // Perimeter of a single turn of the main loop - var multiloop_capacitance = 0.0; // Effective capacitance of a multi-turn loop + var loop_capacitance = 0.0; // Effective capacitance of a single or multi-turn loop + var srf = 0.0; // Self-resonant frequency SRF var conductor_length = 0.0; // Total conductor length var frequencies = []; @@ -167,13 +170,11 @@ 0.1365, 0.475, 1.8, 3.5, 5.0, 7.0, 10.1, 14.0, 18.068, 21.0, 24.89, 28.0, 29.7, 35.0, 40.0, 45.0, 50.0, 52.0, 54.0 ]; - // Max frequency is for multi-turn loops: - var max_freq = calculateSRF(); frequencies = []; hamFrequencies.forEach(freq => { const wavelength = 3e8 / (freq * 1e6); const l = (Math.PI * loop_diameter_slider.value) / wavelength; - if ((l <= 0.30) && ((freq * 1e6) < max_freq)) { + if ((l <= 0.30) && ((freq * 1e6) < srf)) { frequencies.push(freq); } }); @@ -183,7 +184,8 @@ inductance = getInductance(); area = getArea(); perimeter = getPerimeter(); - multiloop_capacitance = (loop_turns_slider.value > 1) ? multiloopCapacitance() : 0.0; + loop_capacitance = (loop_turns_slider.value > 1) ? multiloopCapacitance() : (2.69e-12 * perimeter); + srf = calculateSRF(); conductor_length = ((((perimeter* loop_turns_slider.value) ** 2.0) + ((loop_spacing_slider.value * conductor_diameter_slider.value * 1e-3 * loop_turns_slider.value) ** 2.0)) ** 0.5); } @@ -358,18 +360,17 @@ var l_multiloop_capacitance = 1e-12 * shape_factor * (ctdw(ff, ei, ex) / Math.sqrt(1 - h**2 / loop_diameter_slider.value**2) + ciae(ff, ei, ex)) * loop_diameter_slider.value; return l_multiloop_capacitance; // in Farads } - + /* + function singleloopCapacitance() { + var retval = 2.69 * perimeter; + return (retval*1e-12); // in Farads + } + */ + function tuningCapacitance(frequency) { // frequency is in Hertz const reactance = inductiveReactance(frequency); - /* - var multiloop_capacitance = 0.0; - if(loop_turns_slider.value > 1) { - // Only compensate for multiloop capacitance when we have more than 1 turn: - multiloop_capacitance = multiloopCapacitance(); - } - */ - const capacitance = 1e12 * ((1.0 / (2.0 * Math.PI * frequency * reactance)) - multiloop_capacitance); + const capacitance = 1e12 * ((1.0 / (2.0 * Math.PI * frequency * reactance)) - loop_capacitance); return capacitance; // in picofarads } @@ -514,10 +515,9 @@ } function calculateSRF() { - const capacitance = (loop_turns_slider.value > 1) ? multiloopCapacitance() : 1e-12; // Assume 1 pF for a single loop. Yes it is wrong, but we just don't want a divide-by-zero error below. // According to Knight (2016), SRF for a single coil is equivalent to the circumference being equivalent to a half-wave dipole. const inductance = getInductance(); - return (1.0 / (2.0 * Math.PI * ((inductance * capacitance) ** 0.5))); + return (1.0 / (2.0 * Math.PI * ((inductance * loop_capacitance) ** 0.5))); } metric_radio.oninput = function() { @@ -1291,14 +1291,11 @@ sctx.font = normal_font; // Multi-turn loop, so calculate C and SRF: - if(loop_turns_slider.value > 1) { - const L = multiloopCapacitance() * 1e+12; - const srf = calculateSRF(); - sctx.textAlign = "right"; - sctx.fillText("C = " + L.toFixed(0).toString() + " pF", win_width-8, 18); - sctx.fillText("SRF = ", win_width-8, win_height * 0.1 + 18); - sctx.fillText((srf*1e-6).toPrecision(3).toString() + " MHz", win_width-8, win_height * 0.1 + 33); - } + const L = loop_capacitance * 1e+12; + sctx.textAlign = "right"; + sctx.fillText("C = " + L.toFixed(0).toString() + " pF", win_width-8, 18); + sctx.fillText("SRF = ", win_width-8, win_height * 0.1 + 18); + sctx.fillText((srf*1e-6).toPrecision(3).toString() + " MHz", win_width-8, win_height * 0.1 + 33); sctx.textAlign = "right"; sctx.fillText("cond = " , win_width-8, dim_y + 08); @@ -1318,9 +1315,10 @@ } } + // Set the global variables, which are all determined by physical dimensions, and are thus frequency-independent: + setGlobals(); // Update the frequencies, now that we have the sliders available: updateFrequencies(); - setGlobals(); drawFrontDesign(); drawSideDesign(); diff --git a/magloop_equations.html b/magloop_equations.html index 8dd5f0d..0871655 100644 --- a/magloop_equations.html +++ b/magloop_equations.html @@ -9,36 +9,45 @@
VK3CPU - Magloop Antenna Calculator Equations:

- For single-turn circular loop inductance:
- magloop single-turn loop antenna inductance

- For multi-turn circular loop inductance:
- magloop multi-turn loop antenna inductance

- For octagonal loop antenna inductance:[F W Grover]
- octagonal magloop antenna inductance

- For hexagonal loop antenna inductance:[F W Grover]
- hexagonal magloop antenna inductance

- For square loop antenna inductance:[F W Grover]
- square magloop antenna inductance

- Loss resistance:
+ For single-turn circular loop inductance:
+ magloop single-turn loop antenna inductance
+ [r_loop - loop radius in meters; r_conductor - conductor radius in meters]

+ For multi-turn circular loop inductance:
+ magloop multi-turn loop antenna inductance
+ [k_nagaoka - Nagaoka coefficient; l_coil - length of the coil in meters; r_loop - radius of the loop in meters]

+ For octagonal loop antenna inductance:[F W Grover]
+ octagonal magloop antenna inductance
+ [N - turns; s - section side length m; r - loop radius in m; b - coil length in m]

+ For hexagonal loop antenna inductance:[F W Grover]
+ hexagonal magloop antenna inductance
+ [N - turns; s - section side length m; r - loop radius in m; b - coil length in m]

+ For square loop antenna inductance:[F W Grover]
+ square magloop antenna inductance
+ [N - turns; s - section side length m; r - loop radius in m; b - coil length in m]

+ Loss resistance:
magloop multi-turn loss resistance

- Surface resistance:
+ Surface resistance:
magloop surface resistance of conductor

- Radiation resistance for circular loop:
+ Radiation resistance for circular loop:
multi-turn magloop radiation resistance

- Radiation resistance for octagon, hexagon and square loop:
+ Radiation resistance for octagon, hexagon and square loop:
multi-turn magloop radiation resistance

- Radiation efficiency:
+ Radiation efficiency:
magloop antenna efficiency

- Q factor:
+ Q factor:
magloop antenna Q factor

- Capacitor voltage:
+ Capacitor voltage:
magloop antenna capacitor voltage

- Loop current:
+ Loop current:
magloop antenna loop current

- Bandwidth:
+ Bandwidth:
magloop antenna bandwidth

- Multi-loop capacitance:
- magloop antenna multi-turn loop capacitance

+ Single-loop capacitance:
+ magloop antenna multi-turn loop capacitance
+ [l_perimeter - conductor perimeter length in meters]

+ Multi-loop capacitance:
+ magloop antenna multi-turn loop capacitance
+ [Based on David W Knight's paper "The self-resonance and self-capacitance of solenoid coils: applicable theory, models and calculation methods"]

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