- Characterize existing coils
- Making coils on existing forms
- Silver plated wire
- Making highly optimized coils
Suppose you purchased the coil shown above at a hamfest and would like to know its inductance at 13.56 MHz. You measure the diameter as 50 mm, the length is 200 mm, and there are 35 turns.
Use CoilCalc to identify and characterize the coil.
> CoilCalc --D=50 --l=200 --N=35 --d=1.44 --f=13.562
# QOIL™ — https://hamwaves.com/qoil/ — v20181217
# Coil design 2023-03-11 12:20
#
INPUT
# mean diameter of the coil D = 50.0 mm
# number of turns N = 35.0
# length of the coil ℓ = 200.0 mm
# wire or tubing diameter d = 1.44 mm
# design frequency f = 13.562 MHz
# The (plating) material is annealed copper.
#
INTERMEDIATE RESULTS
# winding pitch p = 5.71 mm
# physical conductor length ℓ_w_phys = 5501.4 mm
# effective pitch angle ψ = 2.09°
#
RESULTS
# Effective equivalent circuit
# effective series inductance @ design frequency L_eff_s = 16.652 μH
# effective series reactance @ design frequency X_eff_s = 1419.0 Ω
# effective series AC resistance @ design frequency R_eff_s = 1.438 Ω
# effective unloaded quality factor @ design frequency Q_eff = 986
# Lumped circuit equivalent
# f-independent series inductance; geometrical formula L_s = 14.105 μH
# series AC resistance @ design frequency R_s = 1.032 Ω
# parallel stray capacitance @ design frequency C_p = 1.5 pF
# Self-resonant frequency f_res = 26.342 MHz
#
DONATE
# If this calculator proved any useful to you,
# please, consider making a one-off donation
# towards keeping me and the server up and running.
# Thank you!
At 13.56 MHz the coil will have an effective inductance of 16.6 uH and the self-resonant frequency is high enough for the coil to be used in that frequency band.
The calculated Q is almost 1000, which is pretty good for a hand-wound coil, but note that it is physically impossible to make coils with this level of quality.
The high calculated Q probably translates into a reasonably high Q for a hand-wound coil of 200 to 400, which is still pretty good.
Suppose you have an existing coil form, a piece of 2" PVC pipe, and would like to make a coil similar to the one shown above. You know the form and wire diameter, you need a 12 uH inductance, and you are willing to use any length and number of turns.
You would like a coil with the highest possible Q.
Use CoilScanL to scan all possible coil lengths, and for each length interpolate the number of turns needed for an inductance of 12 uH, and show the parameters for each coil.
> CoilScanL --LTarget=12 --DForm=48 --lMin=20 --lMax=250 --lInc=10 --d=1.44 --f=13.562
# CoilScan 2023-03-11 13:21
#
# LTarget = 12, d = 1.44, p = 6, f = 13.562
#
# DForm = 48, lMin = 20, lMax = 250, lInc = 10
#
# D(mm), l(mm), Q(plot), Q, N, L(uH), wLen(m), Res(MHz), pitch(mm), Err, Cmd
49.44, 30.00, 621, 621 16.77, 12.00, 2.61, 34.32, 1.79, 0, "CoilCalc --D=49.440 --l=30.000 --N=16.770 --d=1.440 --f=13.562"
49.44, 40.00, 843, 843 17.89, 12.00, 2.78, 34.44, 2.24, 0, "CoilCalc --D=49.440 --l=40.000 --N=17.890 --d=1.440 --f=13.562"
49.44, 50.00, 947, 947 18.98, 12.00, 2.95, 34.40, 2.63, 0, "CoilCalc --D=49.440 --l=50.000 --N=18.980 --d=1.440 --f=13.562"
49.44, 60.00, 981, 981 20.03, 12.00, 3.11, 34.26, 2.99, 0, "CoilCalc --D=49.440 --l=60.000 --N=20.030 --d=1.440 --f=13.562"
49.44, 70.00, 986, 986 21.03, 12.00, 3.27, 34.05, 3.33, 0, "CoilCalc --D=49.440 --l=70.000 --N=21.030 --d=1.440 --f=13.562"
49.44, 80.00, 995, 995 21.98, 12.00, 3.41, 33.79, 3.64, 0, "CoilCalc --D=49.440 --l=80.000 --N=21.980 --d=1.440 --f=13.562"
49.44, 90.00, 983, 983 22.87, 12.00, 3.55, 33.52, 3.93, 0, "CoilCalc --D=49.440 --l=90.000 --N=22.870 --d=1.440 --f=13.562"
49.44, 100.00, 974, 974 23.72, 12.00, 3.69, 33.23, 4.22, 0, "CoilCalc --D=49.440 --l=100.000 --N=23.720 --d=1.440 --f=13.562"
49.44, 110.00, 972, 972 24.53, 12.00, 3.81, 32.94, 4.48, 0, "CoilCalc --D=49.440 --l=110.000 --N=24.530 --d=1.440 --f=13.562"
49.44, 120.00, 972, 972 25.31, 12.00, 3.93, 32.65, 4.74, 0, "CoilCalc --D=49.440 --l=120.000 --N=25.310 --d=1.440 --f=13.562"
49.44, 130.00, 957, 957 26.05, 12.00, 4.05, 32.37, 4.99, 0, "CoilCalc --D=49.440 --l=130.000 --N=26.050 --d=1.440 --f=13.562"
49.44, 140.00, 939, 939 26.76, 12.00, 4.16, 32.09, 5.23, 0, "CoilCalc --D=49.440 --l=140.000 --N=26.760 --d=1.440 --f=13.562"
49.44, 150.00, 923, 923 27.45, 12.00, 4.27, 31.82, 5.46, 0, "CoilCalc --D=49.440 --l=150.000 --N=27.450 --d=1.440 --f=13.562"
49.44, 160.00, 909, 909 28.11, 12.00, 4.37, 31.56, 5.69, 0, "CoilCalc --D=49.440 --l=160.000 --N=28.110 --d=1.440 --f=13.562"
49.44, 170.00, 897, 897 28.74, 12.00, 4.47, 31.30, 5.91, 0, "CoilCalc --D=49.440 --l=170.000 --N=28.740 --d=1.440 --f=13.562"
49.44, 180.00, 886, 886 29.35, 12.00, 4.56, 31.06, 6.13, 0, "CoilCalc --D=49.440 --l=180.000 --N=29.350 --d=1.440 --f=13.562"
49.44, 190.00, 876, 876 29.94, 12.00, 4.65, 30.82, 6.35, 0, "CoilCalc --D=49.440 --l=190.000 --N=29.940 --d=1.440 --f=13.562"
This looks good, so save the output to a CSV data file and display using Gnuplot.
> CoilScanL --LTarget=12 --DForm=48 --lMin=20 --lMax=250 --lInc=10 --d=1.44 --f=13.562 >Data.csv
> gnuplot LPlot.gp
Maximum Q occurs with an 80 mm coil. Consulting the data file we see that at that length the calculated Q is 995, the inductance is 12 uH as expected, and the resonant frequency is 33.75 MHZ. The coil has 22 turns.
Now that we know the maximum Q happens somewhere between 70 and 90, we can rerun the calculations for a more exact answer:
> CoilScanL --LTarget=12 --DForm=48 --lMin=70 --lMax=90 --lInc=1 --d=1.44 --f=13.562 >Data.csv
> gnuplot LPlot.gp
A length of 78 or 79 mm gives us the highest Q, but we would need to be accurate to 1/4 of a turn. A lengh ot 80 mm with 22 turns is more reasonable.
Would the coil benefit from using silver-plated wire? Specify the p ("wire plating") parameter to find out.
> CoilScanL --help
Usage:
CoilScanL --LTarget=<ind-uH> --DForm=<form-dia-mm> \
--lMin=<min-len-mm> --lMax=<max-len-mm> --lInc=<inc-len-mm> \
--d=<wire-dia-mm> --f=<freq-mhz> \
[--LenMM] [--LenFt] [--p=<plating-index>]
Where:
--LTarget=<ind-uH> Target inductance in uH
--DForm=<form-dia-mm> Form diameter, in mm
--lMin=<coil-len-mm> Min coil length to scan, in mm
--lMax=<coil-len-mm> Max coil length to scan, in mm
--lInc=<coil-len-mm> Coil length increment , in mm
--d=<wire-dia-mm> Wire diameter, in mm
--d=<some-number>AWG Wire specified as AWG
--f=<freq-mhz> Frequency of interest
--p=<plating-index> (OPTIONAL) Wire plating
=0 annealed copper (DEFAULT)
=1 hard-drawn copper
=2 silver
=3 aluminium
--LenM (OPTIONAL) Print conductor length in meters
--LenFt (OPTIONAL) Print conductor length in feet
--help Print this message and exit
> CoilCalc --D=49.440 --l=80.000 --N=21.980 --d=1.440 --f=13.562 --p=2
# QOIL™ — https://hamwaves.com/qoil/ — v20181217
# Coil design 2023-03-11 13:35
#
INPUT
# mean diameter of the coil D = 49.44 mm
# number of turns N = 21.98
# length of the coil ℓ = 80.0 mm
# wire or tubing diameter d = 1.44 mm
# design frequency f = 13.562 MHz
# The (plating) material is silver.
#
INTERMEDIATE RESULTS
# winding pitch p = 3.64 mm
# physical conductor length ℓ_w_phys = 3414.9 mm
# effective pitch angle ψ = 1.35°
#
RESULTS
# Effective equivalent circuit
# effective series inductance @ design frequency L_eff_s = 12.006 μH
# effective series reactance @ design frequency X_eff_s = 1023.1 Ω
# effective series AC resistance @ design frequency R_eff_s = 0.986 Ω
# effective unloaded quality factor @ design frequency Q_eff = 1037
# Lumped circuit equivalent
# f-independent series inductance; geometrical formula L_s = 11.358 μH
# series AC resistance @ design frequency R_s = 0.883 Ω
# parallel stray capacitance @ design frequency C_p = 0.7 pF
# Self-resonant frequency f_res = 33.786 MHz
#
DONATE
# If this calculator proved any useful to you,
# please, consider making a one-off donation
# towards keeping me and the server up and running.
# Thank you!
For the coil as designed, using silver plated wire would change the inductance by a negligible amount, but the Q would go up by about 4% (to 1037 from 995).
For most practical purposes, this increase of efficiency is not worth the expense, but if you are designing a high-power system, an inductive heating coil for example, you might want the extra efficiency.
With aluminum wire, the Q drops by almost a quarter (from 995 to 775)! Definitely make the coil out of copper and not aluminum!
Suppose you want to make a power coil with an off-the-chart efficiency (the author's actual goal for the project).
You know the inductance needed, you know how thick your wire is, and you can design a bespoke coil form of any size and length.
Setting some reasonable boundaries, you decide the coil form diameter can range from 20 mm to 300 mm, the length from 20 mm to 300 mm, and you want an inductance of 26 uH to match the corresponding capacitor at 13.56 MHz.
> CoilScanDL --LTarget=26 DMin=20 DMax=280 DInc=5 lMin=20 lMax=300 lInc=5 --d=1.291, --f=13.562
# CoilScan 2023-03-11 14:00
#
# LTarget = 26, d = 6.35, p = 6, f = 13.562
#
# DMin = 20, DMax = 280, DInc = 5
# lMin = 20, lMax = 300, lInc = 5
#
# D(mm), l(mm), Q(plot), Q, N, L(uH), wLen(ft), Res(MHz), pitch(mm), Err, Cmd
60.00, 280.00, 1939, 1939 41.73, 26.00, 25.82, 20.13, 6.71, 0, "CoilCalc --D=60.000 --l=280.000 --N=41.730 --d=6.350 --f=13.562"
60.00, 285.00, 1965, 1965 41.95, 26.00, 25.96, 20.08, 6.79, 0, "CoilCalc --D=60.000 --l=285.000 --N=41.950 --d=6.350 --f=13.562"
60.00, 290.00, 1991, 1991 42.17, 26.00, 26.09, 20.04, 6.88, 0, "CoilCalc --D=60.000 --l=290.000 --N=42.170 --d=6.350 --f=13.562"
60.00, 295.00, 2018, 2018 42.38, 26.00, 26.23, 19.99, 6.96, 0, "CoilCalc --D=60.000 --l=295.000 --N=42.380 --d=6.350 --f=13.562"
60.00, 300.00, 2045, 2045 42.59, 26.00, 26.36, 19.95, 7.04, 0, "CoilCalc --D=60.000 --l=300.000 --N=42.590 --d=6.350 --f=13.562"
60.00, 305.00, 2063, 2063 42.81, 26.00, 26.49, 19.91, 7.13, 0, "CoilCalc --D=60.000 --l=305.000 --N=42.810 --d=6.350 --f=13.562"
65.00, 245.00, 1974, 1974 36.56, 26.00, 24.51, 20.16, 6.70, 0, "CoilCalc --D=65.000 --l=245.000 --N=36.560 --d=6.350 --f=13.562"
65.00, 250.00, 2012, 2012 36.78, 26.00, 24.65, 20.11, 6.80, 0, "CoilCalc --D=65.000 --l=250.000 --N=36.780 --d=6.350 --f=13.562"
: : :
^C
> CoilScanDL --LTarget=26 DMin=20 DMax=280 DInc=5 lMin=20 lMax=300 lInc=5 --d=1.291, --f=13.562 >Data.csv
> gnuplot DLPlot.gp
We see that maximum Q around 7000 (calculated) happens with a coil diameter of 260 mm and a length of 90 mm - a short, squat coil.
The calculated Q (7000) is not achievable phusically: at that level of Q even the tiniest of perturbations will have a massive negative effect on the Q.
Still, the design indicates that the most efficient coils are found at large diameters with reasonable lengths and the indicated coil would make a good starting point for development.
