Several people have asked me about determining the number of turns of wire
for a particular frequency when building QRP radio projects. I have many
times given the ROUGH "starting" point:-
Capacitance(pf) = Wavelength in meters
Coil (turns) = Wavelength in meters
Naturally the size of the coil former you use will affect the turns needed
for a particular frequency, so this "starting" point is very rough and is
only intended to get you in the right vicinity. A GDO is one of the most
tools I posess, and I will describe one of these in another posting in the
near future. To answer the first question for those who are interested in
calculating coil turns, read on.
There are several formulas for calculating the number of turns required in
any given application, but the results seem to differ quite a lot from one
formula to another. I use two variants of Wheelers formula, one for single
layer coils and another for multi-layer (pile wound) coils. I shall give
the formulas twice, in case some of these "special" ASCII characters are
printed as garbage on the text editor you use (I use XTGOLD).
The formulas assume that there is NO ferrite, or brass core to the coil. A
ferrite core will reduce the number of turns by 10% to 25%, depending upon
the size of the ferrite lump, and how far it is screwed into the former. A
long ferrite rod can reduce the number of turns by as much as 50% to 60%.
A brass tuning slug will INCREASE the turns required by typically 5% - 10%
Just in case you have forgotten, you can calculate the value of required
inductance, capacitance and impedance with these formulas, but I will not
insult you intelegence explaining them.
1
Capacitive reactance (Xc) = ------
2ã f C
Incuctive reactance (Xl) = 2ã f L
1
Tuned circuit frequency = ------
2ã ûLC
At resonance Xc = Xl
Tap inductors; Impedance ratio = turns ratio squared
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SINGLE LAYER COILS
L (9r + 10l) L (9r + 10l)
Ný = ------------ N x N = ------------
rý r x r
where L = inductance in micro-henries
l = length of the winding in inches
N = the number of turns
r = outside radius of the coil in inches
EXAMPLE. I want a coil to have 20uH inductance in an HF PA valve anode for
30 MHz. I shall use a toilet roll tube for a former (2 inches in
diameter). I will space the coil out so that the winding length
is one inch.
20 x (9x1 + 10x1) 20 x 19 380
Ný = ----------------- = ------- = ---
1 x 1 1 1
Ný = 380 therefore N = 19.4935 turns (20 turns)
Even 4mm Dia. Cu wire will allow 20 turns per inch, take your pick. If it
burns when you apply power then use a thicker wire.
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MULTI-LAYER COILS
L (3a + 9b + 10c) L (3a + 9b + 10c)
Ný = ----------------- N x N = -----------------
0.2aý 0.2a x 0.2a
where L = inductance in micro-henries
a = winding thickness + former diameter in inches
b = length of winding in inches
c = winding thickness in inches
N = number of turns
EXAMPLE. I want a coil for a 1MHz medium wave QRP pirate-radio transmitter
amplifier stage tuned circuit. The inductance I need is 200uH.
I will use a plastic bottle-top former, 0.5" Dia. I can allow a
a total of 1.0" for the coil diameter, and, it must be 0.5" long.
(L = 200, a = 0.75", b = 1", c = 0.25")
200 (3x0.75 + 9x0.5 + 10x0.25) 200 (2.25 + 4.5 + 2.5)
Ný = ------------------------------ = ----------------------
(0.2 x 0.75)ý 0.0225
200 x 9.25 1850
Ný = ---------- = ------ = 82222.222r
0.0225 0.0225
Ný = 82222.222r therefore N = û82222.2222 = 286.744 turns.
This winding is .25" thick by .5" long. Total cross-sectional area of the
coil is 0.125". I therefore need a wire thickness that will fit into this
area = 2293.953 turns per square inch or thinner. 29 SWG (0.35mm Dia.) is
the max thickness of wire I can use, according to the following table.
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AWG SWG (mm) t/i t/iý ê/100m COPPER WIRE TABLE
--- --- ---- ----- ------ ------- -------------------------
-- 47 0.05 444 197000 894 AWG = American Wire
38 42 0.10 151 22900 224 Guage.
35 38 0.15 109 12000 99
32 36 0.20 85.7 7300 55.8 SWG = Standard Wire
30 33 0.25 74.6 5550 35.7 Guage.
29 31 0.30 67.6 4550 24.8
27 29 0.35 56.5 3190 18.2 (mm) = Diameter of wire
26 27 0.40 51.5 2650 14.0 in millimeters.
25 26 0.45 46.5 2070 11.2
24 25 0.50 42.4 1789 8.9 t/i = Number of turns
23 23 0.60 38.3 1513 6.21 per inch.
21 22 0.70 29.2 852 4.54
20 21 0.80 26.0 676 3.49 t/iý = Number of turns
19 20 0.90 23.5 550 2.76 per square inch.
18 19 1.00 19.7 388 2.26
12 14 2.00 9.3 86 0.567 ê/100m = Ohms per 100meter
9 11 3.00 7.2 51 0.252 length.
6 8 4.00 6.1 38 0.142
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0.05 mm wire will handle 3 mA
0.10 mm wire will handle 12 mA
0.50 mm wire will handle 300 mA
1.00 mm wire will handle 1.25 amperes
4.00 mm wire will handle 20.10 amperes
Further reading:
1. "Radio and Telecommunication Engineers Design Manual" by R. E. Blakley
(Pitman). [Quite detailed]
2. "Coil Design and Construction Manual" by B. B. Babani
(Bernard Babani Publishing) [Simple presentation]
3. "The ARRL Handbook For Radio Amateurs" by the ARRL
(ARRL) [Information a little limited].
Have fun, de HARRY, Upplands Vasby, Sweden.
Frank, G3YCC