Understand simple FM transmitter, inductance, resonance

I learn electronic , I try to understand this project, simplest FM transmitter : The project is describe here : https://makezine.com/projects/super-simple-fm-transmitter/

The inductance of L1 (Strip about 4" of 18AWG solid copper wire and wind 4 turns around the threads of a 1/4-20 bolt.) is not specified for L1, then I try to calculate this with python :

#
# INDUCTOR
#
import math

def cm_to_inches(cm):
return cm / 2.54

Turns         = 4 # 4
Coil_diameter = cm_to_inches(0.102)    # 0.102 , cm to inches (18AWG)
Air_diameter  = cm_to_inches(0.635)    # 0.635 , cm to inches (1/4-20 bolt)
Length        = cm_to_inches(1.200)     # 1.200 , cm to inches

def solenoide_air_coil_inductance():

L = solenoide_air_coil_inductance()

print "Diameter: %.03f inches" % Diameter
print "Length: %.03f inches"   % Length

print L
print "Inductance: %.12f H" % (L/1e6)
print "Inductance: %.09f mh" % (L/1e3)
print "Inductance: %.03f uh" % L
print "Inductance: %.02f nh" % (L*1e3)


OUTPUT

Diameter: 0.290 inches
Length: 0.472 inches
0.0558472400332
Inductance: 0.000000055847 H
Inductance: 0.000055847 mh
Inductance: 0.056 uh
Inductance: 55.85 nh


For my script , my help is this website http://www.66pacific.com/calculators/coil-inductance-calculator.aspx and I can read :

1. Enter the coil diameter (form diameter + wire diameter - see diagram).

But on makezine.com, in comments, 'WH' find approximately 42.74 nH because he not use wire diameter on 'total' diameter.

The result of my code without the (Radius *2) or Diameter of the wire :

Diameter      = Air_diameter
...


OUTPUT

Diameter: 0.250 inches
Length: 0.472 inches
0.042739357227
Inductance: 0.000000042739 H
Inductance: 0.000042739 mh
Inductance: 0.043 uh
Inductance: 42.74 nh


Yes, I find the same value as 'WH'.

Who says true ? Does the formula have to include the diameter of the wire, is my code correct ?

Also I try to calculate output RF frequency, for that I use 'LC' C3 0.01uf and L1 previously calculated (I start and I try to understand current flow, inductance, impedance, magnetic field etc... how this circuit work), then my code :

#
# RESONANCE FREQUENCY
#
...
capacitor = 0.01 # uf (0.01uf = 10 nf)
inductor  = L    # uh
inductance_in_henry  = (inductor/1e6)  # to henry

print "Inductance  : %.12f H" % inductance_in_henry
print "capacitance : %.12f F" % capacitance_in_farad
print "%.02f Hz" %(f0)
print "%.02f KHz" %(f0/1e3)
print "%.02f MHz" %(f0/1e6)


OUTPUT

Inductance  : 0.000000055847 H
capacitance : 0.000000000100 F
67347158.08 Hz
67347.16 KHz
67.35 MHz


And without wire diameter :

Diameter      = Air_diameter + (Coil_radius*2)


OUTPUT

Inductance  : 0.000000042739 H
capacitance : 0.000000000100 F
76985004.32 Hz
76985.00 KHz
76.99 MHz


With my RTL-SDR receiver and GQRX software I find RF signal between 70 and 72 MHz , Sometimes the frequency varies because I work on a breadboard and this is really not suitable (bad connections, noise, frequency change when I touch a wire ( body capacity ) for example and my capacitors do not necessarily have a good tolerance and my inductor is probably not adjusted to the millimeter). My calcul result is 67.35 MHz (with wire diameter), I seem close to the signal found.

But, I'm start RF and electronic and i'm not sure to use the good capacitor for the calcul or if I have to take into account the other 10pf capacitors . I read comments on makezine.com and I see : change C5 capacitor for 2-22pf for frequency adjustement, which would suggest that the frequency should be calculated with C5 and not C3 that I use? Frequency resonance is equal to RF out ?

How to calculate the inductor value and the output Rf (frequency) for this circuit ?

Could someone guide me or give me official documentation ? Thank you.

• The official documentation is original archive web.archive.org/web/20140719004230/http://www.translocal.jp/… translate as required. L1 construction is very critical and must be precise to within <<1% of dimensions to be , C2 can be adjustable. $\omega=1/\sqrt{LC}$ with equivalent C shunting L – Sunnyskyguy EE75 May 19 '18 at 15:04
• @f14284 When making a comment to someone on particular, use the @ in front of its username, that lets the user know someone answered. I haven't used it because my comment is right below your post, so you'd be notified for every comment -- only made an exception now, for exemplification. Type @ and, if there are more users, you can use TAB to select. – a concerned citizen May 19 '18 at 16:01 