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) Coil_radius = (Coil_diameter/2) Diameter = Air_diameter + (Coil_radius*2) Length = cm_to_inches(1.200) # 1.200 , cm to inches Radius = Diameter / 2. def solenoide_air_coil_inductance(): return ((Radius**2) * (Turns**2)) / ((9*Radius)+(10*Length)) L = solenoide_air_coil_inductance() print "Diameter: %.03f inches" % Diameter print "Radius: %.03f inches" % Radius 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)
Diameter: 0.290 inches Radius: 0.145 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 :
- 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 ...
Diameter: 0.250 inches Radius: 0.125 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 # Diameter = Air_diameter + (Coil_radius*2) ... capacitor = 0.01 # uf (0.01uf = 10 nf) inductor = L # uh inductance_in_henry = (inductor/1e6) # to henry capacitance_in_farad = (capacitor/1e8) # to farad W_radians_per_second = 1 f0=(W_radians_per_second / (2 * math.pi * math.sqrt((inductance_in_henry * capacitance_in_farad)))) 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)
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)
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.