Tuesday, 22 August 2017

rf - Understand simple FM transmitter, inductance, resonance


I learn electronic , I try to understand this project, simplest FM transmitter : enter image description here 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)



OUTPUT



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 :




  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
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)


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.




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