Need help understanding simple FM transmitter

I made a simple FM transmitter following https://maker.pro/custom/tutorial/how-to-make-an-fm-transmitter and it worked! Now I need some help to understand how. My coil is made of 1 mm copper wire has 6 turns and 8 mm wire diameter. According to this online calculator: https://www.eeweb.com/tools/coil-inductance this means that: L = 3.9e-7 H

I did not have any 5 pF trim capacitor so I used a 3 pF capacitor instead.

Am I correct in assuming that the frequency this will transmit on can be found by looking at the L1 C2 as a LC oscillator and using the frequency formulae:

fR = 1/(2*pi*sqrt(LC))

?

If so I should get fR = 147 MHz. Which is strange since I received the signal on 91.5 MHz on my radio.

In a LC circuit I understand that the signal decays exponentially over time. That is hopefully not happening here. Why? Because of C4 maybe?

Also what is the purpose of C1?

If I want to increase the range of this FM transmitter somewhat can I do this by simply replacing R2 with a 470 Ohm resistor?

Are there free simulator programs that let me see the resulting spectrum at the antenna?

Answer

Resonant frequency formula is nearly correct. You have mostly one L - stray inductance is not included. But you have four capacitances that can be assumed in parallel:

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  C2 (obviously)

  
  


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  C3 (it is actually combined with \$ C_{be} \$ of the transistor)

  
  


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  \$ C_{bc} \$ of the transistor

  
  


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  Antenna reactance, which is often capacitive.

  
  

  \$ F_r= \frac {1}{2 \pi \sqrt {L(C_2 + C_3 + C_{bc} + C_{ant})}}\$

  
  

Again, stray capacitance hasn't been included - it will cause \$F_r \$ to be even lower. Because L's and C's are so small, using this formula to hit a desired frequency is very difficult.

This is an oscillator whose amplitude doesn't decay, but grows until non-linear losses limit the amplitude. C4 is the element that mostly causes positive feedback - making this transistor oscillate.

C1 is a "bypass" capacitor that grounds the transistor base at the oscillating frequency, but allows low-frequency audio to change base voltage. At audio frequencies, reactance of C1 is mostly insignificant.

Everybody wants more range. Making R2 too small will kill the oscillations. Power output might increase, but you'll hardly notice range improvement. A power amplifier would improve power, but would likely violate FCC rules (in America).

Using SPICE to see the FM modulation would be extremely tedious. You must use a transient analysis with time-step small enough to have many steps at the oscillating frequency (about 100 MHz). Yet the simulation must run for milliseconds.