# How can this circuit oscillate at a VHF frequency?

I am practicing RF. I have looked at an FM transmitter circuit in a video. I went on to analyse it.

When the analysis got to the tank resonant circuit, I could not get it.

This parallel LC circuit is a bandstop circuit. This means it will increase the impedance when the frequency of the signal is like the resonant frequency and will decrease the impedance when the frequency of the signal is something unlike the resonant frequency.

Further, this inductor has 4 turns, a 0.01 m cross-section, and 8 mm length, which means, accordingly to the formula

L = (N²*u*A/l)


that this inductor has a value of:

L = (4²*(1.26*10^-6)*pi*0.01²)/0.008


Which gives us something around 800nH. So, using the formula

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


we discover that the resonance frequency of the tank will be around 80 MHz to 110 MHz, which is the FM band.

Putting these calculations aside, I don't know how this circuit will oscillate in the FM band because the input signal will oscillate only in the frequency of audible sound (20 Hz to 20 kHz) and the LC circuit is just and nothing more than a pass-band circuit.

Is this LC circuit capable of oscillating at a high FM frequency?

And what is the purpose of the transistor? Just amplifying the signal?

• Calculation of resonance is faulty - fortuitously hitting the FM band. Resonating capacitance is not only C4: C3 contributes capacitance, as does capacitance of a short antenna. In addition, the transistor adds $C_{BC}$, and there will be inevitable stray capacitance. Calculating inductance of a spiral wire in air is only an estimate (800 nH is likely too high). Calculating resonant frequency should be regarded as a very rough estimate - it is easily possible to miss the entire FM broadcast band. Dec 14, 2021 at 14:22

I don't know how this circuit will oscillate in the FM band because the input signal will oscillate only in the frequency of audible sound (20 Hz to 20 kHz) and the LC circuit is just and nothing more than a pass-band circuit.

It's a fairly standard Colpitts oscillator. Specifically a common-base Colpitts oscillator so, maybe use that term and, google it to get to grips with how it works.

Here's a link to an ADI article that should help. You even get details of how to build it. However, this build information is only good for a few MHz and not 90 MHz (especially not on breadboard). There is a minor variation between this and your circuit. It's how the emitter gets "tickled" from the collector. It's trivial really (if you did the math).

But here's the important thing - it's positive feedback from collector to emitter that causes it to self oscillate (and not the presence of an audio signal on the base).

The audio signal does have an effect though; it causes the BJTs internal miller capacitance (a parasite) to be modulated in a way that "follows" the audio waveform and, this in turn, modulates the carrier frequency and produces an FM signal.

Is this LC circuit capable of oscillating at a high FM frequency?

It's fine at FM broadcast frequencies but runs out of steam a little before UHF where, preference is given to the common-collector Colpitts oscillator~: - And what is the purpose of the transistor? Just amplifying the signal?

No, it doesn't amplify audio; it's a fundamental part of the oscillator circuit. • A comment regarding the differences between the three configurations - the only difference from the small signal point of view is which point in the circuit is called ground. They operate identically. Also the internal transistor parameters, in particular capacitance, are important to understand the operation. Especially at high frequency where, for example, C1 in your first circuit is often not present physically as in the OP's circuit. Dec 15, 2021 at 2:11
• C1 is present but in a round about way. Dec 15, 2021 at 7:36

Simply try it, it works if it is not built in a mess of wires all over the place on a solderless breadboard. BUT it sounds awful because its simplicity is missing pre-emphasis (treble frequencies boost) that is used on all FM radio stations so the de-emphasis used in all FM radios will cut high frequencies causing muffled sounds.

It is simple then its radio frequency changes if the supply voltage changes (maybe a battery voltage running down). Its radio frequency also changes if something moves towards or away from the antenna because the antenna connects directly to the tuned radio LC and affects the capacitance and therefore affects the frequency.