Actually, for all concerned (regardless of the homework aspect), I would be interested in hearing this circuit being explained and discected too?
I've tried building these things in the past and they just don't work. Stage by stage explanation would be brilliant, as well as design caveats such as grounding. The issue is that almost all of the radio explanations out there explain in terms for the complete layman, rather than how to practically do it right there in front of you and why.
The description actually is descriptive, even though I likely would have used other words.
It's pretty common with schematics to start at the left and move right, so any input or generation is at the left, and any output is at the right.
Hence you have the electret microphone at the left, "mic", and the output of the transmitter, "aerial", at the right.
The microphone picks up the sound, its audio output gets amplified by the first transistor (it's first because of that norm of reading from left to right). The second transistor, ie the one on the right, is an oscillator, generating a signal in the FM broadcast band.
But you want to send that audio signal out on the airwaves, so there is that 100n capacitor between the output (ie the collector) of the first stage and the base of the second stage (ie the oscillator stage). That audio applied to the oscillator causes it to shift frequency, following the audio signal as it varies in amplitude and frequency.
The first stage, ie the audio amplifier stage, just about any small signal NPN transistor should work there, it's not critical. Transistors with a "BC" prefix are from the UK and/or Europe, and you don't generally see them here in North America. The second stage is more critical, since it has to be able to oscillate at 108MHz, but a lot of general purpose transistors will still work there. Note they use the same transistor for both, since it is a cheap transistor. SOmeone else is bound to post about specific replacements for the BC457.
I thought the description on that page of the electret microphone was fairly good, though I'm not sure an internal description was needed for the purpose of the FM transmitter. Most consumer electronics nowadays uses electret microphones when they have built in microphones, so a cordless phone, some sort of tape recorder, cellphones, walkie talkies, baby monitors and answering machines (and I'm sure I've forgotten some) will have one that you can pull out, so watch those garage sales. You do have to wire them in properly, they are polarity sensitive but most I've seen either have color coded leads (red being positive) or have a "+" sign to mark the positive lead. That positive lead would be the side of the microphone that goes to the 22K resistor.
The description that page is fairly good, if it's not enough then you should ask specific questions based on what doesn't make sense to you.
The first thing I tried to build, when I was 11 years old, was an "AM wireless microphone", actually it sent morse code. It never did work, but then I didn't know enough about anything to figure out where I went wrong. IN retrospect, it might have been as simple as my lack of soldering skill, or the parts they offered at the parts store as substitutes (I wouldn't have known whether they were suitable replacements or not), or the coil had the pinouts different from the magazine article so I never wired it in properly. Or I may have simply made a wiring error, and just too inexperienced to see the error when I looked over the wiring, and not having a clue about the theory to work through what might be wrong.
In some ways you have to throw away a few early projects, but you do learn from them. At least I did.
"FM wireless microphones" have the further disadvantage of being higher in frequency, where wiring becomes a little more of a concern. Keep the leads short, or don't expect it to work. Also, most people don't have receivers that cover a lot of the spectrum up there, so if the thing is mistuned (because the coil isn't done properly or a capacitor is wrong, or some other factor), the transmitter might be working fine but the signal not be in the FM broadcast band.
If all you've tried to make are "FM wireless microphones", it makes sense to start with something simpler. Make a simpler audio oscillator, so you can work on soldering skills and get a feel for everything. The wiring and parts won't be so crucial, and the success will likely help with the next step.
That circuit offered up, you might connect an audio amplifier (a boombox with external inputs, or your stereo system) to the collector of the first stage (on the left, where the 10K resistor connects to the transistor), and see if you hear something when you speak into the microphone. Simplifying limits the variables, and if you have success, then you can deal with the second stage. If you get no audio, then you have to make sure the wiring is right and the microphone is good, etc.
The first BC547 is the audio amp/modulator, and the second is the oscillator/output. The audio is fed to the oscillator's base, which changes the interelectrode capacitance, which changes the resonant freq. of the tuned circuit on the fly, frequency modulating it, albeit poorly. ;-)
The electret mic needs bias because it's essentially a capacitor.
Well no, capacitance microphones need bias because they are a capacitor and need the bias.
Electrets are basically capacitors, but are permanently biased, that process of heating it up and placing it in a magnetic field while it cools (I think that description is wrong, the make your own electret in Popular Electronics decades ago used High Voltage from a TV set while it cooled).
Electret micrphones need an external source of voltage because the all have a built in FET buffer, to take the audio signal off the actual microphone element, which is a very high impedance point, and transform it down to an impedance that is workable. The external voltage is used to power the FET, not the actual electret element. (Capacitor microphones needed a buffer too, but when they were common there weren't FETs so a vacuum tube had to be used and those were too bulky to be internal).
Electret microphones are readily available in junk equipment as I pointed out in another post. It actually is worth sacrificing one to see what's inside. I took one apart a few years ago, and had expected to see nothing much. But there was the element, and there was a plastic encased FET in a small case but still recognizable as a transistor (I had expected a blog of epoxy) and a resistor.
The following is a short explanation of the circuit given here:
The electret microphone, when 'biased' (essentially, powered) with a resistor connected to a stable voltage, outputs a small voltage waveform at the resistor/microphone junction, which is proportional to the pressure waves in the sound it 'hears'. That microphone can't put out much voltage/current, though, so the leftmost transistor is used to take this tiny output (through a capacitor) and amplify it to a larger inverted waveform.
That larger waveform is then used to control the frequency of an oscillator, which is initially tuned to output a 'carrier' wave at some high frequency, possibly between 88MHz and 108MHz. The frequency depends on the inductance, and capacitance of the variable capacitor. It also depends on the capacitance between the three terminals of the transistor in a complex way. Finally, it also depends on that 5.6pF capacitor that goes from collector to emitter, and the antenna. The transistor is used to add a tiny bit of energy to the resonant circuit on each cycle to keep it resonating. It resonates whether or not there is any input from the microphone.
The input waveform (through the amplifying transistor) modifies the capacitance of the resonant circuit by changing the biasing of the base terminal. This affects the frequency, since the resonant frequency is inversely proportional to the square root of the capacitance.
So, this causes the frequency to vary from the tuned frequency by some small amount which depends on the input sound. This variance can be picked up and output by an FM receiver as sound.
There are lots of problems with this circuit. It is often difficult to get it to oscillate at all. The capacitance of your hand near the circuit can affect the frequency it is tuned to, so it can interfere with other stations. They often oscillates at the wrong frequency, and instead generates a harmonic in the FM band rather than oscillating at the desired frequency. It undoubtedly generates a lot of stray noise into other bands, but the power is so low that that usually does not matter.
There are much better circuits. For example, here is one:
You can find the circuit it uses around the net, and build it yourself, or just buy the kit, which is very cheap. It is very stable, and can be built in about an hour. It will nearly always work the first time, unless you can't follow instructions.