For data transmission / reception, one of the less expensive options today is a pre-built module around the nRF24L01+ Transceiver IC. These modules typically offer a built-in PCB-trace antenna, 250 Kbps to 2 MBPS bandwidth before error correction, and are tried and tested.
Most important, they save you time in debugging and antenna tuning. After thousands of people have used these modules, which are built on the manufacturer's reference designs after all, most of the kinks are pretty thoroughly ironed out. Also, being able to tap the experience of many others on the internet who have used such a module, counts for a lot when trying to resolve issues.
For instance, this listing on eBay is for a mere US$2.10 with free international shipping. It uses the 2.4 GHz band, which does not need licensing for low power use in most countries.
Another alternative is this 433 MHz band transmit / receive pair of modules (just 9.6 Kbps though), in case you specifically want to stay with transmit-only and receive-only designs. US$1.99 for the pair makes it pretty attractive.
Of course, in each case, you could as well build your own module starting from the IC manufacturer's reference design, and thus learn while implementing your radio functionality.
It is unlikely that the price advantage of massive volume production can be beaten, though.
It intentionally DOES oscillate.
It goes beyond a regenerative receiver and is called a super-regenerative receiver, invented by Edwin Armstrong in 1922.
The values of R3 and C3 are arranged so that after oscillation starts the voltage builds up on the emitter due to rectification of the oscillations. After some period (10's of microseconds typically) the bias will be such that the oscillations stop. The voltage will then decay with the time constant of R3/C3 until oscillations start again. This typically occurs at a frequency in the range of 10's to hundreds of kilohertz.
Normally in an oscillator the oscillations build up from noise however if any signal at the oscillation frequency is present the oscillations will build up more quickly. This is the signal being received. The average supply current will depend upon how quickly the oscillation starts which depends upon the signal present. Thus the supply current is dependent on the received signal, the output from R1 depends on the supply current.
Usually the transmitter is amplitude modulated at an audio frequency and this can be recovered from C7 with suitable filtering and amplification.
A super-regenerative receiver can get extremely high gain out of a single stage but when no signal is present the output will be very noisy. Because the build up of oscillations is exponential it usually has a logarithmic response.
They are used less these days because they tend to radiate and also have a very broad bandwidth. A common application is for garage door openers.
kevin
Best Answer
For a totally passive FM set you can use something like a resonant circuit that is tuned somewhat off the carrier frequency so variations in carrier frequency result in changes in output voltage from the detector at the baseband frequency. This is called 'slope detection'.
For example, from this website:
This should also work to pick up AM signals.
An even simpler circuit is presented here.