Passive FM receiversPieter-Tjerk de Boer, PA3FWM email@example.com
(This is an adapted version of part of an article I wrote for the Dutch amateur radio magazine Electron, January 2017.)
Passive receivers are nice beginners projects, but only if there's something to receive with them. On mediumwave, which most passive radios are built for, that is less and less the case, as more mediumwave transmitters are switched off. In contrast, there are more FM broadcast transmitters than ever, and not just on a few high towers in rural areas (this should be read from a Dutch perspective: a small, densely populated country, so our TV towers tended not to be near big cities, but placed to cover the entire territory with as few towers as possible), but also near and even in cities. So perhaps it's time to start building passive FM receivers?
Let's calculate whether that's feasible, assuming a transmitter with say 10 kW EIRP (effectively radiated power, including the antenna gain over an isotropic antenna). With a dipole at say 3 km distance, one receives 0.1 mW. In 73 ohms (the impedance of an open half-wave dipole) that is almost 0.1 V effective voltage. That's not a lot, taking into account the voltage drop over even a germanium diode. Increasing the voltage by resonance seems desirable, also because the 10 kW transmitter just 3 km away is a bit optimistic.
The figure shows a passive receiver from the early days of FM broacast, 1950 . It is not more than a tune circuit with a diode detector. In fact it is a receiver for amplitude-modulated signals, but by tuning just besides the signal, an FM signal also becomes amplitude-modulated: slope detection. The tuned circuit consists of a variable capacitor from 5 to 30 pF, in parallel to an inductor consisting of just a single, 10 cm diameter, loop of wire, which gives about a quarter microhenry of inductance. The resulting tuning range is 58 to 142 MHz, in practice somewhat less high due to extra capacitance in the circuit. (It's useful to check this, because until far into the 1940s FM broadcast in America was between 42 and 49 MHz, rather than 88 to 108 MHz.)
The thing I find noteworthy about this circuit is that the antenna is connected to the "top" of the tuned circuit; thus there is no voltage increase due to the resonance, and the tuned circuit will be damped strongly by the antenna's low impedance. The editors of  in fact added a warning: "Don't expect multitube set selectivity and sensitivity with this set. We think it's a good gadget if you live very near an FM station."
The website  points to three other passive FM receivers, all using a cavity instead of a simple LC circuit, but which then appear to be good enough for narrowband FM amateur signals, rather than wideband FM broadcast.
B.t.w., for the above calculation of the 0.1 mW received power, I used a formula that is easy to remember: the power loss from an isotropic radiator to a dipole is (10 × distance / wavelength)2, where distance and wavelength must be expressed in the same units, e.g. both in meters. This is in fact the so-called Friis formula; the factor 10 in it is actually an approximation for 4π divided by the voltage gain of a dipole.
References: Donald J. Rathmann: Short Range FM Converter and Pocket Radio, Radio Experimenter, 1950. (available online.)
 https://mwsherman.com/fmonly/fm_only_lowtech.html (originally at http://www.somerset.net/arm/fm_only_lowtech.html)