I forget. But just search for "kit FM transmitter". I'd fully intended to build a "proper" transmitter, and was keenly disappointed that you could just buy a cheap single-chip board.
Nowadays you don't even need that. You can turn the RPi itself into an FM transmitter. Search "how to FM broadcast on raspberry pi"
> You can turn the RPi itself into an FM transmitter.
Never tried it, but given the way it works, you definitely need some output filtering unless you accept to pollute all harmonics of your channel (which might be licensed spectrum too, and interfere with services you don't want to interfere with in the first point)
Pico caps and appropriate impedance miss-match can be used to round-off square waves.
But yes, if you look at high-speed Pi GPIO with a Rigol it looks more like an EKG readout than the thing you might see on a logic analyser. Smoothing it enough to feed a line-amp is very lossy.
Pi for audio frequencies is lovely and square, Pi at radio frequencies has distinct rise and fall and "just taking a moment to think about it" segments.
A spectrum analyser has probes!?!? This might be where I am going wrong... But the bench scope is largely in agreement about the distinct phases of a cycle at RF freq.
One can go on Amazon and order himself a high powered FM transmitter direct from China. Stick an antenna in the attic and you'll be heard for miles. If you don't gaf about spurious emissions or laws or anything like that you too can be Christian Slater in Pump Up the Volume. The fines for this in the US can be pretty severe but Amazon is happy to sell you the rope to hang yourself with free shipping.