Start with what chokes you can readily get.

NO! Start with Specification of Load: voltage, current, susceptibility to crap.

(If you are powering a TL072 with any reasonable Vbias filter, the raw 9V supply can be full of crap, because of high PSRR.)

I will postulate 9V 18mA for an example.

Since 1,000uFd 16V caps are cheap, we can probably do well right off a rectifier with such a cap. Even 220uFd gives "only" 0.5V ripple. But you gotta go fancy...

In any case, you want the C facing the load to be "small" compared to load at the lowest frequency of interest, to bypass the circuit being powered. 9V/18mA= 500 Ohm load. By rule of thumb I would use >10uFd for 1K, so >20uFd for 500r.

We want the L to be larger than the load at the incoming crap frequency. Take 1 Henry. At 100Hz it is 628 Ohms.

We probably want much more than 22uFd and 1 Henry.

OK, Hammond has 154E 20H 20 ma. 1666 Ohms. That 1.7K resistance is far too large for a 9V/18mA= 500 Ohm load. We get just a couple of Volts out.

Hammond 154M 2H 100 ma. 175 Ohms is the same size (/cost) and a more likely Ohms. With just 22uFd on its output we get 13mV ripple. Going 470uFd gives less than a mV ripple.

Still you expect 175 Ohms to be a large loss against a 500 Ohm load. And since you may not know the load exactly, it may even vary in use, we prefer to aim for quite-small loss.

All of this CAN be figured on a matchbook, maybe with a sliderule. However graphs make people go "wow!" and computers graph-and-post faster than me scanning a doodle.

Duncan PSUD. Get it! Don't give any backtalk about your computer/sellfone won't run it; push the neighbor's kid off his Win-machine if you must.

Indeed 175 Ohms into 500r drops from 9V to 6.7V.

We want >1H with much lower R. One candidate is Hammond 159V 1.5H 500 ma. 27 Ohms. It will drop from 9V to 8.36V, so we can probably work with it. With 470uFd out we get 1mV ripple. It is 9X the weight (cost?) of the 154 models. It is bigger than some pedals.

Compare to a "capacitor multiplier", 1K to base of NPN, 1,000uFd to ground, load at NPN emitter. The drop will be a steady 0.7V over a fair range of current, and about 1mV ripple out. The R+NPN is far cheaper and smaller than any of these chokes.

Oddly, none of these sims "rang" significantly, even on a bang-start. It CAN happen, but may be more frightening than likely.