Sorry if this blathers on, but I'll input my experiences on small loops.
I've built tons of loops here, both passive-tuned and hard wired for the DSP radios.
I will hazard a guess here and say the rough passive-tuned loop equivalent to a 200 mm ferrite is in the range of 8-9 inches square.
I have built smaller ones, on the order of 6 inches. They produce a signal strength about equivalent to the existing ferrite in a Tecsun PL-380. The problem I've had with the really small loops of that size is that the nulling is pretty poor. The figure-8 pattern is not well-defined.
I have a hacked Tecsun PL-380 with the ferrite removed, and also an Eton Traveler 3 with the ferrite removed. I soldered wire leads in place and brought them out the tops of the radios for testing hard wired loops. I use micro-clips for all connections here for testing.
I use two loops currently, an 8 inch and an 18 inch. Both are square loops, close-wound with insulated telephone wire, about 24 gauge solid. The 8 inch has 26 turns and the 18 inch has 12 turns. If you wind a 12 inch loop, use 16 turns.
Both the 8 inch and 18 inch give good hard-wired results. Of course the 18 inch blows the doors off the 8 inch, and is the better nuller. You don't need a 5:1 step up transformer for impedance matching. Use the fully-wound loop. Inductance for both these loops is ballpark around 240 uH. I've found that is a good value to shoot for.
I will say, be careful if hard-wiring directly to the input of the DSP radios. They are very sensitive to static. I haven't blown one out yet, but I've come close. Any static or spike on the line when clipping to the chip will send it into desense for a few minutes. It eventually recovers, at least mine have so far.
Both 8 inch and 18 inch loops can be made passive and tuned with a 365 uuF capacitor very nicely. The 18 inch ranges out nicely from 530-700 KHz without further attention. The 8 inch only tunes to about 1430 KHz, so I jumper a clip wire across a few turns to get to 1700 KHz.
At night, the PL-380 handles an 18 inch hard-wired loop pretty well without overloading. Not so much the Eton Traveler 3. It's sensitivity is a touch better than the PL-380, and otherwise will occasionally overload. A 12 inch loop might be a better bet for the Traveler 3. You shouldn't have any overload trouble with the 8 inch loop.
The advantage of the passive-tuned loops is that you can reduce the coupling by moving the loop a bit farther away from the radio, thus reducing the signal overload problem.
As others have stated, coupling a passive-tuned loop to a modern DSP chipped radio can be finicky because the radio gets de-tuned by the loop, then it re-tunes, then the loop is upset again.. I have best results by coupling the passive loop off the end of the radio's ferrite. The tuning interaction is less. As so:
O --RADIO FERRITE--
These DSP radios will start to overload much above 80 or 90 dBu on the RSSI meter. The Eton Traveler 3 measures to 99 dBu and the PL-380 only measures to 63 dBu.
Remember, an RSSI reading of 34 dBu is the equivalent of the old S-9 on vintage receivers us hams remember. 50 microvolts to the input = S-9. A respectable signal.
Also, consider that the induced voltage in a loop increases linearly with the number of turns, the area of the loop, and the frequency. An 8 inch loop has nearly twice the voltage output as a 6 inch loop. Area 64/36 = 1.77 times the output.
Here's a curious tuning tip that may not be apparent at first. It requires two DSP radios. Hard-wire the loop to the first DSP radio (ferrite removed). This DSP radio tunes the loop in place of a 365 uuF variable capacitor if you don't have a spare. Sort of a "digitally tuned passive loop". Couple this loop inductively to the second DSP radio like you normally would. Now you can accurately tune the passive loop by reading the frequency on the first DSP radio. Overkill, yes. But an interesting hack.
Bottom line on wanting a very small fold-able loop - 8 inch would be an ideal size if you can go that big.