sparse information indeed. By neglecting to talk about specifics, or application you, you have completely 'not allowed' imaginative solutions, like "active" coupling transformers that are 1/4 inch cube and go down below 0.001Hz, but using the givens...
the max turns ratio you will need to match worst case 16 ohm to 100 ohm is 2.5:1 which is not too uneven.
The 'gotcha' is going ot be that low cutoff frequency. 10Hz not so bad, but even going down to 1 Hz, you will need 1.25 to 2.5H on the 16 ohm side. That can be a lot of turns depending. Going down to 0.1 Hz just makes it 10 times worse.
Years ago I made a very small transformer that had 100 turns on the core and measured 1H, but that was a SMALL core!
Just to operate down to 1 Hz, you have to get that 2.5 H inductance, yet keep the Rdc below 2 ohms, not an easy fete.and you still haven't said how much volt-seconds you're trying to hold off. You could easily end up with a 100 pound transformer, barely meeting your "... like at DC (via DMM)..." requirement.
*IF* you have absolutely no DC current in any winding, and *IF* you are somewhere between 1 to 5 Vrms; I'd recommend you look into the cores made of amorphous material. . These are often wound onto a torroid core, so they're even more fun to wind. *IF* you don't need over 50Vrms isolation; you can easily wind the torroid in a single pass using bifilar or trifilar wire sets with the wires of 'proper' size and 'matched' for balance.
I've wrapped single torroids using a bobbin made of a 1 foot long 1/8 inch wooden dowel with all the wire you need on the bobbin. If that's too fat to fit through the center hole, make the bobbin longer until it all fits. If you need more copper crossection than 18 Awg, I'd use multiple strands, rather than going to 14, or 12 Awg, simply too hard to work with. ...and don't splice in the middle!
More complete Primary specs: Zp matching to Zs over what bandwidth how much power thru Secondarily important specs: EMC /shielding /field containment DC bias current? Isolation breakdown voltage? Isolation impedance? DC will probably be gigohms, but what about measured at 1kHz, 100kHz, 1MHz? Noise?
NOW you can talk about how to make the transformer.- select core shape/ material, find core cross section, wire size, performance predictions a lot more than is possible from your description.
The "DC" referred to measurement of the winding resistance via DMM, not an impedance meter. IOW it was not the lower freq limit.
Some "audio" transformer will do 10Hz, but 20Hz would be OK. Top end
2KHz. 10W power rating. Apart form the 16R pri and 50/100R sec, that's all that matters.
I am really looking for a supplier who has a wide range these things off-the-shelf. If not, I would need to source a type of core I can wind myself without industrial equipment.
The suggestion to use the secondary of a mains transformer is something I had looked into. But a center-tap is not going to provide complete isolation. And completely split secondary windings are usually equal resistance, ie 12-0-12V. This does not provide the desired ratio.
Keyword is 'might work', because many of those AC mains transformers have their performance peak at 50/60Hz and purposely reduce higher frequencies. Worse, they're usually higher coercivity material [since with AC mains the 'signal' is always there] which means that if used for audio the transformer disappears at low signal levels, nothing to 'activate' the magnetic properties of the core and thus it's practically acting like an air core and not much signal goes through..
Thanks Phil, I've GOT to do a better job of reading. then I would have caught the OP's follow-on contradictory statement, "I am using the low end of the band, so these resistances would be more like at DC (via DMM) than the usual 1KHz."
Why do you say "** Absurd nonsense." ?? Even new materials in audio transformers have some coercivity to them and require a certain amount of 'energizing' to 'wake up' the magnetic material.
To demonstrate to yourself this statement is true, make the following test with an old analog storage scope using very slow horizontal sweep, or do X-Y plot of input/output transfer function on a regular scope: Drive transformer using an audio source at 300Hz. Vary the amplitude of the source uniformly in time. Watch the signal that gets through the transformer. As you turn the amplitude down, you will find a 'nonlinear' transfer function as the coercivity of the transformer comes into play. Essentially, coercivity is like something that must be 'overcome' by the input signal, else the transformer acts almost like an AIR core, the metal is just not there.
When I was first starting out as an Engineer, this phenomenon caught me way off guard. I was using a Stancor 1:1 600 ohm telephone coupling transformer, which usuallly has over 1 H core. At very low signal the low end of the pass band simply disappeared, implying core inductance of less than 0.1H ??!! Luckily, my mentor used to own [as CTO] a transformer company and educated me on the basics of real transformer design/operation.
Only if you're operating in the low frequency limit where inductance is critical. Generally, where mu_r is over a thousand under all conditions, it's high enough not to notice.
To be precise, coercivity isn't the property that produces this effect, because coercivity is measured with a fully saturating waveform. Small signal effects occur in their own (very small) hysteresis loops. However, the physical mechanism ("sticky" magnetic domains) is the same.
As for frequency response, Phil is correct about toroidials -- they are good enough to have been used in some fairly involved tube amplifiers. The leakage is small enough that lots of NFB can be used (cathode feedback, global, etc.) while maintaining the high bandwidth (~50kHz).
Deep Friar: a very philosophical monk.