By transmission line techniques do you mean things using a chain of magnetic material to enclose turns of a transformer - one or many- thats probably also why binocular cores make good broadband transformers, often.
Not specifically due to core type, but some cores are easier to work with than others.
The transmission line approach is only concerned with the relationship between the wires. The underlying mechanism is that, at high frequencies, energy only travels in the space between wires -- the core is irrelevant to HF characteristics, and can be ignored.
The space between wires is also the space where leakage inductance and parasitic capacitance arise. Indeed, these are the LF equivalent properties of the transmission line structure.
The leakage inductance, of a normal build transformer (like a shell style bobbin, or toroid with full winding layers; but not so much a common mode choke, where the windings are in separate sections), is largely independent of the core. You can measure LL with and without the core, and find the measurements differ by maybe 10%.
The coupling factor of course varies with the core, because the magnetizing inductance varies with the core. And thus also the LF cutoff. But the HF cutoff* is determined by the windings.
*A Guanella TLT does not have an HF cutoff**, though it still has finite LL and Cp parameters. The lumped equivalent model only tells you what you can expect below HF cutoff: above, the transformer becomes a complex circuit, and may exhibit peaks and dips, weird impedances, or, in the case of a TLT, no peaks or dips at all, just a constant ratio all the way.
**Well, loss in the transmission line itself, and dispersion due to waveguide modes. But that's extreme (GHz+ for most coax). Alternately, an abstract Guanella TLT, made with ideal, lossless, one-dimensional transmission line, has unlimited bandwidth.
The most basic TLT is a transmission line with cores stacked on it (or wrapped around a core, or both; same thing, to the first order). This is a 1:1 transformer, also known as a common mode choke, current balun*, or semi-ideal transmission line. (The SPICE transmission line component has this behavior: there is no galvanic connection, even at DC, in the common mode, between the two ports of the transmission line. We can't achieve that in practice, but we can do a good job of it at AC.)
*A particularly poor application for it, as the current can never be perfectly balanced, because the core will never have infinite impedance.
If you take that and run with it, you can do tricks like, connect transmission line ports in parallel at one end, and in series at the other, to get whole numbered turns ratios. The impedance at each end is the TL's Zo in parallel or series, respectively. (So, a 50 to 450 ohm transformer is 3 x 150 ohm TL in parallel at one end, and in series at the other.)
Rational ratios can be made by making suitable series-parallel combinations of transmission lines, or by cheating the system with an extra turn here or there (but you lose bandwidth then).
If all the transmission lines are equal length, then the delays match, and the bandwidth is unlimited. If not, then you get peaks and dips at frequencies where the wavefronts interfere. This is the difference between a matched delay (Guanella) transformer and not (Ruthroff).
The widest generalization: all transformers are TLTs, they're just really bad at it if they aren't made in the usual TLT style. A transformer made with a single layer winding for primary and secondary, one on top of the other, has useful TLT properties, and will have a wide bandwidth. A transformer made with multiple layers per winding, will have those TLT properties confined within each winding, where it's not useful (the transmission line modes are short circuited by the wire doubling back at the end), and the HF characteristics will be awful.
This is one of those domains where "industry standard best practice" is almost diametrically opposite from "best physics". Another domain is electrical wiring, where noisy power switching cables are routed directly alongside control signals, for maximum EMI coupling, and where grounds are DC only (rarely continuous like coaxial shields).
Also, using different materials in combination.. thats sort of the inverse of using a bunch of different capacitors to make for more effective bypassing, perhaps.
Sort of. You don't have to worry about complex impedance, because the Q is very low (the core impedance is largely resistive). More like electrolytic capacitors in parallel.
The equivalent circuit is series, but inductors in series is actually equivalent to capacitors in parallel, so you are actually quite correct there!
Cheers,
Tim
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