It was me who stated that ferite materials have both upper and lower bounds for best efficiency, though this information is very well known in the industry and has been for a long time. All the ferite materials most familiar to hams have published spec's which show their maximum Q, losses, maximum flux density, and/or volts-per-turn - each as a function of frequency. These published figures and nomographs (charts) clearly illustrate that there is no single ferite material that is "best" for Q, Efficiency, and coupling across such a wide range of frequencies as 3~30Mhz.
Take a look at http://www.amidoncorp.com/product_images/specifications/43_Material.pdf
Amidon is re-working their website, and the spec-sheet for material #31 is not currently published, so I can't link to the current copy of their spec's for that Material.
Note that Permeability-vs-Frequency and Impedance-vs-Temperature for Material #43 "swing" far further [within our frequency range of interest, 2~30Mhz) than the same measurements on Material #61 across the same range of interest. Most importantly, note the huge difference in the [single frequency] measurement for core loss: <= 250x10^-6 @ 1Mhz for #43, but only <=40x10^-6 @ 2.5Mhz for Material #61.
For various reasons, there persists an overwhelming collection of 'ham lore' with regard to Material #43 being "the best for ham radio use at HF". But how many hams actually know how/why this (grossly incorrect) belief came into being in the ham community? Fewer know how far from the truth this 'lore' actually is - so here's the why and how of it:
Material #43 was developed specifically to make multi-octave transformer matching possible in Solid State (vy. low impedance) power amplifiers for military and marine radios (which are required to cover all frequencies in the 2~20Mhz or 2~30Mhz range). The design criteria were -
1. high power handling for unit of volume (size);
2. to be used in low-impedance and low-Q circuits where peak RF voltages (and currents) are well controlled; and
3. designed specifically for use where significant mismatches at the ports of the RF transformer are well outside normal operational characteristics,
- i.e. NO UN-COMPENSATED REACTIVE POWER COMPONENT present at any port of the transformer.
Substantial transformer losses were acceptable with Material #43, so long as the total amplifier efficiency remained above 50%.
Stated another way, the spec for material #43 assumes it will be used in a power amplifier; and that 1.5dB to 2.x dB of loss is an acceptable trade off in order to obtain 3+ octaves of operating range from the amplifier. They purposely introduced a certain quotient of loss into the formulation of Material #43, in order to obtain their other requirements - multi-octave RF range matching AT POWER, IN AN AMPLIFIER, with "acceptable efficiency".
Not "highest efficiency", but "acceptable efficiency" - meaning as low as they could get the losses and still meet all the other design criteria.
Applying Material #43 to "other uses" such as BALUNs/UNUNs is a plain after-thought, and not a particularly good one, either. Using #43 for BALUN/UNUN construction is a compromise employing a previous compromise. That's "one step shy of cheating" IMHO. But for a long time, Material #43 was the ONLY ferite widely available to hams, and so among amateurs it is the best-known... thus today we have 50+ years experience in using a twice-compromised component to build our "best" impedance transformers, and very few hams think to ask "why?" These 'compromised compromises' worked well enough for hams, and over the decades that "well enough" endorsement has grown into the oral history we have today.... "because that's how we've always done it."
At the time (late 1960s), ferite materials and their properties werel a "trade secret" and sometimes even a "military secret". So, when Material #43 became readily available to amateurs, specifications were thin and experimentation was the rule. Hams of that generation were used to the lower efficiency of tube PAs and air-core coils in matching units, so Mix #43 wasn't a "bad" compromise in their estimation because it was no worse -efficiency wise- than what they already had, but was much lighter and more compact than air-core transformers or non-loaded transmission-line sections; hence Material #43 became very popular despite it's shortcomings - it was the only game in town.
But when we look at the (ferite) materials on the market today, we find that #31 and #61 each offer substantial improvement vs. #43 --
Material #31 has far lower losses than #43 in the range of 0.5 to 5.0Mhz, and #61 material has far lower losses than #43 in the 10~30Mhz frequency range, even though this is the "sweet spot" for Material #43. The irony is that Material #43 gives best efficiency in the frequency range ~15Mhz, i.e. in the 20 Meter band, and that many products and designs for BALUNs/UNUNs have been offered, where performance spec's on 20 Meters are the only ones published.
Or, in other words, the companies selling these products don't want you to know how much of a compromise you're buying, due to the fact that they used a cheap ferite (Material #43). And yes, #43 is almost always the cheapest ferite material (which has any utility at HF) when purchased in bulk quantities these days. This further suggests that when buying small quantities of material #43 at retail, the seller's profit margin is higher than with other ferite materials.
So in part Material #43 is embedded in the ham mentality because it came first, and we have of 50+ years of habitual use of Material #43; you can blame the bulk of the maintenance of this fallacy on common ignorance, and the rest on corporate marketing weenies. And yes, "corporate marketing weenies" is a technical term, ask any design engineer.
To put a sharp point on it, Material #43 is the least suitable choice for BALUNs/UNUNs because of it's very high losses where uncompensated reactances are present at any port of the transformer. Period. Overall, material #43 should have been retired about 20 years ago. Over the range of 3~30Mhz, material #61 has far higher efficiency for broad-band power matching (although more turns are generally required); and below 10Mhz Material #31has far less losses than #43 while using a comparable number of turns.
I highly recommend the following two articles for folks seeking a deeper understanding of the particulars in applying ferite material to various use-cases (high-Q a.k.a. "Resonant circuits", vs Power transfer, vs. wideband "choking" of RF signals), without having to wade through lengthy and formula-laden academic texts.
Warmest 73, Chuck