Gents --
I have really, really tried to understand this myself -- and for me it has required reading a lot about detector theory and electronics, areas that are not within my area of education/vocational experience. I started off in Electrical Engineering in college; maybe I should have continued on instead of switching into science...
THAT SAID, I am going to try to briefly say what I believe to be the case, in the simplest terms I can. A detector design engineer may cringe a bit, but this should be close, to the best of my understanding. Hopefully this helps some...
The return signal received by a metal detector can be split into two components, an X and an R. A return signal, of course, always includes BOTH the TARGET signal, and GROUND signal. (Ground signal is usually primarily composed of "X" signal, with not much "R;" also, the ground signal is of course MUCH stronger than the target's "X" and "R" signal). For simplicity, the X part of the signal is generally used to determine ferrous vs. non-ferrous, and the R part of the signal used to determine "conductivity" of the target.
That is overly simplified, but if we just go with that, then let's talk single freq. vs. multi.
On a single frequency unit, you have just one transmit signal, lighting up a target, and then the machine reads the return signal. The return signal includes TARGET X and R, AND-- GROUND X (and a little R). So, to read the target signal and then ID a target, ground signal must be "removed," or "subtracted out" of the return signal. THAT IS WHERE ground balance comes in. The machine determines what needs to be "subtracted out" based on the ground balance value. Using the ground balance number, the machine can subtract the "ground signal X" from the total return signal, such that what's left, theoretically, is entirely "target signal." Then, by examining the remaining "target signal," the machine can determine ferrous vs. non-ferrous properties of the target (from the remaining "X" signal after subtracting out ground X), AND the "conductivity" of the target, from the "R" signal -- in other words, the machine can "ID" the target. This is why, with a single freq. machine, ground balance is so important. You have to remove that ground component of the return signal accurately (which again, is mostly composed of "X" signal), in order to accurately ID the target.
NOW -- Minelab multi-frequency units work differently, in terms of target ID. With multiple transmit frequencies running, the machine thus receives multiple, DIFFERENT return signals emanating from each target. Each return signal is different because each metal reacts differently, electrically, when "lit up" by a different frequency transmit signal. So, for each of the different transmit frequencies, you have a different "read" on the target.
Given that there are now multiple "reads" on each target available, you can now do "target conductivity ID" differently. INSTEAD of having your target ID based on a single receive signal, where you have to subtract out "ground X" signal, hope you do it "accurately," and then ID the target based on the remaining X and R signal, you now have the ability to ID things completely differently.
Since the strength of ground "X" signal is a problem, which can overwhelm the target signal, and since improper ground balance will throw off target ID -- the Minelab approach is to utilize SPECIFICALLY the "R" part signal much more heavily, for target ID. Once the ferrous vs. non-ferrous determination has been made, on a given target, the rest of the "ID" -- i.e. "conductivity" of the target, is derived through a comparison of R signals. Remember, in a single freq. unit, there is only one single R signal available (due to only one transmit frequency), and so no "comparison between different R signals" is possible. Further, on the single freq. unit, this single "R" signal is being "pulled out of" that single return signal -- a signal that is by definition contaminated by ground "X" signal. So, a lot of things have to happen just right for accurate ID on a single freq. unit, and since things are often not "just right," we as users experience issues with target ID on single freq. units, ESPECIALLY on deeper targets.
But, with multiple different "R" signals available when running a multi-frequency unit (due to MULTIPLE transmit frequencies seeing the target simultaneously), the X signal can now be ignored when computing "conductivity" (as opposed to "subtracted out"), and thus a more conductivity ID value is achieved -- again, through comparisons/computations utilizing the multiple R signals available, totally independent of "X".
(To elaborate just a bit on this idea of "multiple R values resulting in more accurate ID" ... remember, each target, depending upon its metal composition, will behave differently depending upon what transmit frequency it gets "lit up" by; a 5 kHz transmit frequency will affect a target differently than a 40 kHz transmit frequency will, for instance, and so if you light up a target with BOTH frequencies, you can exploit the differences in target response to each different frequency, so as to arrive at a much more accurate "read" on the ID of the target -- and all of this occuring WITHOUT the X signal from the ground biasing the target ID process).
SO -- this is why ground balance is not as important in multi-freq vs. single freq. Again -- utilizing multiple transmit frequencies permits identification of targets in a way that "eliminates" ground contamination much more effectively. Rather than a subtraction of ground contamination based on the setting of a ground balance value, ID is instead arrived at moreso by essentially ignoring the part of the return signal that is contaminated by the ground, in favor of using the "uncontaminated" part of the signal (emanating from MULTIPLE transmit frequencies) to thus achieve accurate ID -- even on deep targets.
This -- while convoluted, is over-simplified, and I don't understand it all completely.
So -- here is my guess. FBS uses a FIXED ground balance (again -- this is my guess) to simply to answer the "ferrous vs. non-ferrous" question (i.e. the assigning of the FE number). Then, it uses separately the "compare a bunch of R signals from multiple transmit frequencies" to determine the "conductivity" of the target (the CO number).
On the CTX, things are of course similiar. BUT -- Minelab included the ability to adjust ground balance if necessary -- but we are told to do so only if the soil is REALLY BAD. My guess is, this is so that accurate "ferrous vs. non-ferrous" determination of the target can be maintained when soil gets REALLY bad, which thus allows maintenance of proper assignment of a "good target" to the FE 12 line when hunting in highly mineralized dirt.
Finally, on the Equinox, my guess is that it's very similar. IF running one of the single freq. modes, obviously ground balance IS important (due to all of the above explanation). Otherwise, though, if running Multi in any of the modes, it is much LESS important. BUT, as the ground gets more and more mineralized, benefits are there to be had by setting a proper ground balance, even in Multi mode. My guess is that the WORST effects of improper ground balance, in really bad ground and running Multi, would be exhibited through more "wrap around falsing," and, in a related sense, the loss of ability of your "iron bias" setting to function well -- because it is within the "iron bias" adjustment where the machine is focused specifically on accounting for the ferrous vs. non-ferrous aspects of the target (and thus, I'd assume, using primarily "X" signals in making these determinations).
LONG-winded, I know. Hopefully, this proves somewhat helpful to some.
Steve