Originally posted by Carl-NC
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The fact that we don't live in a perfect world therefore means that we need to effectively knock the EFE component out of the equation of X = A1 (S1 – S3) – A2 (S2 – S4).
Given that EFE and ground/target signals are independently driven (assuming no major interplay here), from a purists perspective, I would have therefore thought that it's more straight forward to simply have a circuit that permanently makes A1(S3) - A3(S4) = 0 (with A3 being a new independent gain setting for the GB EFE sample), thereby avoiding any change to the ideal A1(S1)- A2(S2) (i.e. perfect world) equation. Otherwise, when you change A2 in A2(S2 - S4), the gain of the S4 sample will also be changed, and adverse consequences may arise.
In thinking this through further as I type (always a dangerous thing!), I'm sure your methodology will work, but it would be reliant upon the ground (i.e mineral) samples being more consistent when sampling, which kind of counteracts the effectiveness of the need to Ground Balance in the first place. Whereas, I suggest that my proposed approach better separates the impact of the two truly independent variables (i.e. EFE and ground/target samples). I'm always open to be shown otherwise though.
Separately, if one was to adopt the changing GB target sample width approach to ground balancing, wouldn't this enlarge the target "hole"?

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