Though the Applicant in Ex parte Cogdill didn't identify it as such, the threshold legal issue here is whether or not an Examiner-introduced diagram can be used in a rejection – even if is equivalent. As commenters pointed out, such a diagram is not prior art under § 102 or § 103.
I haven't run across this sort of "drawing equivalence" before. I have run across plenty of cases where the Examiner has annotated a drawing, but that's usually about further explaining what's already in the drawing, e.g., by adding the text "lever" to show that reference number 42 allegedly corresponds to the claimed lever. Is this sort of annotated drawing also prohibited because it's not prior art? I don't see it that way. I view this drawing-plus-added-text as the Examiner's assertions about the teachings of the reference.
I've also seen a few cases where the Examiner annotates with something like a box around something in the drawing in order to explain that, e.g., the components within the box allegedly correspond to claimed assembly 42. Once again, I see this as an Examiner assertion about the teachings of the reference.
So maybe what happened in Cogdill's equivalent circuit drawing is analogous to the Examiner asserting that the "lever" in the reference corresponds to the "member" in the claim. It's well-settled law that the reference doesn't have to use the same terminology as the claim in order to anticipate. Is redrawing the circuit diagram that much different than substituting the term "lever" in the reference with the word "member"?
That sounds weird, because Examiners don't literally introduce paragraph [0043B] with the substituted text in order to make this point. Instead, an Examiner writes something like
Johnson anticipates claim 1 as follows: a member (lever 42 in FIG. 1); ...Is the Examiner-created Fig. 3B in the Cogdill case just a way for the Examiner to better illustrate how he was reading Johnson's Fig. 3? In other words, is Fig. 3B an Examiner finding about the teachings of the reference rather than a type of evidence that is inadmissible because it doesn't qualify as prior art?
Could the Examiner have introduced Fig. 3B as evidence through a personal affidavit? Surely an Applicant could introduce an equivalent circuit diagram as declaration evidence, along with an explanation of how the claim limitation at issue is not disclosed by the diagram. So could the Examiner do the same thing through a personal affidavit?
If we get past the threshold legal issue, then the next issue might be the burden of proof on the equivalence of the circuit diagrams. Does a mere assertion of equivalence by the Examiner shift the burden to the Applicant to explain why they are not equivalent? Can the Applicant attack the asserted equivalence with attorney argument, or is real evidence required?
If we get past all that, we reach the questions of fact as to whether Figs. 3 and 3B in Ex parte Cogdill really were equivalent and whether the limitation at issue was disclosed. I'm not a EE, so I'll refrain from expressing an opinion on that ultimate question. I will, however, ask a few questions about the issue.
As far as circuits go, the claim and the diagrams in Cogdill look pretty simple. You have to understand the difference between parallel and serial. But that's covered in a basic physics class, so I'm not convinced you need to be a EE to interpret this aspect of the circuit. (And yeah, you also have to understand what impedance is, but that doesn't appear to be at issue).
The rest of the claim appears to describe how the impedance elements are connected, using terms such as "between," "one end" and "branch points." With all this talk about connections, it this more of a mechanical-type claim? Or do we need to understand something about circuits in order understand what those positional relationships mean in a circuit context?