Two different Agilent patents vs Dunsmore's book.
I've only been briefly looking again at Section 3.2.3 in Dunsmore's book, but the notation there seems to be consistent, and I cannot spot an obvious error in the equations.
The E00, E01, E12, E11 are the error terms of the error box at port 1 of the 8-term error model, and E22,, E23, E32, E33 of the error box at port 2, see Figure 3.3. When you want to convert from the 8-term model to the 10/12-term model, the load match errors are
\[
\begin{align*}
ELR&=E_{11}+\frac{E_{10}E_{01}\Gamma_R}{1-E_{00}\Gamma_R}=E_{11}+\frac{ERF\cdot\Gamma_R}{1-EDF\cdot\Gamma_R},\\
ELF&=E_{22}+\frac{E_{32}E_{23}\Gamma_F}{1-E_{33}\Gamma_F}=E_{22}+\frac{ERR\cdot\Gamma_F}{1-EDR\cdot\Gamma_F}.
\end{align*}
\]
That is simply equations (3.8 ) together with equation (3.11) and (3.12). So it is all there in Section (3.2.3) to convert between the 8-term and the 10/12-term model. Also, the conversion from the 10/12-term model to the 8-term model is spelled out explicitly, see equations (3.13) to (3.16).
The only notational glitch I see in that section is that Dunsmore switches between, e.g., \$E_{LF}\$ and \$ELF\$, etc., in equations (3.14) to (3.16).
Edit: I should have pointed out that \$E_{11}\$ of the 8-term error model actually is equal to \$ESF\$ of the 10/12-term model. But that is a result, not just a notational oversight. Similarly, \$E_{22}=ESR\$. See equations (3.8 ).
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