# Extra Element Theorem

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The N-Extra Element Theorem (NEET) derives from the NGNT using N injections. A transfer function is decomposed in terms of its value when $N$ extra elements (EEs) $W_i$ are absent, and a correction factor expressing the modifications due the EEs. An element is absent if it is assigned either a zero or infinite value, select by appropriate injection.

The NEET can be written as, a.o.:

\begin{align} H &= \Href D \Dn \end{align}

#### 1EET

For one extra element $W$ and a single injection, the 1GNT can be written as the 1EET:

\begin{align} H &= \Href D \Dn \\ &= \Href \frac{1+\frac{1}{\Tn}}{1+\frac{1}{T}} \\ \end{align}

Depending on whether current or voltage injection is used, $T$ and $\Tn$ can be interpreted as: \begin{align} T &= \frac{W}{W_d} \\ \Tn &= \frac{W}{W_n} \end{align} or \begin{align} T &= \frac{W_d}{W} \\ \Tn &= \frac{W_n}{W} \end{align} with $W_d$ and $W_n$ the driving point immitance and null driving point immitance, respectively.

#### 2EET and NEET

See references.

References:

1. R D Middlebrook. Null double injection and the extra element theorem. IEEE Transactions on Education 32(3):167–180, 1989. URL, DOI

2. R D Middlebrook, V Vorperian and J Lindal. The N Extra Element Theorem. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 45(9):919–935, 1998. URL, DOI

3. R D Middlebrook. Structured Analog Design. 2004.

4. R D Middlebrook. Low-entropy expressions: The key to design-oriented analysis. łdots in Education Conference, 1991. Twenty-First łdots, pages 399–403, 1991. URL