The Substitution Theorem#

The Substitution Theorem

Let \(\mathcal{N}_1\) and \(\mathcal{N_2}\) be two networks which are connected through four terminals \(T_{\mathcal{N}_1,1} \leftrightarrow T_{\mathcal{N}_2,1}\) and \(T_{\mathcal{N}_1,2} \leftrightarrow T_{\mathcal{N}_2,2}\) such that \(T_{\mathcal{N}_1,1}\), \(\leftrightarrow T_{\mathcal{N}_1,2}\) form a port and \(T_{\mathcal{N}_2,1}\), \(\leftrightarrow T_{\mathcal{N}_2,2}\) also form a port:

If it is possible to determine \(v(t)\) solely from \(\mathcal{N}_2\) and \(\mathcal{N}_1\) is voltage-controlled, then \(\mathcal{N}_2\) is equivalent to an ideal voltage source:

If it is possible to determine \(i(t)\) solely from \(\mathcal{N}_2\) and \(\mathcal{N}_1\) is current-controlled, then \(\mathcal{N}_2\) is equivalent to an ideal current source:

Proof

TODO