**3. Oscillator Circuits**

In this section we analyze the possible VCII−-based oscillators based on the scheme of Figure 2. The passive NGC is assumed as a general *n*-node network consisting of *b* possible branches between two nodes. Each node is a junction where two or more branches are connected, and each branch is an admittance connected between two nodes represented as:

$$Y\_{\bar{i}} = s\mathbb{C}\_{\bar{i}} + \mathbb{G}\_{\bar{i}}.\tag{12}$$

In the following, we analyze the CE to see if oscillation is possible for the particular case study of a five-node network. From this analysis we see that for a four-node network it is not possible to obtain a second-order polynomial for (7), whereas for a six-node network (or more) only non-canonic oscillators using more than the minimum number of passive components are possible.
