Terminals and ports

The behavioral approach to dynamical systems is applied to electrical circuits. This offers an attractive way to introduce circuits pedagogically. An electrical circuit is a device that interacts with its environment through wires, called terminals. Associated with each terminal, there are two variables, a potential and a current. Interconnection is viewed as terminals that share their potential and their current after interconnection. A port is a set of terminals that satisfies port-KCL. If terminals {1, 2, ..., p} form a port, and V_k denotes the potential and I_k the current at the k-th terminal, then we define the power that flows into the circuit at time t along these p terminals as V₁(t)I ₁(t)+V₂(t)I₂(t) + ···+V_p(t)I_p(t), and the energy that flows into the circuit along these p terminals during the time-interval [t ₁, t₂] as ∫^t2_t1(V₁(t)I₁(t)+V₂(t)I₂(t) + ···+V_p(t)I_p(t))dt. These expressions for power and energy are not valid unless the set of terminals forms a port. We conclude that terminals are for interconnection, and ports are for energy transfer. We formulate a theorem stating that a connected RLC circuit forms a 1-port.