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<inf>k</inf> denotes the potential and I<inf>k</inf> 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 V<inf>1</inf>(t)I <inf>1</inf>(t)+V<inf>2</inf>(t)I<inf>2</inf>(t) + ···+V<inf>p</inf>(t)I<inf>p</inf>(t), and the energy that flows into the circuit along these p terminals during the time-interval [t <inf>1</inf>, t<inf>2</inf>] as ∫^t2<inf>t1</inf>(V<inf>1</inf>(t)I<inf>1</inf>(t)+V<inf>2</inf>(t)I<inf>2</inf>(t) + ···+V<inf>p</inf>(t)I<inf>p</inf>(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.