- #1

cianfa72

- 2,111

- 235

- TL;DR Summary
- Conditions to be fulfilled to employ (one of ) the 2-port network representation of a quadripole (four-terminal electrical network) in the analysis of a complete 'external' electrical network.

Hello,

I'm struggling with the conditions under which makes sense employ a two-port 'external' representation of a quadripole (four-terminal electrical network) when interconnected to an external circuit (to take it simple assume a linear + permanent electrical network).

Starting from circuit theory I elaborated the following:

Take a quadripole (four-terminal network) interconnected to an 'external' circuit. Do not place any constrains about the current entering in each of the four terminal (no 'port' constrains for the currents). From a network analysis point of view we can proceed as follows:

The other way around, a solution of the second one (the complete network you get replacing the quadripole with its 2-port representation) might

Thus, we have to explicitly check for those KVL when taking in account any solution of the last network to be sure it is actually a solution of the network we started with.

What do you think about, does it make sense ?

ps. same question shows up in other (italian) forum.

I'm struggling with the conditions under which makes sense employ a two-port 'external' representation of a quadripole (four-terminal electrical network) when interconnected to an external circuit (to take it simple assume a linear + permanent electrical network).

Starting from circuit theory I elaborated the following:

Take a quadripole (four-terminal network) interconnected to an 'external' circuit. Do not place any constrains about the current entering in each of the four terminal (no 'port' constrains for the currents). From a network analysis point of view we can proceed as follows:

- choose a tree spanning just the quadripole internal structure (directed graph) up to its four terminals
- extend this tree to the overall 'external' network starting from those 4 terminals
- write the equations for the equilibrium of currents at each node belonging to the complete network (actually N-1 nodes suffices)
- write the KVLs for the voltage equilibrium at the fundamental loops (f-loop) w.r.t the chosen tree
- write the BCEs (Branch Constitutive Equations) for each element branch

- add 2 constrain equations for the 'port' current condition at each of the 'coupled' terminal pair (port)
- add 2 auxiliary unknowns for the port voltages + the 2 related equations defining them w.r.t the branches of the chosen tree spanning the quadripole internal structure

*only*the unknowns for branches inside the quadripole, is formally the same as the set of equations for the same quadripole closed on 2 external indeterminate bipoles (one for each port). A solution of the first system of equations is actually also a solution for the network you get replacing the quadripole with (one of) its 2-port network 'representation' (note that the set of equations for the last one is actually obtained as linear combinations of the equations belonging to the first one).The other way around, a solution of the second one (the complete network you get replacing the quadripole with its 2-port representation) might

*not*be a solution of the first one (the fundamental loops involving the not 'coupled' quadripole's terminals are actually*not*included in the equations set)Thus, we have to explicitly check for those KVL when taking in account any solution of the last network to be sure it is actually a solution of the network we started with.

What do you think about, does it make sense ?

ps. same question shows up in other (italian) forum.

Last edited: