3-terminal device external modeling

[cianfa72]

TL;DR Summary

About the number of independent equations needed to externally model a 3-terminal device

Very basic question. Consider a 3-terminal device with terminals say A,B,C. Kirchhoff Current Law (KCL) and Kirchhoff Voltage Law (KVL) establish two relationships between the 3 currents entering the terminals and the 3 terminal's voltage pairs respectively.

So we have 2 equations in 6 unknowns. To proceed further we need two more (independent) equations in order to solve the circuit the 3-terminal device is connected to (basically one treats such a device as an unbalanced two-port element).

My question: from a theoretical point to view, is it possible, aside from KCL and KLV, that the number of equations describing the 3-terminal device could be less or more than 2 ?

 

[Baluncore]

I think you need to identify the meaning of the terms terminal and port.

A three terminal device could be a two port black box, with the third terminal representing the reference ground. As an example, a BJT can be modelled as a three terminal device, but in three different ways, as common-emitter, common-collector, or common-base. That reduces the number of equations needed to fully describe the device.

Three terminal, two port networks, can be modelled as a scattering matrix with four parameters, S11, S12, S21, and S22.
https://en.wikipedia.org/wiki/Scattering_parameters#Two-port_S-parameters

 

[cianfa72]

A three terminal device could be a two port black box, with the third terminal representing the reference ground. As an example, a BJT can be modeled as a three terminal device, but in three different ways, as common-emitter, common-collector, or common-base. That reduces the number of equations needed to fully describe the device.

Three terminal, two port networks, can be modeled as a scattering matrix with four parameters, S11, S12, S21, and S22.
https://en.wikipedia.org/wiki/Scattering_parameters#Two-port_S-parameters

Yes, the three terminal device can be modeled as an unbalanced two port black box with the terminal picked as reference ground representing the terminal shared between the two ports.

But the question is: is such a three terminal device as black box always described externally by two equations in 4 unknowns (two currents + two port's voltages) ?

 

[Baluncore]

But the question is: is such a three terminal device as black box always described externally by two equations in 4 unknowns (two currents + two port's voltages) ?

Nothing is forever, always.

If the impedance of the ports are defined, then only one voltage or current is needed. The other ports can be shorted, terminated, or left open.

 

[cianfa72]

If the impedance of the ports are defined, then only one voltage or current is needed. The other ports can be shorted, terminated, or left open.

Right, but it isn't my point.

Consider a three terminal electronic device, whatever. What is the number of equations that the 3 current through terminals plus the 3 voltages across terminals must obey ?

We have 1 KCL and 1 KVL plus a number of independent equations where 6 - 2 = 4 unknown enter.

The question is: from a theoretical standpoint is always two the number of such equations ?

 

[DaveE]

I think the only thing you can say for the most general case is that the terminal currents all sum to zero (KCL) and that there are two independent voltage potentials between the three nodes (KVL). Other constructs, like two port networks, have extra requirements.

PS: $i_1+i_2+i_3=0$ and $v_{12}+v_{23}+v_{31}=0$ are the two equations.

 

[DaveE]

My question: from a theoretical point to view, is it possible, aside from KCL and KLV, that the number of equations describing the 3-terminal device could be less or more than 2 ?

You can't really describe a network without seeing what's inside of it.

For a passive LTI network you should be able, with source transformations, to reduce it to the Thevenin (or Norton) equivalent. This could look like a voltage source with a series impedance between each node, for example.