EC-1.5 Two-Port Networks

What this is and why it exists

Sometimes you do not want to know what is inside a network. You want to use it as a building block inside something larger, and all that matters is how its two ends relate.

A two-port description keeps exactly that, and deliberately forgets everything else. That is what makes the block reusable.

The vocabulary

• Port — a pair of terminals where the current going in equals the current coming out.
• Impedance parameters — express both port voltages in terms of both port currents.
• Admittance parameters — express both port currents in terms of both port voltages.
• Hybrid parameters — mix the two, using one voltage and one current as the knowns.
• Transmission parameters — express the input quantities in terms of the output ones.
• Reciprocal network — one whose behaviour is unchanged by swapping excitation and measurement.
• Symmetric network — one that looks the same from either port.
• Wye and delta — three impedances arranged as a star, and as a triangle.

The mental model

A two-port has four quantities: a voltage and a current at each end. Any two of them can be treated as known and the other two as unknown, and each choice gives a different parameter set. That is the whole reason several sets exist.

Impedance parameters take both currents as known. Each parameter is then a ratio measured with one port left open, because an open port carries no current. Admittance parameters take both voltages as known, so each is measured with one port shorted. Knowing which condition defines which set is what stops them being confused, and it is also exactly how you would measure them on a bench.

Hybrid parameters mix an open-circuit and a short-circuit condition. That combination happens to match how a transistor behaves, which is why transistor models are written this way.

Transmission parameters are different in kind. They relate the input end to the output end, rather than relating both to each other. That makes them the right choice when networks are placed one after another.

Now the point of all this. Each set makes one kind of connection trivial.

Stack two networks so their ports are in series and their impedance parameters add. Place them side by side so their ports are in parallel and their admittance parameters add. Put them end to end and their transmission matrices multiply. Picking the set that matches the connection turns a one-line combination into a one-line combination. Picking the wrong one turns it into an hour of algebra.

The conversions between sets exist and are worth looking up rather than memorising. The insight is choosing the set, not converting between them.

Two quick checks close the topic. A reciprocal network shows an equality between the two off-diagonal parameters. A symmetric network shows an equality between the two diagonal ones. Both are fast tests that a set of measured parameters is self-consistent, and both will catch a sign error.

The wye and delta forms are a separate tool with the same spirit. Three impedances in a star and three in a triangle can each be converted into the other. That unlocks networks which no amount of series and parallel reduction will touch. In those networks no two elements are actually in series or in parallel. Derive the conversion once, then look it up.

What you should now be able to explain or do

Say what a port is and what a two-port description throws away. Measure each parameter set by knowing which port is opened and which is shorted. Say why transistor models use hybrid parameters. Choose the parameter set that makes a given interconnection an addition or a product. Apply the reciprocity and symmetry checks, and convert between wye and delta forms.

Check yourself