Cascading S-Parameters in Plain English: Part 4

This is part 4 of a 5 part series: Cascading S-Parameters in Plain English

Previous << Part 3: T-Parameters in Plain English

We expanded our knowledge of T-Parameters in part 3 of this series, but there was also that troubling statement that the definition of T-parameters I shared was one way of defining them. The problem is that there isn't a 'standard' definition. But the definition I used assumes, given an even number of ports, the first half are inputs, and the second half are outputs.

This is very straightforward for a a 2 port network, but the real power is expanding to multi-port networks. As long as the device is symmetric, eg, equal number of inputs and outputs, and the inputs are arranged so the first half are inputs and the second half are outputs, we can use the exact same algebraic transform that we used on a two port network simply by substituting the matrix of each respective quadrant per below

So that is super handy. We can now essentially deal with any multi-port network which is symmetric, we just need to operate on matrices instead of scalars.

A Gotcha for Balanced S-Parameters

Maybe I'm stupid, but when I started playing around with this, I was working with balanced devices and I didn't fully appreciate the meaning of an input port vs an output port. Balanced devices generally follow an 'evens and odds' port arrangement. In other words, differential port 1 consists of single ports 1 and 3 (odd) and differential port 2 consists of single ports 2 and 4 (even). In this case, single port 1 is assumed DC connected to single port 2, and single port 3 is assumed DC connected to single port 4. But when we do our algebraic transform per above, ports 1 and 2 are inputs, and ports 3 and 4 are outputs, so the T transform I will share in part 5 will not work. The simple solution is to row and column swap port 2 and 3 in the S-parameters so that 1 and 2 are inputs and 3 and 4 are outputs.

To re-iterate, you could definitely make a a T transform that allows for ports 1 and 3 as the input ports, but enforcing that the first half of the ports are input ports (1 and 2 of a 4 port network) and the 2nd half ports are output ports (3 and 4 of a 4 port network) enables us to scale up to more complex components fairly easily.

Next >> Part 5: TLDR; Show Me the ****ing Code

By: Matt Wright 7/15/2020

Tags: Tech, S-parameters