Brune test

The test determines whether the network still meets the port condition after the two-ports have been combined.

Only if there is no voltage drop in both cases, a combination of the two-ports networks is permissible.

The first example fails the series-series test because the through path between the lower terminals of 2-port #1 short-circuit part of the circuitry in 2-port #2.

The third example is the same as the first example, except that it passes the Brune test because ideal isolating transformers have been placed at the right side terminals which break the through paths.

To check if two two-port networks can be connected in a parallel-parallel configuration, first of all just the input ports are connected in parallel, a voltage is applied to the input and the open-circuit voltage is measured/calculated between the outputs that are short-circuited each.

Brune test for connecting two-port networks in series.
Brune test for connecting two-port networks in parallel.
Brune test for connecting two-port networks in series-parallel.