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DISCONTINUITY IN FEED LINES 381

On the left, all reflected waves in port1 and port2 are grouped while the right side collects all
incident waves in the same ports. Therefore, the matrix between them is the overall S-matrix
of two connected networks. The described procedure can be reiterated (one port at a time) as
many times as it requires by the number of network port connections. It seems rather
complicated in comparison with the conventional multiplication of T-matrices for the cascaded
network because the operation of matrix inverse in (7.33) is far from being trivial and good
predictable. Nevertheless, analyzing more carefully the structure of (7.17) – (7.20) we can
observe that the matrix inversion is actually shifted into the transition from S- to T-matrix.
It is a remarkable fact that the equation (7.33) is universal and formally valid for networks with
any number of free and to be connected ports [1]. All we need is to spread the known S-matrix
elements among the matrices in (7.33) correctly. Suppose we have a network with N+M ports
where the first set of ports with the numbers from 1 to N belongs to be not interconnected, i.e.
free ports. If so, all the relations between free ports should be included in square matrix
11
(dimensions are N x N). The remaining numbers from N+1 to N+M should be assigned to the
ports to be connected that allows filling all the left over
matrices ( x ), ( x ), ( x ). The final two steps are the development of
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12
22
the interconnection matrix C ( x ) of 0 and 1 similar to (7.32) and application of (7.33).
Some disadvantage of the described S-matrix algorithm through the straight application of
(7.33) is the matrix structure. It is possible to show and can be seen from (7.30) and (7.32) that
in the case of multiple connections these matrices belong to the class of sparse matrices, i.e.
most of their elements are zero and require a lot of memory to store. There are plenty of ways
to go around this problem, and we refer the reader for more details to the monograph [1] written
by the author who has proposed the technique. The computer programs based on this algorithm
are typically the excellent and universal engineering tool for analysis and synthesis of complex
microwave circuits [1].

REFERENCES

[1] J. A. Dobrowolski, Microwave Network Design Using the Scattering Matrix, Artech
House, 2010.
[2] D. M. Pozar, Microwave Engineering, 4 Edition, Wiley, 2012
th
[3] S. J. Orfanidis, Electromagnetic Waves and Antennas, Rutgers University, 2016,
http://eceweb1.rutgers.edu/~orfanidi/ewa/

FURTHER TEXTBOOK READING

[3] L. G. Maloratsky, Integrated Microwave Front-Ends with Avionics Applications,
Artech House, 2012
[4] L. G. Maloratsky, Passive RF and Microwave Integrated Circuits, Elsevier, 1999