Single-Ended and Differential S-Parameters

Differential circuits have been important in
communication systems for many years. In the past,
differential communication circuits operated at low
frequencies, where they could be designed and
analyzed using lumped-element models and
techniques. With the frequency of operation
increasing beyond 1GHz, and above 1Gbps for
digital communications, this lumped-element
approach is no longer valid, because the physical
size of the circuit approaches the size of a
wavelength.
Distributed models and analysis techniques are now
used instead of lumped-element techniques.
Scattering parameters, or S-parameters, have been
developed for this purpose [1]. These S-parameters
are defined for single-ended networks. S-parameters
can be used to describe differential networks, but a
strict definition was not developed until Bockelman
and others addressed this issue [2]. Bockelman’s
work also included a study on how to adapt single-
ended S-parameters for use with differential circuits
[2]. This adaptation, called “mixed-mode S-
parameters,” addresses differential and common-
mode operation, as well as the conversion between
the two modes of operation.
This application note will explain the use of single-
ended and mixed-mode S-parameters, and the basic
concepts of microwave measurement calibration.