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Mixed-Mode Hybrid Parameters for High-Speed Differential Lines
Keywords: signal integrity, differential lines, mixed-mode scattering parameters
High-speed transmission lines are commonly routed as differential lines to control sensitivity to noise on the reference planes at higher speeds. The preferred method of characterization of differential lines is in terms of mixed-mode scattering parameters, as they provide insight into the behavior of differential and common signals, as well as the mode conversion among them. These mixed-mode scattering parameters can be mathematically obtained from single-ended parameters, which can for example be measured with a 4-port vector network analyzer. There has been recent concerns about the so-obtained mixed-mode scattering parameters, especially for tightly-coupled lines, resulting in extended or modified definitions of mixed- mode scattering parameters. This can be a point of confusion in interpreting the behavior of differential lines. In this paper we introduce the mixed-mode hybrid parameters, which do not suffer from any such ambiguous definitions. The hybrid parameters are the most natural way to represent any 4-port network in terms of its mixed-mode parameters, as they are based on intuitive differential and common-mode excitations of the network. As such, mixed-mode hybrid parameters can be used to analyze the mixed-mode performance of any arbitrary 4-port network, certainly including coupled or asymmetrical lines, without any ambiguity. Single-ended to mixed-mode conversion can be considered as a linear transformation of nodal voltages and currents into modal ones. A differential and common-mode voltage and current can be associated with each port pair to define mixed-mode impedance, admittance, or ABCD parameters. For the more commonly used mixed-mode scattering parameters, the transformation is from single-ended power waves into differential and common-mode power waves [1]. These linear transformations can be done with arbitrary coefficients, resulting in various definitions of mixed- mode parameters [2]. It is therefore more meaningful to discuss the usefulness or advantages of such a definition, rather than its correctness. A major advantage of working with mixed-mode parameters is that they allow to gain intuition into the properties of a network with a quick glance. In this paper, we introduce mixed-mode hybrid parameters, which provide an intuitive view into the definition of differential and common-mode signals, while not suffering from ambiguities existing in earlier mixed-mode parameters. To develop the intuitive nature of the mixed-mode hybrid parameters, we start by defining possible port excitations for the differential and common mode signals. This allows us to relate the developed parameters to a possible simulation or measurement setup. We define the differential port across the two single-ended ports while leaving the ground reference open. The common port is across the shorted single- ended ports and ground reference. An advantage of such a mixed-mode port definition is that these ports can be realized in electromagnetic simulators, and implemented on test boards. A. Modal voltages and currents The traditional definition of differential voltage and common-mode current are Vd=V1-V2 and Ic=I1+I2 , where the subscripts 1 and 2 represent the pair of single-ended ports. From these modal voltages and currents, differential and common-mode power waves can also be defined, which result in mixed-mode scattering parameters. The mixed-mode scattering parameters can be measured directly by exciting both single-ended ports in-phase and with a 180 phase shift with a balun. These parameters are intuitive especially for RF designs where baluns are frequently used. For high-speed transmission lines, a solution without baluns would be preferable. Towards this goal, mixed-mode excitations can be defined in terms of voltages and currents rather than power waves. Specifically, we excite the differential mode by defining a port across the two single-ended ports while leaving the ground reference open. This differential excitation results in Ic = 0. The common mode is excited by defining a port across the shorted single-ended ports and ground reference, which results in Vd = 0. As a result, we obtain a straightforward way to enforce either Ic or Vd to zero, which results in mixed-mode hybrid parameters. B. Four-port networks An important special case is when the network is a four- port, such as in a differential line. We define the mixed- mode hybrid parameters in this case as (Id Vc) = G (Vd Ic). Since we can enforce Ic or Vd terms on the right hand side to be equal to zero by differential and common-mode port excitations, the mixed mode hybrid parameters present a new intuitive approach for characterization of differential lines. In the full paper, we discuss the details of these new microwave network parameters.
A. Ege Engin, Associate Professor
san diego, ca

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