Mixed-mode S-parameter Characterization Of Differential Structures 3o2i5f

Mixed-Mode S-Parameter Characterization of Differential Structures W. Fan*, Albert Lu, L. L. Wai, B. K. Lok

ing Technology Group Singapore Institute of Manufacturing Technology (SIMTech) 71 Nanyang Drive, Singapore 638075 *[email protected] definitions, normalized power waves can be defined in stimulus and response. Stimulus power waves are defined as propagating into the device-under-test (DUT), and response power waves propagate away from it. A block diagram of a four-port device is shown in Fig. 1.

Abstract Combined differential-mode and common-mode (mixedmode) scattering parameters (s-parameters) are well adapted to accurate measurements of linear networks at RF and microwave frequencies. The relationships between standard s-parameters with two-port vector network analyzer (VNA) and mixed-mode s-parameters with four-port VNA are derived in this paper. An example differential structure was measured with standard two-port VNA and mixed-mode four-port VNA. The correlation of standard s-parameters and mixed-mode s-parameters is presented as well.

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1. Introduction The differential structures are widely used in RF, microwave and high-speed broadband applications. The evaluation of differential structures is necessary to ensure optimal circuit and system performance. Combined differential-mode and common-mode (mixed-mode) scattering parameters (s-parameters) are well adapted to accurate measurements of linear networks at RF frequencies. However, differential stmcture measurements with a traditional two-port vector-network analyzer (VNA) present many challenges [1][2]. The major obstacle in RF application of differential structures is that most test equipment is intended for single-ended devices. The related infrastructure is also unbalanced, such as calibration standards, transmission lines and connnectors, and even industry standard reference impedance [3][4]. This paper presents the transformation between standard s-parameters and mixed-mode s-parameters. An example of differential structure is measured with two-port VNA and four-port mixed-mode VNA, respectively, and the correlation data is presented as well. Although the transformation could ideally be used to allow a traditional two-port VNA to make measurements of mixed-mode s-parameters, a mix-mode measurement system is necessary to accurately measure the mode-conversion in the real differential test structures [l]. The paper is organizered as follows. In section 2, singleended four-port and differential-ended two-port structures are introduced, and the transformation between standard sparameters and mixed-mode s-parameters is derived. The test hoard, measurement setup and experimental results are presented in section 3. The conclusions are given in section

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DUT

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Fig. 1. Diagram of Single-Ended 4-port DU'I An s-parameter is defined as the ratio of two normalized power waves: the response divided by the stimulus. A full smatrix (1) describes every possible combination of a response divided by a stimulus. The matrix is arranged in such a way that each column represents a particular stimulus condition, and each row represents a particular response condition. The standard four-port s-parameters matrix is given below [I].

Or Est, = S,, AI,, , where Er,, and Artd are response and stimulus waves matrix respectivly; S,, is the standard fourport s-parameters matrix. They are shown in (2) and (3).

(3)

4.

2. Standard and Mixed-Mode S-Parameter of Differential Structure For a single-ended device, RF voltages and currents relative to a common ground can be defined at each terminal of the device. From the voltage, current and impedance

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For a balanced device, differential- and common-mode voltages and currents can be defined on each balanced port. Differential- and common-mode impedances can be defined also. A block diagram of a two-port differential DUT is shown in Fig. 2.

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Fig. 2 Diagram of Differential 2-port DUT

A mixed-mode s-matrix in (4) can he organized in a way similar to the single-ended s-matrix, where each column (row) represents a different stimulus (response) condition. The mode information as well as port information must he included in the mixed-mode s-matrix [3].

The transformation matrix in (12) between mndard sparameters and mixed-mode s-parameters can hs derived from the relationships of the following equation:;: mixedmode incident waves A,, in (7); mixed-mode response S in waves B,, in (8); mixed-mode s-parameters matlix , (11); standard four port s-parameters matrix S,, in (3); and the conversion matrix M in (9) and M' in (IO). =

Sdj& and SCj, (i, j=1, 2) are the differential-mode and common-mode s-parameters respectively. sdjcj and SCj4 (i, j=l, 2) are the mode-coovertion or cross-mode s-parameters. The parameters Sdj4 (i, j=1, 2) in the upper left comer of the mixed-mode s-matrix (4) describe the performance with a differential stimulus and differential response. SdiCj(Scidi) (i, j=1, 2) describes the conversion of common-mode (differential-mode) waves into differential-mode (commonmode) waves. The mixed-mode s-parameters in (4) can be directly related to standard four port s-parameters (3). If nodes 1 and 2 in Fig. 1 are paired as a single differential port, and nodes 3 and 4 are also paired as another differential port [ 5 ] . The relations between the response and stimulus of standardmode and mixed-mode are shown in ( 5 ) and (6). Where ai and bj (i=l to 4) are the waves measured at ports 1-4 in Fig. 1.

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3. Test Board Characterization and Analysis The test board is a 4-layer FR4 substrate with a coupled differential smcture design. The cross section and photo of test hoard are show in Fig. 3 and Fig. 4, respectively. The cross section shows top copper, prepreg and ground plane. The geometric parameters of test hoard are show in Table I. The differential microstrip is tight-coupled differential structure. The differential impedance of coupled microstrip is IOOOhm. The SMA connectors are used for the connection with VNA.

PI&P3, Pl&P4, P2&P3, P2&P4 and P3&P4. These twoport measurement results can be used to form standard fourport s-parameters matrix S,,d in (3). Standard s-parameters matrix ss,d will be converted into mixed-mode s-parameters matrix S,,,, in (12). The setup of differential-ended four-port VNA measurement is shown in Fig. 5 (b). All of four ports are connected to mixed-mode four-port VNA in the same time. The mixed-mode s-parameters have been measured and drawn in the same figures as a comparison. The calibration method of short-open-load-through (SOLT) is used both two-port and four-port VNA.

, Cu Trace,

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2-Port Differential

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Ground Plane (a) For Single-Ended 2-Port VNA Fig. 3. Cross-Section of Test Board 4-Port

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(b) For Differential-Ended 4-Port VNA Fig. 5. The Setup of S-Parameters Measurement Fig. 4. The Photo of Test Board Table I. Test Board Parameters Thickness (bm) Spacing (pm) Thichess(pm) Prepreg

Dielectric Constant Er

1 Loss Tangent 6

~

42.5 510 190 4.0 0.02

The setup of single-ended two-port VNA measurement is shown in Fig. 5 (a). During the two-port VNA measurement, two ports are connected to two-port VNA respectively, and the rest two ports should be terminated with 50 Ohm. All combinations of four individule ports are measured to get standard s-parameters matrix, i.e. all of the two-port: P1&P2,

In Fig. 6 to Fig. 14, the curves “Standard” represent the mixed-mode s-parameters converted from two-port VNA measurements, and curves “Mixed” represent the mixedmode s-parameters measured with mixed-mode four-pon VNA. In Fig. 6 , the insertion loss of differential response and differential stimulus bas very good agreement between ‘Standard” and “Mixed”. The curve “Single-Ended S 12” is the insertion loss between single-ended port 1 and single-ended port 2 as a reference. The insertion (return) loss of fesponse and stimulus with same mode has very good agreement between “Standard and “Mixed” mixed-mode s-parameters in Fig. 7 to Fig. 10. For the response and stimulus with the different mode, there is slightly difference of insertion (retum) loss between “Standard and “Mixed’ mixed-mode s-parameters in Fig. 11 to Fig. 14. The transformation method between standard

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and mixed-mode s-parameters can be used to characterize the differential structures for the s who only have traditional two-port VNA.

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Fig. 9. Differential-Mode of Response and Stimulus Fig. 6. Single-Ended and Differential-Ended S-Parameters

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parameters between the two methods have good agreement for the stimulus and response with the same mode, and slightly difference for the stimulus and respone with the different mode. Although the transformation could be ideally used to measure mixed-mode s-parameters with a uaditional VNA, a mixed-mode VNA system is necessary to accurately measure the mode conversion in real integrated differential test smcmres [I].

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References 1. D. E. Bockelman and W. R. Eisenstadt, “Pure-Mode Network Analyzer for On-Wafer Measurements of Mixed-Mode S-Parameters of Differential Circuits,” IEEE Trans. Microwave Theory Tech., vol. 43 (Jul. 1997), pp107 1-1077. 2. D. E. Bockelman and W. R. Eisenstadt, “Combined differential and common-mode scattering parameters: Theory and simulation,” IEEE Trans. Microwave Theory Tech., vol. 43 (Jul. 1995), pp. 1530-1539. 3. Application Notes: “Balanced Device Characterization,” Agilent Technoloies, Jun. 2002. 4. Application Note 1373-1: “An 1nh.oduction to Multiport and Balanced device Measurements,” Agilent Technologies, Nov. 2002. 5 . K. Kurokawa, “Power Waves and the Scatering Matrix,” IEEE Trans. Microwave Theory Tech., vol. 13 (Mar. 1965). pp. 194-202.

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Fig. 13. Differential-Mode Response and Common-Mode Stimulus

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4. Conclusions The transformation between standard s-parameters and mixed-mode s-parameters has been presented in this paper. An example differential stmcture has demonstrated the transformation and the good agreement between the mixedmode s-parameters converted from two-port VNA measurements and the mixed-mode s-parameters measured with mixed-mode four-port VNA. The mixed-mode s-

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