MIXED-MODE SCATTERING PARAMETERS

1. MIXED-MODESCATTERING PARAMETERS Pat Zabinski 21 May 2004

2. TOPICS FOR DISCUSSION • Fundamentals • Two-port S-parameters • Mixed-mode S-parameters • Conversion basics • Mixed-mode analysis capability • Simulation tools • Direct-measurement tools • Indirect-measurement tools

3. SINGLE-ENDED TRANSMISSION LINE I2 + V2 - + V1 I1 -

4. TWO-PORTSCATTERING PARAMETERS Where: Vi- and bi is the signal out from Port i Vj+ and aj is the signal into Port j With this definition, we can determine voltages at each node: Note that S-parameters are defined to be linear relationships between port voltages with respect to both magnitude and phase.

5. + - + - WHAT IS MIXED-MODE? • “Mixed Mode” refers to the fact that the trace signals have both even-mode and odd-mode components • Respectively, there exists a non-zero potential between the traces (odd mode) • Combined, the pair of traces has a non-zero potential to ground (even mode)

6. + - + - DIFFERENTIAL-TO-DIFFERENTIAL PARAMETERS: SDD • Analogous to single-ended S-parameters but specific to odd-mode propagation of signal • Generally of most interest in characterizing differential devices • Poor SDD performance results in direct degradation in bit error rate and attainable data rate or bandwidth aD bD

7. + - + - COMMON-TO-DIFFERENTIAL PARAMETERS: SDC • Measure of susceptibility to noise from outside sources • Due to imbalance between true and complement traces • Poor SDC performance can result in outside noise affecting differential signal performance bD Note Convention aC

8. + - + - DIFFERENTIAL-TO-COMMON PARAMETERS: SCD • Measure of signal emission to outside environment • Due to imbalance between true and complement traces • Poor SCD performance can result in generation of unwanted noise coupling into other interconnect aD Note Convention bC

9. + - + - COMMON-TO-COMMON PARAMETERS: SCC • Analogous to single-ended S-parameters but specific to even-mode propagation of signal • Poor SCC performance can result in common-mode shifts in signals and ground/supply-loop currents aC bC

10. COUPLED TRANSMISSION LINES Note that the traces do not need to be symmetric I3 I4 + + V3 V4 - - + + V1 V2 I1 I2 - -

11. MIXED-MODESIGNAL IDENTIFICATION We can relate the differential- and common-mode voltages directly to the single-ended voltages b is the voltage out of the port; a is the voltage into the port Scaling factor used to normalize power levels

12. MIXED-MODESCATTERING PARAMETERS Using the definitions of port voltages from the previous page, we can now define the mixed-mode S-parameters. For example, the differential-voltage out of Port 1 is: Extending the same process to the full matrix results in:

13. CONVERSION FROMSINGLE-ENDED PARAMETERS Through variable substitution and carrying through the math, we can now obtain the relationship between single-ended and mixed-mode S-parameters Differential-to-Differential Common-to-Differential Differential-to-Common Common-to-Common

14. MIXED-MODE PARAMETER SUMMARY • Mixed-mode parameters are analogous to and logical extensions of two-port S-parameters • Similar to two-port parameters, mixed-mode parameters are defined as linear relationships between port voltages • As a result, S-parameters are not applicable to nonlinear devices • Useful insight into second-order issues can be gained from mode-conversion parameters

15. MIXED-MODE S-PARAMETERANALYSIS TOOLS • Simulation tools • Synopsys Hspice • Agilent Advanced Design System • Others? • Lab measurements • Direct methods • Indirect methods

16. EXAMPLE HSPICE DECK - 1 * DIFFERENTIAL S-PARAMETER SIMULATION EXAMPLE VIN INP INN AC=1 TLINE INP INN OUTP OUTN ZO=100 TD=1ns ROUT OUT OUTN 100K RDUMMY1 INN 0 100K RDUMMY2 OUTN 0 100K .NET V(OUTP,OUTN) VIN RIN=100 ROUT=100 .AC LIN 401 45MEG 26.045G .PRINT AC S11(db) S12(db) S21(db) S22(db) .OPTIONS POST=2 INGOLD=2 .END

17. EXAMPLE HSPICE DECK - 2 Differential Input Source * DIFFERENTIAL S-PARAMETER SIMULATION EXAMPLE VIN INP INN AC=1 TLINE INP INN OUTP OUTN ZO=100 TD=1ns ROUT OUT OUTN 100K RDUMMY1 INN 0 100K RDUMMY2 OUTN 0 100K .NET V(OUTP,OUTN) VIN RIN=100 ROUT=100 .AC LIN 401 45MEG 26.045G .PRINT AC S11(db) S12(db) S21(db) S22(db) .OPTIONS POST=2 INGOLD=2 .END DUT Connections to Ground to make Hspice happy Differential Port 2 is Between OUTP and OUTN Reference Impedance is 100 Ohms Differential Port 1 is VIN Sweep from 45 MHz to 26 GHz With 401 Points Display S-Parameters in dB Scale INGOLD Sets Output to Exponential Format POST Sets Output to ASCII Format

18. HSPICE SUMMARY • Early releases only allows for single-mode analysis • Single-ended, differential, or common mode • With Release 2003.09, Hspice should be directly compatible with Touchstone S2P files • With Release 2004.03 • Can suck in and spit out Touchstone SnP files • Can perform mixed-mode conversions and analysis

19. EXAMPLE ADS SCHEMATIC Differential Output Port Differential Input Port DUT

20. EXAMPLE ADS DISPLAY

21. ADS SUMMARY • Readily accepts and generates Touchstone SnP file formats • Can perform single-mode or mixed-mode analysis

22. OTHER SIMULATION TOOLS • Expect other tools might provide mixed-mode S-parameters as well • HFSS? • SONNET?

23. DIRECT-MEASUREMENT METHOD -BALUNS • Use baluns to provide differential signals • Bandwidth limited to available baluns • Only provides differential-mode parameters • Appropriate calibration standards not available

24. DIRECT-MEASUREMENT METHOD -RAT-RACES • Use rat-races (i.e., 180º hybrids) to convert single-ended signals • Provides  and  ports for differential and common modes, respectively • Obtains all mixed mode parameters with exception of return loss • Bandwidth limited to available hybrids • Appropriate calibration standards not available • Time consuming to make the full matrix of measurements

25. DIRECT-MEASUREMENT METHOD -PURE-MODE VNA • Directly measures all sixteen true mixed-mode parameters through differential- and common-mode excitation • Automated extension of “rat-race” approach • Utilizes internal 180º hybrids to produce and measure various voltage modes • Will be limited to bandwidth of 180º hybrids • Much available literature on concept, theory, and calibration • Not able to find a commercial product (yet) • Error analysis indicates a PMVNA has the potential for the best accuracy

26. INDIRECT-MEASUREMENT METHOD -TDR/TDT CONVERSION • Using FFT, convert differential TDR/TDT measurements to S-parameters • NIST developed code that is available to public • Unaware of its present status • Limited to TDR bandwidth (roughly 10 GHz for 35 ps edge rates) • Proven to be reasonably accurate

27. INDIRECT-MEASUREMENT METHOD -FOUR-PORT VNA • Measures two-port parameters and converts them to mixed-mode parameters • Subtle non-linearity in DUT will dramatically affect accuracy • A few vendors are offering four-port VNAs up to 50 GHz

28. INDIRECT-MEASUREMENT METHOD -POST-MEASUREMENT CONVERSION • Using custom scripts/tools, two-port S-parameter measurement data can be converted into mixed-mode data • Using matrix conversion presented earlier • Requires a minimum of three measurements for a balanced, bidirectional DUT • Up to six measurements for unbalanced, unidirectional DUT • Subtle non-linearity in DUT will affect accuracy

29. The VNA port connections must follow a consistent convention for the conversion to work The bottom (or top) three measurements are optional for a balanced, bidirectional DUT Unused ports must be properly terminated NEEDED MEASUREMENTS 3 1 + + S31 IN(1) S21 OUT(2) 4 2 - S41 - - AND - 3 1 + + S32 S43 IN(1) OUT(2) S42 4 2 - -

30. MIXED-MODE ANALYSISSUMMARY • Many tools exist to simulate and measure mixed-mode S-parameters • Great care must be taken to appropriately address port numbering • Different tools use different conventions • Measurement capability is still a bit problematic • Good four-port calibration tools do not exist • Port reference-plane locations must be consistent • Many separate calibrations and measurements are needed to obtain a single set of mixed-mode parameters

31. CONCLUSIONS • Mixed-mode S-parameters are becoming more important as we proceed into higher data rates • There is much existing simulation, analysis, and measurement capability • Future enhancements are likely • Companies are developing analogous time-domain tools (i.e., TDR/TDT)

32. REFERENCES • David E. Bockelman and William R. Eisenstadt, “Combined Differential and Common-Mode Scattering Parameters: Theory and Simulation,” IEEE Trans. On MTT, vol. 43, pp.1530–1539, July 1995. • Anritsu Application Note “Three and Four Port S-Parameter Measurements”, November 2001. • Guillermo Gonzalez, “Microwave Transistor Amplifiers, 2nd ed.,” Prentice Hall, 1997.