MIXED-MODE SCATTERING PARAMETERS

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## MIXED-MODE SCATTERING PARAMETERS

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**MIXED-MODESCATTERING PARAMETERS**Pat Zabinski 21 May 2004**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**SINGLE-ENDED TRANSMISSION LINE**I2 + V2 - + V1 I1 -**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.**+**- + - 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)**+**- + - 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**+**- + - 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**+**- + - 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**+**- + - 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**COUPLED TRANSMISSION LINES**Note that the traces do not need to be symmetric I3 I4 + + V3 V4 - - + + V1 V2 I1 I2 - -**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**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:**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**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**MIXED-MODE S-PARAMETERANALYSIS TOOLS**• Simulation tools • Synopsys Hspice • Agilent Advanced Design System • Others? • Lab measurements • Direct methods • Indirect methods**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**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**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**EXAMPLE ADS SCHEMATIC**Differential Output Port Differential Input Port DUT**ADS SUMMARY**• Readily accepts and generates Touchstone SnP file formats • Can perform single-mode or mixed-mode analysis**OTHER SIMULATION TOOLS**• Expect other tools might provide mixed-mode S-parameters as well • HFSS? • SONNET?**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**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**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**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**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**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**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 - -**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**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)**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.