MIXED-MODE SCATTERING PARAMETERS

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MIXED-MODESCATTERING PARAMETERS

• Pat Zabinski
• 21 May 2004

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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

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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.
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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)

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DIFFERENTIAL-TO-DIFFERENTIAL PARAMETERS SDD
aD
bD

• 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

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COMMON-TO-DIFFERENTIAL PARAMETERS SDC
bD
Note Convention
aC

• 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

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DIFFERENTIAL-TO-COMMON PARAMETERS SCD
aD
Note Convention
bC

• 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

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COMMON-TO-COMMON PARAMETERS SCC
aC
bC

• 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

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COUPLED TRANSMISSION LINES
I3
I4


V3
V4
-
-


V1
V2
I1
I2
-
-

• Note that the traces do not need to be symmetric

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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
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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-voltag
e out of Port 1 is
Extending the same process to the full matrix
results in
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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
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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

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MIXED-MODE S-PARAMETERANALYSIS TOOLS

• Simulation tools
• Synopsys Hspice
• Agilent Advanced Design System
• Others?
• Lab measurements
• Direct methods
• Indirect methods

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EXAMPLE HSPICE DECK - 1

• DIFFERENTIAL S-PARAMETER SIMULATION EXAMPLE
• VIN INP INN AC1
• TLINE INP INN OUTP OUTN ZO100 TD1ns
• ROUT OUT OUTN 100K
• RDUMMY1 INN 0 100K
• RDUMMY2 OUTN 0 100K
• .NET V(OUTP,OUTN) VIN RIN100 ROUT100
• .AC LIN 401 45MEG 26.045G
• .PRINT AC S11(db) S12(db) S21(db) S22(db)
• .OPTIONS POST2 INGOLD2
• .END

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EXAMPLE HSPICE DECK - 2
Differential Input Source

• DIFFERENTIAL S-PARAMETER SIMULATION EXAMPLE
• VIN INP INN AC1
• TLINE INP INN OUTP OUTN ZO100 TD1ns
• ROUT OUT OUTN 100K
• RDUMMY1 INN 0 100K
• RDUMMY2 OUTN 0 100K
• .NET V(OUTP,OUTN) VIN RIN100 ROUT100
• .AC LIN 401 45MEG 26.045G
• .PRINT AC S11(db) S12(db) S21(db) S22(db)
• .OPTIONS POST2 INGOLD2
• .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
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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

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EXAMPLE ADS SCHEMATIC
Differential Output Port
Differential Input Port
DUT
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EXAMPLE ADS DISPLAY
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ADS SUMMARY

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

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OTHER SIMULATION TOOLS

• Expect other tools might provide mixed-mode
  S-parameters as well
• HFSS?
• SONNET?

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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

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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

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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

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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

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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

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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

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NEEDED MEASUREMENTS
3
1


S31
IN(1)
OUT(2)
S21
4
2
-
-
S41
- AND -
3
1


S32
S43
IN(1)
OUT(2)
S42
4
2
-
-

• 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

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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

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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)

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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.15301539, July 1995.
• Anritsu Application Note Three and Four Port
  S-Parameter Measurements, November 2001.
• Guillermo Gonzalez, Microwave Transistor
  Amplifiers, 2nd ed., Prentice Hall, 1997.