MIXED-MODE SCATTERING PARAMETERS

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MIXED-MODE SCATTERING 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.

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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
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

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

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
• 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

Differential Output Port

Differential Input Port

DUT

• 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.