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Multi Port Measurements

Multi Port Measurements. Slides from Dave Blackham and Ken Wong At Agilent Technologies With some additions by Doug Rytting. Dave Blackham & Ken Wong. Agenda. Two Port Network Analysis Multiport Network Analysis Multiport Network Analysis Port Match Correction

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Multi Port Measurements

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  1. Multi Port Measurements Slides from Dave Blackham and Ken Wong At Agilent Technologies With some additions by Doug Rytting Dave Blackham & Ken Wong

  2. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  3. Network Analyzer Block Diagram

  4. 8-Term Error Model

  5. 8-Term Error Model

  6. 8-Term Error Model

  7. 8-Term Error Model

  8. 8-Term Calibration Examples

  9. Measuring S-parametersRemoving Port Match Changes Caused by Switch

  10. Measuring S-parameters

  11. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  12. Multiport error correction • Is multiport error correction hard? Dave Blackham & Ken Wong

  13. Multiport error correction • Is multiport error correction hard? • No, multiport error correction with constant match is as easy as single port error correction. Dave Blackham & Ken Wong

  14. Multiport error box diagram Dave Blackham & Ken Wong

  15. Multiport error box diagram Dave Blackham & Ken Wong

  16. Multiport error box diagram Dave Blackham & Ken Wong

  17. Multiport error box diagram Dave Blackham & Ken Wong

  18. Multiport error box diagram Dave Blackham & Ken Wong

  19. Multiport error box diagram Dave Blackham & Ken Wong

  20. Multiport error box diagram Dave Blackham & Ken Wong

  21. Multiport error box diagramwith “12 term” crosstalk Dave Blackham & Ken Wong

  22. Multiport error box diagramwith full leaky model Dave Blackham & Ken Wong

  23. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  24. Multiport error correction • Models presented thus far assume a constant port match • similar to 8 term two-port model for non-leaky case • similar to 16 term two-port model for leaky case • Due to switching, port match is not constant • similar to 12 term two-port model Dave Blackham & Ken Wong

  25. What Is Switch Correction? • TRL and unknown thru algorithms belong to a class that assumes a constant match at each test port. • In reality, the match at each test port will vary as the source is switched from port to port. • Switch correction is the process of characterizing the match difference then factoring it out of the calibration process • Generalized s-parameters factor out match differences during raw measurements for receivers that have dual couplers at each port (reference receiver at each port). • Two-tier calibration approaches characterize match differences with a first tier calibration using SOLT. This allows the use of generalized s-parameters approach for systems that have a single reference receiver. Dave Blackham & Ken Wong

  26. Ideal S-Parameters • Ideal s-parameters • Non-source ports terminated in perfect match—incident signal only from source port Dave Blackham & Ken Wong

  27. Use Generalized S-Parameters • Ideal s-parameters • Non-source ports terminated in perfect match—incident signal only from source port • Generalized s-parameters • Uses incident signals from all ports & removes port match error Dave Blackham & Ken Wong

  28. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  29. Single Reference Receiver Dave Blackham & Ken Wong

  30. S-parameter measurement (two-port, ideal) Reverse s-parameters Source at port 2 Forward s-parameters Source at port 1 Dave Blackham & Ken Wong

  31. S-parameter measurement (two-port, ideal) Dave Blackham & Ken Wong

  32. S-parameter measurement (two-port, non-ideal) Generalized s-parameters • Dual reflectometers at each testport allow measurement of all signals required to determine s-parameters. • Using this method will correct for the changing port match caused by the switch. Dave Blackham & Ken Wong

  33. S-parameter measurement (two-port, non-ideal) Generalized s-parameters • Dual reflectometers at each testport allow measurement of all signals required to determine s-parameters. • Benefit allows constant match to be assumed for error correction (eight term model) • Match variations tracked by incident wave measurements Dave Blackham & Ken Wong

  34. S-parameter measurement (two-port, non-ideal) • Non dual reflectometer analyzers can’t measure signals reflected from switch in off position. • Requires mathematical equivalent computed from difference between source and load match at each port (delta match) • Generalized S-parameter in ratio form: Dave Blackham & Ken Wong

  35. S-parameter measurement (two-port, non-ideal) Dave Blackham & Ken Wong

  36. Calculate GF and GRFor Single Reference Receiver • Error terms were measured during the first tier calibration using SOLT. • With GF and GR determined the generalized s-parameters can be used to remove the port match variations. • Also TRL or unknown thru, etc. can be used in a second tier calibration. Dave Blackham & Ken Wong

  37. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  38. Multiport Using a 2-port VNA Example Switches Terminated in off state Dave Blackham & Ken Wong

  39. Multiport Using a 2-port VNA • Let: • Smi:j = measured S-parameters between ports i and j. • Rmi:j = Port impedance normalized Scattering Matrix • Gi:j = Diagonal matrix of reflection coefficient of imperfect port terminations at ports i and j. [Gi..N values must not change when signal paths are changed.] Dave Blackham & Ken Wong

  40. Multiport Using a 2-port VNA • Let: • Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix • Fill Rn matrix with calculated Rm sub-matrices • i=1, j=2 Dave Blackham & Ken Wong

  41. Multiport Using a 2-port VNA • Let: • Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix • Fill Rn matrix with calculated Rm sub-matrices • i=2, j=3 Dave Blackham & Ken Wong

  42. Multiport Using a 2-port VNA • Let: • Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix • Fill Rn matrix with calculated Rm sub-matrices • i=1, j=3 Dave Blackham & Ken Wong

  43. Multiport Using a 2-port VNA • Let: • Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix • Fill Rn matrix with calculated Rm sub-matrices • Do N(N-1)/2 2-port measurements to fill Dave Blackham & Ken Wong

  44. Multiport Using a 2-port VNA • Let: • Rn = Composite port impedance normalized N-port Scattering Matrix • Gn = Diagonal matrix of reflection coefficient of imperfect port terminations at ports 1 to N. • Sn = S-parameters of corrected N-port • Normalize Result back to System Impedance Dave Blackham & Ken Wong

  45. Agenda • Two Port Network Analysis • Multiport Network Analysis • Multiport Network Analysis Port Match Correction • Single Reference Receiver Example • Multiport Using a 2-port VNA Example • Multiport Calibration ApproachHow Many Connections Are Needed • Examples

  46. Multiport calibration Approach • Use all of the same calibration standards used by two port calibrations. • Brute force method: calibrate all possible two-port pairs • This will get tedious very quickly as the number of ports increases Dave Blackham & Ken Wong

  47. Multiport calibration error terms Path terms Port terms Dave Blackham & Ken Wong

  48. Minimizing Connections During Multiport calibration • Characterize each set of port terms once (n). • Characterize (n-1) thru standards to characterize (n) load match terms and 2x(n-1) sets of transmission tracking terms. Compute the other (n-1)x(n-2)transmission tracking terms. • If desired, connect loads to each port then characterize n x (n-1) sets of crosstalk terms. • Full leaky model would connect multiple permutations of one port reflection standards to the ports and measure n x (n-1) paths for each permutation. Dave Blackham & Ken Wong

  49. Required Number of Thrus • Connect (n-1) thru connections and characterize 2x(n-1) transmission tracking terms. • The other (n-1)x(n-2) terms can be calculated. Port 1 Port 2 Port 3 Port N Required Thrus Dave Blackham & Ken Wong

  50. Compute Transmission Tracking • Characterize transmission tracking between ports i and j • Characterize transmission tracking between ports i and k • Compute transmission tracking between ports j and k • Accuracy of computed transmission tracking terms less than characterized transmission tracking terms. • Actual equation includes compensation for varying port match (source match not equal to load match at port i). Dave Blackham & Ken Wong

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