-Parameter Calibration of Two-Port etup: How to choose the optimal calibration method? Gavin Fisher Cascade Microtech Content Error Modeling of a two-port setup Calibration methods OLT elf-calibration routine: OLR LRM/LRM+ LRRM Conclusion lide 2 1
Error Modeling of a Two Port etup Influencing Factors: VNA architecture Crosstalk between ports Commonly used models: 10(12) Terms 7(8) Terms 15(16) Terms lide 3 Reference Channel VNA N=n+1 receivers 10(12)-term error model where : N - number of receivers n - number of ports lide 4 2
Double Reflectometer VNA N=2n receivers 7(8)-term or 10-term (converted) model where : N - number of receivers n - number of ports lide 5 10-Term Model Reflection terms: Directivity, E D ource match, E Reflection tracking, E R Transmission terms: - Transmission tracking, E T - Load match, E L - Crosstalk, E X Forward direction: lide 6 3
OL Calibration Reflection measurements: 11M E D 11A = E ( 11M E D ) + ER Three independent measurement conditions: 1: 2: 3: ( EDE E R ) I ( EDE E R ) II ( E E E ) III I I I ED + 11 A11M ER 11 A = 11M II II II ED + 11 A11M ER 11 A = 11M III III III ED + 11 A11M ER 11 A D R = 11M Commonly used standards: - hort, Open, Load (OL) lide 7 Experiment Error Correction lide 8 4
Wincal / OL demonstration Objective: To show how calibration (and Wincal) works Verification conditions Verification series: same standards Experimental Conditions: Regular OL calibration and measurement of standard Observation: How to use Wincal to apply calibration and show use of Wincal processing raw data directly lide 9 Wincal / OL demonstration In this example we will be using Wincal with measured data to perform the measurement, but the data has been measured previously creen shots are shown in case existing Wincal users may want to use the same techniques for off line processing of raw measurement lide 10 5
Wincal / OL demonstration Folder set-up is done in order for Wincal to find the raw data for process under calibration. Note - MeasFiles folder used to store raw measurements Files have Vmeas_ as start of file name to denote Wincal will process the raw measurement. lide 11 Wincal / OL demonstration Wincal system set-up restores default conditions of instrument, probes, stimulus etc lide 12 6
Wincal / OL demonstration Opening the calibration set-up allows the old calibration state to be restored, including measurements if present lide 13 Wincal / OL demonstration With the cal loaded we can hit compute which calculates the error terms as discussed. Normally we would send these to the instrument lide 14 7
Wincal / OL demonstration Hitting the measure button brings up a new blank report We can store hundreds of individual measurements in a single report lide 15 Wincal / OL demonstration From the report window we can open pre-saved reports with preset viewing and processing options lide 16 8
Wincal / OL demonstration Wincal can either take a measurement from an instrument or use the currently applied cal to correct a named raw measurement in the measurement folder lide 17 Wincal / OL demonstration Here we have -parameter measurements of the OL standards used for the calibration and also an additional open standard which is on wafer and has positive capacitance lide 18 9
Wincal / OL errors Objective: To show effect of standard misplacement and other errors Verification conditions Verification series: same standards for cal Experimental Conditions: Regular OL calibration and measurement of standard Observation: How OL is only as good as the standards you measure lide 19 Wincal / OL errors New calibration loaded ame standards for cal re-measured (hort / Open iss) Independent standard re-measured (Air open) pot the problem... lide 20 10
OL Calibration Recap.. Reflection measurements: 11M E D 11A = E ( 11M E D ) + ER Three independent measurement conditions: 1: 2: 3: ( EDE E R ) I ( EDE E R ) II ( E E E ) III I I I ED + 11 A11M ER 11 A = 11M II II II ED + 11 A11M ER 11 A = 11M III III III ED + 11 A11M ER 11 A D R = 11M Commonly used standards: - hort, Open, Load (OL) lide 21 OLT Calibration 10 unknowns have to be defined tep 1. OL on Port 1 and 2: E D, E, E R, and E D, E, E R - tep 2. Connect two port together ( Thru ): E L = 11M E 11M E ( E E E ) D D R T 21M ( E E ) E = 1 L - From reverse direction: E L, E F prime, double-prime parameters correspond to the forward and reverse measurement directions respectively. lide 22 11
Calibration tandard Requirements THRU OPEN HORT LOAD Known: Known: Known: Known: 11, 21, 12, 22 11 ( 22 ) 11 ( 22 ) 11 ** ( 22 ) Example: THRU OPEN HORT LOAD Z 0 =50Ω R=inf R=0 R=50 α=0,τ=0.5p C=0.3fF L=9pH L=10.6pH lide 23 Experiment OLT lide 24 12
OLT Experiment lide 25 Objective: To prove sensitivity to standard models Verification conditions: eries of CPW different length Experimental Conditions A: Define wrong OL coefficients (different probe type/pitch) Observation: Accuracy decreases with the frequency, RF noise on 21 Experimental Condition B: Define extracted data-file models for OL standards Observation OLT is as good as you know your standards OLT Experiment Wincal settings loaded from file Calibration settings loaded from file Calibration populated with measurements and calculated Measurements of line standards carried out lide 26 13
OLT Experiment lide 27 OLT Experiment Looking at coefficients lide 28 14
OLT Experiment Open / Load standards look as they should lide 29 OLT Experiment But Lines look terrible lide 30 15
OLT Experiment Load inductance now set to correct value lide 31 OLT Experiment Comparison between same line different calibration lide 32 16
Content Error Modeling of a two-port setup Calibration methods OLT elf-calibration routine: OLR LRM/LRM+ LRRM Conclusion lide 33 elf Calibration Requires double reflectometer VNA Two error matrices [A] and [B] of [T] parameters 7 error terms are in use (normalized to A22) More information is measured than required This additional information allows some parameters to be calculated from within the calibration routine ' m1 ' m2 '' m A 1 = '' m2 A 11 21 A A 12 22 T T 11 21 T T 12 22 B B 11 21 B B 12 22 1 ' m3 ' m4 '' m 3 '' m 4 lide 34 17
elf Calibration (cont.) Measured matrix: m M = m ' 1 ' 2 '' m 1 m '' m 2 m ' 3 ' 4 1 '' m 3 '' m 4, M X = AT B X 1 Three measurement conditions give [A] and [B]: tandard Requirements Definitions T 1 Fully known 4 T 2 Maximum of two free parameters 2 T 3 Maximum of three free parameters 1 H. J. Eul and B. chiek, "A generalized theory and new calibration procedures for network analyzer self-calibration," Microwave Theory and Techniques, IEEE Transactions on, vol. 39, pp. 724-731, 1991. lide 35 OLR tandards used: Reflection: hort, Open, Load Transmission: Reciprocal tandard Requirements Definitions hort 11, 22 : known 2 Open 11, 22 : known 2 Load 11, 22 : known 2 Reciprocal unknown, 21 = 12 1 A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru'," Microwave and Guided Wave Letters, IEEE, vol. 2, pp. 505-507, 1992. lide 36 18
Experiment OLR lide 37 OLR Experiment Objective: To prove sensitivity to standard models Verification conditions: eries of CPW different length Experimental Conditions A: Define wrong OL coefficients (different probe type/pitch) Observation: Accuracy decrease with the frequency Experimental Condition B: Define extracted data-file models for OL standards Observation OLR is as good as you know your OL standards lide 38 19
OLR Experiment OLR line measurements using initial value for load inductance lide 39 OLR Experiment Calibration carried out again with correct probe definitions. Correction applied to original data lide 40 20
Content Error Modeling of a two-port setup Calibration methods OLT elf-calibration routine: OLR LRM/LRM+ LRRM Conclusion lide 41 LRM and LRM+ tandards used: Transmission: Thru (Line) Reflection: Load (Match), Reflect tandard Requirements Definitions Thru/Line Fully known 4 Load/Match 11, 22 : known 2 Reflect unknown, 11 = 22 1 H. J. Eul and B. chiek, "Thru-Match-Reflect: one result of a rigorous theory for de-embedding and network analyzer calibration," in European Microwave Conference, 18th, B. chiek, Ed., 1988, pp. 909-914. lide 42 21
LRM vs. LRM+ Differ in requirements for Load standard: LRM for coaxial applications LRM+ for on-wafer calibration Method Load R X LRM Known R 1 =R 2 =50Ω 0 LRM+ Known R 1, R 2 Arbitrary X 1, X 2 Arbitrary R. F. cholz, F. Korndorfer, B. enapati, and A. Rumiantsev, "Advanced technique for broadband on-wafer RF device characterization," in ARFTG Microwave Measurements Conference-pring, 63rd, 2004, pp. 83-90. lide 43 Experiment LRM/LRM+ lide 44 22
LRM/LRM+ Experiment 1 Objective: To prove sensitivity to the Load Verification conditions: Open, hort, Load, CPW s Experimental Conditions A: Asymmetrical Load Observation: Offset in reflection coefficient for high-reflective elements lide 45 LRM/LRM+ Experiment 1 Calibration applied for LRM+ and measurements computed LRM is calculated and the same raw data is computer with LRM For both calibrations Reflect was short so open makes good validation structure Loads were assymetric RH was 49 ohms which LRM+ is set up for lide 46 23
LRM/LRM+ Experiment 1 LRM shows divergence in Port1 and Port 2 Open (not used in cal) due to load inductance assymetry lide 47 LRM/LRM+ Experiment 2 Objective: To prove sensitivity to the Load Verification conditions: Open, hort, Load, CPW s Experimental Conditions A: Load as a resistor (50 Ohm) Observation: Impact of Zref lide 48 24
LRRM tandards used: Transmission: Thru (Line) Reflection: Reflect(Open), Reflect(hort), Load(Match) tandard Requirements Definitions Thru/Line Fully known 4 Reflect (Open) unknown, 11 = 22 1 Reflect(hort) unknown, 11 = 22 1 Load(Match) 11 (or 22 ) known 1 A. Davidson, K. Jones, and E. trid, "LRM and LRRM calibrations with automatic determination of load inductance," in ARFTG Microwave Measurements Conference-Fall, 36th, 1990, pp. 57-63. lide 49 LRRM(cont.) Requirements to the Load standard Load Impedance R L Inductance approximation Z = R+jωL Known Arbitrary, unknown Unknown L can be found by the automated load inductance extraction algorithm L. Hayden, "An enhanced Line-Reflect-Reflect-Match calibration," in ARFTG Microwave Measurements Conference-pring, 67th, 2006, pp. 143-149. lide 50 25
Experiment LRRM lide 51 LRRM Experiment 1 Objective: To show LRRM relative immunity to probe misplacement Verification conditions: CPW s Experimental Conditions A: Observation: Line measurements comparatively immune to probe misplacement lide 52 26
Probes in normal position lide 53 Probes misplaced lide 54 27
LRRM Experiment 1 lide 55 OLT based calibrations show much more noise in line measurement Choosing Calibration trategy Understanding of strengths and limitations is essential! Re-measuring of calibration standards verification! Method Application OLT Well defined conditions Frequencies < 40GHz OLR Rectangular configurations Double-side probing LRM Not recommended for wafer-level applications LRM+ Broadband on-wafer calibration LRRM Broadband I calibration lide 56 28