Using the unknown-thru method for waveguide/coax systems with the 8510

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1 Using the unknown-thru method for waveguide/coax systems with the 8510 Jörgen Stenarson

2 Unknown Thru algorithm Requires: four receiver VNA reciprocal thru standard switch corrected raw S-parameters approximate value of electrical delay of thru standard A. Ferrero and U. Pisani, Two-port network analyzer calibration using an unknown thru, Microwave and Guided Wave Letters, pp , 1992 K. Wong, The unknown thru calibration advantage, in 63 rd ARFTG Conference, 2004

3 Adapter removal vs. unknown thru calibration procedure

4 Seven term model & raw S-parameters Switch correction: S raw = " b1m,f a 1m,f b 2m,f a 1m,f b 1m,r a 2m,r b 2m,r a 2m,r #" a 1 1m,r a 2m,r a 2m,f a 1m,f 1 # 1

5 Measurement equations for seven term model S 11,raw = e 00 + e 01e 10 (S 11 e 22 S ) S 22,raw = e 33 + e 23e 32 (S 22 e 11 S ) S 12,raw S 21,raw = e 01e 23 S 12 e 10 e 32 S 21 q 2 = q 2 S 12,raw = e 01e 23 S 12 q S 21,raw = qe 10e 32 S 21 S = S 11 S 22 S 12 S 21 = 1 + e 11 e 22 S e 11 S 11 e 22 S 22 q = ± r S12,raw S 21,raw

6 Correction using seven term model S 0 11 = S 11,raw e 00 1 S 0 21 = S 21,rawe 01 q 1 S 0 22 = S 22,raw S 12,rawS 21,raw e = e 01 e 10 + e 11 (S 11,raw e 00 ) S 11 = S 0 11 S0 12 S0 21 e 22 2 S 0 12 = qs 12,rawe 10 1 S 12 = S0 12 e 32 2 S 21 = S0 21 e 23 2 S 11 = S0 22 e 33 2 = e 23 e 32 + e 22 (S 0 22 e 33 ) 2

7 Calibration procedure (1) 1. Do one-port calibrations at each port 2. Measure raw S-parameters of thru standard 3. Compute q 4. Determine correct sign of q from phase response of thru standard

8 Calibration procedure (2) oneport calibration at port 1 1 Γ S,1M S,1 Γ S,1 1 Γ O,1 M O,1 Γ O,1 1 Γ L,1 M L,1 Γ L,1 e 00 e = e 00 e 11 e 01 e 10 = M S,1 M O,1 M L,1 e 01 e 10 = e 00 e 11 1 e 01 = e 10 = p e 00 e 11 1

9 Calibration procedure (3) oneport calibration at port 2 1 Γ S,2M S,2 Γ S,2 1 Γ O,2 M O,2 Γ O,2 1 Γ L,2 M L,2 Γ L,2 e 33 e = e 22 e 33 e 23 e 32 = M S,2 M O,2 M L,2 e 23 e 32 = e 22 e 33 2 e 23 = e 32 = p e 22 e 33 2

10 Calibration procedure (4) compute initial calset q = Measure raw S-parameters of thru standard r S12,raw S 21,raw

11 Calibration procedure (5) generate smooth phase Choose sign of q to obtain smooth phase

12 Calibration procedure (6) Group delay model Fit model to group delay τ(f) =τ c + τ g f p f2 f 2 c 1. 1 f 1 f 2 1 f 2 c. f N f 2 N f 2 c τ c = τ g τ f1. τ fn

13 Calibration procedure (7) Determine correct solution from phase model ϕ(f) = 2πτcf 2πτg q f 2 f 2 c

14 Unknown thru for the 8510 Internal ten term model, does not measure raw S- parameters Need to compute q externally Need to convert seven term model to ten term model

15 Extracting one port error-terms from 8510 calsets e 00 = E DF e 11 = E SF e 01 = e 10 = p E RF e 22 = E SR e 33 = E DR e 23 = e 32 = p E RR

16 Relation between seven term and ten term model R. B. Marks, Formulations of the basic vector network analyzer error model including switch terms, in 50th ARFTG CONFERENCE DIGEST, vol. 50, IEEE, 1997.

17 Conversion from seven term to ten term model Γ F = a 2 b 2 = a 2 a 1 1 S 21,ratio Γ R = a 1 b 1 = a 1 a 2 1 S 12,ratio E DF = e 00 E SF = e 11 E RF = e 01 e 10 E XF = 0 E TF = qe 10e 32 E LF = e 22 + e 23e 32 Γ F 1 e 33 Γ F 1 e 33 Γ F E DR = e 33 E SR = e 22 E RR = e 23 e 32 E XR = 0 E TR = e 01 e 23 q(1 e 00 Γ R ) E LR = e 11 + e 01e 10 Γ R 1 e 00 Γ R

18 Algorithm for 8510C 1. Do firmware one-port calibrations 2. Extract error coefficients 3. Measure thru standard, S 11, S 12, S 21, S 22 a 2 /a 1 and a 1 /a 2 4. Compute raw S-parameters and Γ F and Γ R. 5. Compute q=sqrt(s 12 /S 21 ) 6. Create new 8510 calset. Download calset and activate 7. Read corrected S-parameters for thru standard 8. Create continuos phase for S 21. By changing sign on q when necessary. 9. Create calset1 using the sign changed q s 10. Create calset2 by using q. 11. Download calset1 and calset2 to Determine correct calset

19 Choice of solution easy for coax case

20 To be presented at the 67 th ARFTG conference J. Stenarson, K. Yhland, Automatic root selection for the unknown thru algorithm, in 67th ARFTG CONFERENCE DIGEST, IEEE, 2006.

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