Multi Port Measurements Slides from Dave Blackham and Ken Wong At Agilent Technologies With some additions by Doug Rytting Dave Blackham & Ken Wong 1 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 Approach How Many Connections Are Needed Examples 2 Network Analyzer Block Diagram RF Source a0 IF IF a3 LO Source IF IF b0 b3 Port - 1 Cable a1 b2 DUT b1 Port - 2 Cable a2 3 8-Term Error Model a0 b0 a0 b0 X Error Adapter a1 b1 Perfect Reflectometer Imperfect Switch DUT Y Error Adapter a3 b3 a3 b3 a2 b2 8 Error Terms To remove the effects of an imperfect switch, use the procedure described later. 4 8-Term Error Model a0 a0 a1 e10 e00 e11 X Error Adapter e01 b0 b0 DUT b1 b1 S12 a3 a3 b3 S21 S22 a2 a2 e23 e33 a1 S11 b2 e22 Y Error Adapter e32 b3 b2 One of the 8 error terms can be normalized to yield 7 error terms 5 8-Term Error Model b0 b 3 a 0 a 3 T1 T 3 a1 T2 a2 T4 b1 b2 T1 X 0 0 kY e T2 00 0 e T3 11 0 0 ke22 1 0 T4 0 k k 0 ke33 e10 , X e00 e11 e10 e01 , Y e22 e33 e32 e23 e23 6 8-Term Error Model Measured S-Parameters SM = (T1S + T 2)(T3S + T4)-1 Actual S-Parameters S = (T 1 - SMT3)-1(SMT4 - T2) Linear-in-T Form T1S + T 2 - SMT3S - SMT4 = 0 Expanding Yields: e00 + S11S11Me11 - S11X +0 + S21S12M(ke 22) +0 +0 = S11M 0 + S12S11Me11 - S12X +0 + S22S12M(ke 22) +0 - S12Mk =0 0 + S11S21Me11 +0 +0 + S21S22M(ke 22) - S21(kY) +0 = S21M 0 + S12S21Me11 +0 + (ke 33) + S22S22M(ke 22) - S22(kY) - S22Mk =0 7 8-Term Calibration Examples Seven or more independent known conditions must be measured A known impedance (Z 0) and a port-1 to port-2 connection are required TRL & LRL Thru (T) or Line (L) with known S-parameters [4 conditions] Unknown equal Reflect (R) on port-1 and port-2 [1 condition] Line (L) with known S11 and S 22 [2 conditions] TRM & LRM Thru (T) or Line (L) with known S-parameters [4 conditions] Unknown equal Reflect (R) on port-1 and port-2 [1 condition] Known Match (M) on port-1 and port-2 [2 conditions] TXYZ & LXYZ Thru (T) or Line (L) with known S-parameters [4 conditions] 3 known Reflects (XYZ) on port-1 or port-2 [3 conditions] Traditional TOSL (Overdetermined) Thru (T) with known S-parameters [4 conditions] 3 known Reflects (OSL) on port-1 [3 conditions] LRRM Line (L) with known S-parameters [4 conditions] 2 unknown equal Reflects (RR) on port-1 and port-2 [2 conditions] 3 known Reflect (OSL) on port-2 [3 condition] Known match (M) on port-1 [1 condition] UXYZ Unknown Line (U) with S12 = S21 [1 condition] 3 known Reflects (XYZ) on port-1 [3 conditions] 3 known Reflects (XYZ) on port-2 [3 conditions] 8 Measuring S-parameters Removing Port Match Changes Caused by Switch a0 b0 a0 a1 b0 Forward Error Adapter Perfect Reflectometer Reverse b1 a3 DUT [S] a2 b3 a3 b2 b3 Forward b0 = S11Ma0 + S12Ma3 b3 = S21Ma0 + S22Ma3 Reverse b' 0 = S11Ma'0 + S12Ma'3 b' 3 = S21Ma'0 + S22Ma'3 9 Measuring S-parameters By defining 1 S11M S 21M a a0 and 2 3 b3 b0 b0 b'0 b 3 2 a0 a'3 a0 d S12M b3 b'3 b3 2 a0 a'3 a0 d S 22M d 1 b'0 b0 b'0 1 a'3 a0 a'3 d b'3 b3 b'0 1 a'3 a0 a'3 d b3 b'0 12 a0 a'3 10 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 Approach How Many Connections Are Needed Examples 11 Multiport error correction Is multiport error correction hard? Dave Blackham & Ken Wong 12 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 13 Multiport error box diagram bmi ei00 ami ei01bi a1 am1 E1 Ideal VNA bm1 b1 am 2 a2 ai ei10 ami ei11bi E2 bm 2 b2 amn an DUT En bmn bn Dave Blackham & Ken Wong 14 Multiport error box diagram bmi ei00 ami ei01bi a1 am1 E1 Ideal VNA bm1 b1 am 2 a2 ai ei10 ami ei11bi bmi ei00 a 10 i ei E2 bm 2 b2 amn an ei01 ami 11 ei bi DUT En bmn bn Dave Blackham & Ken Wong 15 Multiport error box diagram a1 am1 bmi ei00 ami ei01bi E1 b1 bm1 bmi ei00 a 10 i ei a2 am 2 Ideal VNA ai ei10 ami ei11bi E2 bm 2 b2 amn an DUT ei00 Ei 10 ei ei01 ami 11 ei bi ei01 11 ei En bmn bn Dave Blackham & Ken Wong 16 Multiport error box diagram bmi ei00 ami ei01bi a1 am1 E1 Ideal VNA bm1 b1 am 2 a2 ai ei10 ami ei11bi bmi ei00 a 10 i ei E2 b2 bm 2 DUT bi e e bmi ai 00 ei b ami 1 ei11 i ai En bmn ei01 11 ei 10 01 i i an amn ei00 Ei 10 ei ei01 ami 11 ei bi bn Dave Blackham & Ken Wong 17 Multiport error box diagram bmi ei00 ami ei01bi ai ei10 ami ei11bi a1 am1 E1 Ideal VNA bm1 b1 am 2 a2 E2 bm 2 b2 amn an DUT En bmn bn Dave Blackham & Ken Wong a1 b1 a ai ; b bi ; an bn am1 bm1 a m ami ; b m bmi ; amn bmn b m 00 01 a m a 10 11 b 18 Multiport error box diagram a1 am1 b m 00 a 10 E1 Ideal VNA bm1 b1 am 2 a2 01 a m 11 b S m b m a m 1 S a b a 1 E2 1 bm 2 b2 amn an DUT S m 00 01 S a I 11 S a 10 1 1 Sˆ n 01 S m 00 10 ˆS S I 11 S 1 n a a S a Sˆ n I 11 Sˆ n 1 En bmn bn Dave Blackham & Ken Wong 19 Multiport error box diagram For the non-leaky model 00 , 10 , 01 , and 00 are a1 am1 each diagonal matricies E1 Ideal VNA bm1 b1 am 2 a2 E2 b2 bm 2 DUT S11 e100 10 01 e1 e1 S 21 01 Sˆ n e10 2 e1 S n1 e10 e01 n 1 an amn En bmn e1ik 0 0 ik 0 e ik 2 0 0 enik 0 1 1 Sˆ n 01 S m 00 10 bn Dave Blackham & Ken Wong S12 e110 e201 S 22 e200 01 e10 2 e2 S1n e110 en01 00 S nn en 01 e10 n en 20 Multiport error box diagram with “12 term” crosstalk am1 For the multiport equivalent to two-port a1 12 term model 00 fills out to include E1 Ideal VNA additional isolation terms bm1 b1 am 2 a2 E2 bm 2 b2 amn DUT S11 e100 10 01 e1 e1 S e00 21 2:1 ˆS e10 e01 n 2 1 S n1 en00:1 e10 e01 n 1 an En bmn 00 e100 e1:2 e1:00n 00 00 e e 00 2:1 2 00 en00 en:1 1 1 Sˆ n 01 S m 00 10 bn Dave Blackham & Ken Wong 00 S12 e1:2 e110 e201 S 22 e200 01 e10 2 e2 S1n e1:00n e110 en01 S nn en00 01 e10 n en 21 Multiport error box diagram with full leaky model am1 1 bm1 b1 am 2 a2 include additional crosstalk terms n+2 E bm 2 00 , 10 , 01 , and 11 all fill out to n+1 2 Ideal VNA For the multiport full leaky model a1 b2 DUT ij e1ij e1:2 ij e2:1 e2ij ij ij en:1 e1:ijn enij S m 00 01 I S a 11 S a 10 1 1 1 01 S m S a 11 01 Sm amn n bmn 1 1 S a 11 01 00 10 01 00 0 an K Sm Sa L Sm Sa H M 0 2n S a K S m M L S m H 1 bn Dave Blackham & Ken Wong 22 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 Approach How Many Connections Are Needed Examples 23 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 24 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 25 Ideal S-Parameters Ideal s-parameters Non-source ports terminated in perfect match—incident signal only from source port aˆii aii ii bˆii S11 S 21 Sn1 aki N port DUT bii ki aji ji bˆji bki bˆki bji ani ni bni bˆni Dave Blackham & Ken Wong S12 S22 Sn 2 S1n bˆ11 bˆ12 S2 n bˆ21 bˆ22 Snn bˆ bˆ n1 n 2 bˆ11 bˆ12 aˆ11 aˆ22 bˆ ˆ 21 b22 aˆ11 aˆ22 bˆ bˆn 2 n1 aˆ11 aˆ22 bˆ1n bˆ2 n bˆnn aˆ11 0 0 0 0 aˆnn 0 aˆ22 0 bˆ1n aˆnn bˆ2 n aˆnn ˆ bnn aˆnn 26 1 Use Generalized S-Parameters Ideal s-parameters aˆii Non-source ports terminated in perfect match—incident signal only from source port aii ii bˆii S11 S 21 S n1 aki N port DUT bii ki aji ji bˆji bki bˆki S12 S 22 Sn 2 bˆ11 aˆ11 S1n bˆ S 2 n 21 aˆ 11 S nn bˆ n1 aˆ11 bˆ1n aˆnn bˆ2 n aˆnn ˆ bnn aˆnn bˆ12 aˆ22 bˆ22 aˆ22 bˆn 2 aˆ22 Generalized s-parameters bji ani ni Uses incident signals from all ports & removes port match error bni bˆni S11 S 21 S n1 S12 S 22 Sn 2 Dave Blackham & Ken Wong S1n b11 b12 S 2 n b21 b22 S nn bn1 bn 2 b1n b2 n bnn a11 a 21 an1 a1n a2 n ann a12 a22 an 2 27 1 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 Approach How Many Connections Are Needed Examples 28 Single Reference Receiver RF LO Recr R Rcvr A Port-A Port-B Rcvr D Rcvr C Rcvr B Port-C Dave Blackham & Ken Wong Port-D 29 S-parameter measurement (two-port, ideal) b1f S11 S12 a1f f S S b 22 0 2 21 b1f b2f S11 f ; S 21 f a1 a1 Forward s-parameters Source at port 1 b1r S11 S12 0 r a r S S b 2 21 22 2 b1r b2r S12 r ; S 22 r a2 a2 Reverse s-parameters Source at port 2 Dave Blackham & Ken Wong 30 S-parameter measurement (two-port, ideal) b1r S11 S12 0 r a r S S b 2 21 22 2 b1r b2r S12 r ; S 22 r a2 a2 b1f S11 S12 a1f f S S b 22 0 2 21 b1f b2f S11 f ; S 21 f a1 a1 b1f f b2 S11 S 21 b1r S11 r b2 S 21 S12 b1f f S 22 b2 S12 a1f S 22 0 b b r 1 r 2 a1f 0 Dave Blackham & Ken Wong 0 a2r 0 r a2 1 31 S-parameter measurement (two-port, non-ideal) Generalized s-parameters S11 S 21 S12 b S 22 b f 1 f 2 b b r 1 r 2 a a f 1 f 2 a a r 1 r 2 1 • 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 32 S-parameter measurement (two-port, non-ideal) Generalized s-parameters S11 S 21 S12 b S 22 b f 1 f 2 b b r 1 r 2 a a f 1 f 2 a a r 1 r 2 1 • 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 33 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: S11 S 21 b S12 a f S 22 b2 f a1 f 1 f 1 b 1 a b2r a2f r f a2 a1 r 1 r 2 Dave Blackham & Ken Wong a a 1 r 1 r 2 1 34 S-parameter measurement (two-port, non-ideal) Need to replace a2f and a1r terms. 1 a2f f a1 1 a2f f a1 1 1 a 1 a f f b2 a2 1 f f a1 b2 r 1 r 2 a b b a 1 a S11 S12 a a b f f f S 21 b2 Sa222 b2 1 f f 1f a1 b2 a1 r 1 r 2 1 b a 1 a b f b2 1 f f a1 r 1 r 2 r f 1 1 r f 21 r 1 r 1 r 1 r 1 1r b1 a a r 11 a 2 b2r ba2f2f r f f f 1 a2 aa11 Dave Blackham & Ken Wong r 1 r 2 b r a 1 r 1 r 2 1 r 1 r 2 b a r 1 1 1 35 Calculate F and R For Single Reference Receiver Error terms were measured during the first tier calibration using SOLT. With F and R 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. a1 ERR/ b2 EDR ELF F ETF F ESR ELF ESR ERR EDR ( ELF ESR ) a2f b2f F R ERF ELR ESF EDF ( ELR ESF ) and a1r b1r R Dave Blackham & Ken Wong 36 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 Approach How Many Connections Are Needed Examples 37 Multiport Using a 2-port VNA Example RF Rcvr A Rcvr B Recr R Recr R LO Switches Terminated in off state Dave Blackham & Ken Wong 38 Multiport Using a 2-port VNA Let: Smi:j = measured S-parameters between ports i and j. Rmi:j = Port impedance normalized Scattering Matrix i:j = Diagonal matrix of reflection coefficient of imperfect port terminations at ports i and j. [i..N values must not change when signal paths are changed.] i ij i S S i:j 11 12 Sm ji ; i:j j S21 S22 0 0 ; i 1 j Rmi:j *i:j Smi:j I i:jSm i:j 1 Dave Blackham & Ken Wong R i:i j:i R N, ji R i:j R j:j 39 Multiport Using a 2-port VNA Let: Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix R1:1 R2:1 R1:2 R2:2 •Fill Rn matrix with calculated Rm sub-matrices i=1, j=2 Dave Blackham & Ken Wong 40 Multiport Using a 2-port VNA Let: Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix R1:1 R2:1 R1:2 R2:2 R3:2 R2:3 R3:3 •Fill Rn matrix with calculated Rm sub-matrices i=2, j=3 Dave Blackham & Ken Wong 41 Multiport Using a 2-port VNA Let: Rn = Composite port impedance normalized N-port Scattering Matrix [Rn] matrix R1:1 R2:1 R3:1 R1:2 R2:2 R3:2 R1:3 R2:3 R3:3 •Fill Rn matrix with calculated Rm sub-matrices i=1, 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 R1:1 R2:1 R3:1 Ri:1 Rj:1 RN:1 R1:2 R2:2 R3:2 R1:3 R2:3 R3:3 Ri:i Rj:i Ri:j Rj:j R1:N R2:N R3:N Ri:N Rj:N RN:N •Fill Rn matrix with calculated Rm sub-matrices Do N(N-1)/2 2-port measurements to fill Dave Blackham & Ken Wong 43 Multiport Using a 2-port VNA Let: Rn = Composite port impedance normalized N-port Scattering Matrix n = 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 1 0 0 0 0 0 1 2 Sn I Rn n Rn n * ; n 0 0 N Dave Blackham & Ken Wong 44 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 Approach How Many Connections Are Needed Examples 45 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 Cn:r Cn:2 n n! r r ! n r ! n n n 1 2 2 n 2 3 4 6 Cn:2 1 3 6 15 28 66 Dave Blackham & Ken Wong 8 12 46 Multiport calibration error terms Path terms Port terms n * n 1 sets of path terms n sets of terms Directivity ei00 Reflection tracking e e 10 01 i i Source match ei11S ek01 Transmission tracking ei10 e01 j Crosstalk e 00 ij Load match ei11L e e10 k e01 j ei10 ei11 ei00 ei01 Dave Blackham & Ken Wong ek00 11 k e00 j e11j e10j 47 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 48 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 49 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). transmission tracking transmission tracking port j to port i port i to port k e 10 01 j i e e e 10 01 i k 10 01 i i e e e10j ei10ei01 ek01 reflection tracking port i Dave Blackham & Ken Wong e 10 01 i i e e 10 01 j k e transmission tracking port j to port k 50 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 Approach How Many Connections Are Needed Examples 51 Multiport Mechanical Cal Port 1 Mechanical Cal Method Port 2 Precision Mechanical 2-port Cal (SOLT or TRL) Port 3 Port 1 Port 4 AND Port 2 Finish 4-port Cal Using Unknown Thru. Only Transmission tracking needs to be determined. Port 3 Port 4 Unknown Thrus (adapters) Dave Blackham & Ken Wong 52 ECal 1 Multiport ECal Cal Port 1 ECal 2 ECal Method Port 3 Port 1 AND Port 2 Port 4 Port 2 Finish 4-port Cal Using Unknown Thru. Only Transmission tracking needs to be determined. Port 3 Port 4 Unknown Thrus (adapters) Dave Blackham & Ken Wong 53 Multiport Unknown Thru Cal Port 1 Can have different connector on Each Port Port 2 1-Port Calibrations, ECal or Mech Port 3 Port N Port 1 Port 2 Finish 4-port Cal Using Unknown Thru. Only Transmission tracking needs to be determined. Port 3 Port N Unknown Thrus (Adapters) Dave Blackham & Ken Wong 54 Multiport On-Wafer Cals Port 1 Straight Thrus Port 2 TRL on Wafer Cal Port 3 Port 4 AND Port 1 Port 2 Finish 4-port Cal Using Unknown Thru. Only Transmission tracking needs to be determined. Port 3 Port 4 Imperfect Unknown Thrus Dave Blackham & Ken Wong 55 Advantages of Unknown Thru Calibration in Multiport Systems Unknown Thru is very convenient for right-angle or notin-line thru calibrations. S-parameters of the thru standard need not to be characterized. Eliminates the need to move test ports and cables or probes. Passive DUTs may be used as the unknown thru. Noninsertable cal (mix connectors, transitions, F-F or MM combinations) is just as easy as an insertable cal Dave Blackham & Ken Wong 56
© Copyright 2026 Paperzz