Precise Microwave Vector Measurements

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1 Precise Microwave Vector Measurements Karel Hoffmann Czech Technical University in Prague Faculty of Electrical Engineering Department of Electromagnetic Field Technická 2, 162 Prague 6, Czech Republic Tel.: (+42) Fax: (+42)

2 Content - Introduction - Vector measurements of single-ended devices - Vector measurements of multiport devices - Vector measurements of differential devices - Conclusion Acknowledgement This work has been supported by research program No. MSM "Research of Methods and Systems for Measurement of Physical Quantities and Measured Data Processing " of the CTU in Prague sponsored by the Ministry of Education, Youth and Sports of the Czech Republic.

3 Single-ended s-parameters a = V + /sqrt(zo) b = V - /sqrt(zo) V = V + + V - I = I + + I - a i = (1/2) (V i + Z oi I i )/sqrt(z oi ) b i = (1/2) (V i - Z oi I i )/sqrt(z oi ) b 1 = S 11d a 1 + S 12d a 2 b 2 = S 21d a 1 + S 22d a 2 Measurement of s-parameters Perfect match on all is ports necessary!

4 Single-ended cascading t-parameters The relationship between the S and T parameters T-parameters are useful in the analysis of cascade connections of two-port network.

5 Gamma-R parameters Designed by Rautio in They make possible correct measurement of S-parameters of n-ports with unmatched ports. Normalized voltage waves of S-parameters and R-parameters S-parameters create a linear transformation ( b ) = ( S) *( a) where a = for Z = Z, it is Γ = and α for i i i i R-parameters form a different linear tranformation Γ i ( β ) = ( R) *( α ) where the demand is: α = for Z it is i i Z Γ i Definition where diagonal complex matrices ( α ) = ( A )*( a) + ( B) *( b) ( β ) = ( C )*( a) + ( D) *( b) A1 A = A n ( ) ; ( B) = B1 B n ; ( C) = C1 C n ; ( D) = D 1 D n are determined by 4 conditions α = for i A i 2 Γ i ( A B )* = 1+ Γ i, i i B i Ci, Bi * = Di Ci 2 ( C ) D * = 1+ Γ ( ) A i, i i D i i

6 It yields where ( α ) = ( a ) ( Γ) *( b) ; ( β ) = ( Γ )*( a ) + ( b) ( Γ) = Γ1 Γ n is the diagonal matrix of nonzero reflection coefficients of impedances connected on individual ports of the n-port. Tranformation between S an R parameters ( R) = ( [ Γ ) ( S )]* ( ( ) ( 1) + ( R) * ( Γ) [ 1) ( Γ) * ( )] 1 + S 1 [ ] [( ) ( Γ )] S = * R S-parameters of balanced (differential) devices Balanced circuit topologies have been used in traditional low frequency analog circuits for years because of their many desirable properties. Compared to single-ended devices they have: improved power supply noise imunity lower susceptibilty to EMI (crosstalk imunity) improved even-order distorsion characteristic (greater dynamic range) What is a Balanced Circuit? Single ended circuit Balanced circuit - Signal paths referenced to a common ground potential - Constructed with a pair of signal paths where each side of the pair is a mirror image of the other.

7 Two modes on both ports of a balanced two-port are possible. Common mode (CM) - both nodes of a port are stimulated in phase, signal is referenced to a common ground potential Differential mode (DM) - both nodes of a port are stimulated 18 deg out of phase There are four possible Stimulus/Respons Combinations for a device with two balanced ports, DD, CC, DC, CD. Standard s-parameters were developed for single-ended devices, they cannot characterise balanced structures. Mixed-Mode Scattering Parameters Introduced by D. E. Bockleman and W. R. Eisenstadt (1995) In general, a differential circuit responds to both a differential-mode and a common-mode stimulus. Therefore, a complete characterisation of a differential circuits includes the differential-mode, commonmode, and any mode conversion responses.

8 The DD Quadrant (Differential-Mode Terms) The DD quadrant describes the behaviour of the circuit with a differential stimulus and differential respons. In this mode 2x2 DD matrix gives the differential-mode input and output reflection coefficients, and the forward and reverse transmission characteristic. The CC Quadrant (Common-Mode Terms) The CC quadrant describes the behaviour of the circuit with a common-mode stimulus and common-mode response. In this mode, the 2x2 CC matrix gives the common-mode input and output reflection coefficients, and the forward and reverse transmission coefficients. The CD Quadrant (Mode Conversion Terms) The CD quadrant describes the behaviour of the circuit with a differential stimulus and common-mode response. In this mode, the 2x2 CD matrix gives the input and output reflection coefficients, and the forward and reverse transmission coefficients. In an ideal balanced device, these terms are equal to zero, that is, there is no mode conversion. In practice, there will be some amount of mode conversion. The more mode conversion from differential-mode to common-mode that exists, the more likely there will be radiation from the system. The DC Quadrant (Mode Conversion Terms) The DC quadrant describes the behaviour of the circuit with a common-mode stimulus and differentialmode response. In this mode, the 2x2 DC matrix gives the input and output reflection coefficients, and the forward and reverse transmission coefficients. In an ideal balanced device, these terms are equal to zero, that is, there is no mode conversion. In practice, there will be some amount of mode conversion. The more mode conversion from common-mode to differential-mode that exists, the more susceptible the system will be to common-mode noise. Like for the standard s-parameters, it is valid for the of mixed-mode s-parameters characterisation of a two port: a dmi = (v dmi + i dmi Z dmi )/2.SQRT(Z dmi ) b dmi = (v dmi + i dmi Z dmi )/2.SQRT(Z dmi ) a cmi = (v cmi + i cm i Z cmi )/2.SQRT(Z cmi ) b cmi = (v cmi + i cmi Z cmi )/2.SQRT(Z cmi ) where i=1 and 2 for the port 1 and 2.

Basic principles of vector netvork analyzers - Systems with frequency conversion - Systems with six-ports Systems with frequency conversion In principle vector information is obtained as complex

9 Basic principles of vector netvork analyzers - Systems with frequency conversion - Systems with six-ports Systems with frequency conversion In principle vector information is obtained as complex ratio of two microwave signals in the Test Chanel and the Reference Chanel. Microwave signals with information about amplitude and phase are down converted typicaly to 1 khz and the amplitude and phase determination is provided on this low frequency. High precission, high dynamics, high price. HP 841 Vector Networ Analyzer.1-18 GHz (197)

10 Agilent E8364A Vector Network Analyzer 45 MHz - 5 GHz (23) Test fixture for transistor measurements with adapters and bias T

11 Agilent E8364A System Simplified Block Diagram Measurement errors - random noise, mounting of conectors - drift temperature and humidity influence -systematic reproduceble, can be eliminated by a proper procedure

12 Sources of systematic errors - Directivity errors - Source match errors - Gain tracking errors - Output match errors - Adapter errors - Cross-talk errors - Calibration elements errors Directional couplers - coaxial and microstrip

13 On the output of directional coupler b1 will occur a parasitic signal which was not reflected by the DUT. On the output of directional coupler b1 will occur a parasitic signal which was reflected two times from the DUT and once from the generator. Gain tracking errors Different frequency dependences of the Test Chanel and the Reference chanel. Output match errors Non perfect matching at the output of the measured DUT. Adapter errors Parasitic reflections and transmission losses of adapters. Cross-talk errors Parasitic signal on the VNA receiver which has no relationship with the transmission of the DUT. Calibration elements errors Differences between supposed and actual parameters of calibration elements

14 Basic principle of correction methods A real VNA can be understood as a cascade of an ideal VNA with no systematic repeatable errors and a linear 4-port representing all these errors. Calibration Calibration standards with known s-parameters (S c ) are connected at the reference plane 2-3. The corresponding s-parameters are measured in reference plane 1-4 as (S m ). With (S c ) and (S m ) known the error model s-parameters (S) are calculated. Verification Some two-port not used in calibration with known actual s-parameters (S ka ) is measured and its measured s-parameters (S km ) determined at the reference plane 1-4 are transformed thru the known error 4-port to the reference plane of measurement 2-3 giving (S kt ). These (S kt ) should be very close to actual (S ka ) for a correct calibration. Correction DUT is measured and its measured s-parameters (S dm ) determined at the reference plane 1-4 are transformed thru the known error 4-port to the reference plane of measurement 2-3. Actual (S da ) s- parameters of the DUT are derived by this process.

15 General error model with cross-talk direct paths and leakage (crosstalk) paths consists of 16 unknown s-parameters. System of 16 linear equations must be solved. 4 full known calibration standards are necessary. Simplified error model with cross-talk 1-terms error model Cross-talk characterized only by S41 and S14. Necessary full known calibration standards: Open, Short, Match, Line or Thru.

16 Non cross-talk error model a) Methods with full knowledge of calibration elements 8 unknowns in the error model Different calibration method can be used to determine the unknowns S 11, S 22, S 21* S 12, S 33, S 44, S 34* S 43. OSM (Open, Short, Match ) SSM (Short, offset Short, Match) SOS (Short, Open, offset Short) OSO (Open, Short, ofset Open) SSS (Short, ofset Short, more offset Short) Further calibration element like Thru or Line and transmission measurement must be used to determine the rest of unknowns S 21.S 43 and S 12.S 34, 4 full known calibration standards enable the system of linear equations to be solved

17 b) Methods using redundancies in calibration There are 8 unknowns in the error model. Even only 3 full-known calibration standards make possible to set a system of 12 linear equations if scattering transfer parameters are used. Measured t-parameters (M) ca be expressed: where (X) are unknown t-parameters of DUT. (M) = (A). (X). (B) For 3 calibration standards 3 matrix equations can be formed. (M1) = (A). (C1). (B) (M2) = (A). (C2). (B) (M3) = (A). (C3). (B) The system of matrix equations forms 12 linear equatins for unknowns of the error model. Only 7 equations are independent. The solution for (A) is therefore in the form and corrected t-paramaters of DUT can be detrmined (X) = (1/a).(A') -1. (M). (M1) -1. a.(a'). (C1)

18 Theoretical minimum demands on calibration elements 1. 4 parameters full known (thru) 2. only 2 parameters full known ( 2 matched loads, attenuator, thru line) 3. only 1 parameter full known ( full known short at one port, symetrical two-port with high reflection) The most used - TRL and TSD TRL (Thru, Reflect, Line) 1. Thru. 2. Well matched line with unknown transmission. 3. Two identical one-port with high reflection (symetrical two-port). The phase is aproximately known. TSD (Thru, Short, Delay) 1. The same as in TRL. 2. The same as in TRL. 3. One full known short. TAN (Thru, Attenuation, unknown Network) 1. Thru. 2. Well matched attenuator with unknown transmission. 3. Symetrical reflecting two-port with non-zero unknown transmission. The phase is approximately known. TLN (Thru, Line, unknown Network) 1. Thru. 2. Well matched line with unknown transmission. 3. The same as in TAN. TRM ( Thru, Reflect, Match) 1. Thru well matched one-ports identically reflectin one-ports with unknown reflection. The phase is approximately known.

TRA ( Thru, Reflect, Attenuation) 1. Thru. 2.

The same as in TRM. LRL ( Line, Reflect, Line) 1.

Well matched line with different length. 3.

The same as in LRL. 2. The same as in TRM. 3.

19 TRA ( Thru, Reflect, Attenuation) 1. Thru. 2. Well matched attenuator with unknown transmission. 3. The same as in TRM. LRL ( Line, Reflect, Line) 1. Well matched line. 2. Well matched line with different length. 3. The same as in TRM. LRM ( Line, Reflect, Match) 1. The same as in LRL. 2. The same as in TRM. 3. The same as in TRM. Further combinations are possible. Calibration elements APC7 Open APC7 Short APC7 Match APC7 Match and APC7 Sliding Load

20 Microstrip Open Microstrip Short Microstrip Match Verification Microstrip Open in the test fixture Verification microstrip line

21 Open GHz Mag 1.1 Ang Deg Swp Max 18GHz Short GHz Mag.9915 Ang Deg Swp Max 18GHz Swp Min.45GHz Swp Min.45GHz Microstrip Open verification Microstrip Short verification Match Swp Max 18GHz GHz Mag.165 Ang 18.3 Deg Verification line Swp Max 18GHz GHz Mag 1.36 Ang Deg Swp Min.45GHz Swp Min.45GHz Microstrip Match verification Microstrip line verification Verification with calibration elements demonstrates only good reproducibility of mounting and measurement. Verification with a piece of microstrip line not used for calibration demonstrates some significant error in calibration element description.

22 Correction Measured data - transistor SPF276 5V, 5 ma Corrected data - transistor SPF276 5V, 5 ma

23 Vector measurement of N-ports a) N-port VNA complicated hardware, high price b) measurement with 2-port VNA and Multiport Test Set Agilent 8714ES Two-port VNA and HP 875E Multiport Test Set Measurement connectors

24 Measurement errors N-port measurement with 2-port VNA n.( n 1) / 2 measurements of 2-ports Correct only for Z i =Z it is Γ i =a i /b i = Example: 3-port measurement with 2-port corrected VNA a3 non perfect match at port 3 Γ = b 3 3 S11 M b = a 1 1 = S 11 S13. S + 1 S Γ. Γ 3 3 S21 M b = a 2 1 = S 21 S23. S + 1 S Γ. Γ 3 3

1 Out ; 2 Tv ; 3 In Typical values: In Tv 8dB S = 8dB,398 In Out Return loss on Out 23 3dB S13 = S31 S 1dB 33 8 db TV wall outlet = 3dB,78,316 Standard demand on isolation Tv Out 28dB S 21 28dB,398 Γ

25 1 Out ; 2 Tv ; 3 In Typical values: In Tv 8dB S = 8dB,398 In Out Return loss on Out 23 3dB S13 = S31 S 1dB 33 8 db TV wall outlet = 3dB,78,316 Standard demand on isolation Tv Out 28dB S 21 28dB,398 Γ 3 S23. S31. Γ3 max 1 S33. Γ3 1dB,316, 99 3 times greater error compared to measured value 18dB,126, 37-18dB corresponds to HP 875E Multiport Test Set It results in: Isolation value Tv Out,398 determined with uncertainity ±,397 it is from -51dB to -22.3dB!

26 Correction method Idea: N-port is measured corrected 2-port VNA. It means that N-port is perfectly matched on two ports where the VNA is connected. Other N-2 ports are terminated imperfectly with Γ i which results in measurements errors. Standard S-parameters require Γ i = as references. New n-port parameters, Gamma-R parameters, with Γi as references can be introduced. Every port has its own termination Γi and these terminations must not be interchanged. N-port Gamma-R parameters can be measured step by step by standard 2-port VNA. When VNA is connected to two ports of the n-port, N-2 ports of the n-port are properly terminated with corresponding Γ i. Two ports connected to VNA are imperfectly matched with respect to Gamma-R definition. Measured 2-port S-parameters must be therefore transformed on 2-port Gamma-R parameters with respect to Γ i corresponding to the two ports just connected to VNA. It means 2-port transformation of ( S ) ( R). The procedure is then repeated for all n.(n-1)/2 pairs of ports of the n-port. (n*n) Gamma-R matrix can be then created from individual (2*2) Gamma-R matrices. Correct S-parameters of the n-port can be consequently determined by the backward tranformation of matrice R S. s ( ) ( ) Correction needs a) n.(n-1)/2 two port vector measurements b) n.(n-1)/2 transformations of (2*2) matrices ( S) ( R) R R ii ji R R ij jj Γi = Γ j S + S ii ji S S ij jj 1 * Γi 1 S * Γ j S ii ji S S ij jj 1 c) creation of (n*n) (R) matrice d) transformation of (n*n) matrice ( R) ( S) S S 11 n1 S S 1n nn = R + 1 R Γ1 * Γ n R * R R1 n 11 R1 n 1 n1 R nn n1 R nn Γ Γ n

27 Measurement of Mixed-Mode S-parameters Common 2-port VNA are single-ended instruments and cannot be used directly for mixed-mode s- parameters measurement. Hardware approach The traditional approach to characterize balanced devices is to convert each balanced pair to a singleended port using a balun, assuming that the balun is nearly ideal. In practice the accuracy is limited by the balun loss, amplitude unbalance, limited isolation. The relative narrow bandwidth of the balun limits frequency wideband measurements. Baluns do not allow for measurement of mode-conversion behaviour. Measurement with 4-port vector network analyzer (FPVNA) If one is to make a general purpose RF measurement port, the values of characteristic port impedances must be chosen. For symetrical case common-mode and differential-mode characteristic impedances become the even and odd impedances of a standard coupled line. It is useful to require the even and odd-mode characteristic impedances of the measurement system to be equal (and 5 ohms). It results in the coupled line with zero coupling, it means two standard non coupled lines (5 ohms coaxial line). Therefore a standard 4-port VNA can be used for the measurement. It can be derived. adm a1 adm a2 = * * a cm a acm2 1 1 a4 It is a = M * ( ) ( ) ( ) mm a std where ( M ) = 1 1 *

28 Similarly, for the responce waves b, it is found (b mm ) = (M)*(b std ) Which yields (S mm ) = (M) * (S std ) * (M) -1 This equation illustrates the possibility to calculate the mixed-mode s-parameters from the standard singleended s-parameters. Advantage: Standard FPVNA can be used for mixed-mode s-parameter measurments Disadvantage: Uncertanities of mode-conversion s-parameters may be too high (magnitude uncertanities are in the order of 1-2 for HP 851 VNA) It cannot be used for measurement of balanced circuits with low mode conversion properties.

29 Measurement with pure-mode vector network analyzer (PMVNA) The system was designed by D. E. Bockleman and W. R. Eisenstadt in 1997.

31 Measurement procedure

32 Advantage: Uncertanities of mode-conversion s-parameters are low (magnitude uncertanities are in the order of 1-4 for HP 851 VNA) Disadvantage: More complicated system Comparison of PMVNA and FPVNA: PMVNA has about equal magnitude error as FPVNA when pure mode S dd and S cc s-parameters of a differential device are measured. PMVNA can have substantially lower error compared to FPVNA when mixed-mode S dc and S cd s- parameters of a differential device are measured. FPVNA has lower uncertanities when measuring a device that naturally operates with ground referenced modes Calibration and correction

33 The error model includes all possible error terms, including all port-to-port leakage paths. There are 8x8=64 error terms including 4x4(4-1)=48 leakage terms. Possible simplification - neglecting all leakage between ports (crosstalks) gives no-leakage model, leaving total of 4x4=16 error terms The relationship between measured s-parameters (S m ) and actual s-parameters (S a ) is given by: (T 11 )(S a ) + (T 12 ) + (S m )(T 21 )(S a ) - (S m )(T 22 ) = () where (T ij ) are submatrices of cascadable (chainable) t-parameters. It can be shown that at least five 4-port calibration standards is necessary to determine unknown submatrices T ij in the case of the full error model. (Each standard generates 16 equations). At least two transmission standards are necessary for the no-leakage error model. The corrected s-parameters of the DUT are then determined by: (S x ) = [(T 22 )(S m ) - (T 12 )].[-(T 21 )(S m ) + T 11 ] -1 Conclusion 4 years old history of microwave wideband vector measurement Still increasing applications of vector measurement

34 References D. E. Bockleman and W. R. Eisenstadt, "Combined differential and common-mode scattering parameters: Theory and simulation." IEEE Trans. Microwave Theory Tech., vol. 43, pp , July 1995 D. E. Bockleman and W. R. Eisenstadt, "Pure-Mode Network Analyzer for On-Wafer Measurements of Mixed-Mode S-parameters of Differential Circuits," IEEE Trans. Microwave Theory Tech., vol. 45, No. 7, pp , July 1997 D. E. Bockleman and W. R. Eisenstadt, "Calibration and Verification of the Pure-Mode Vector Network Analyzer," IEEE Trans. Microwave Theory Tech., vol. 46, No. 7, pp , July 1998 D. E. Bockleman and W. R. Eisenstadt, "Accuracy Estimation of Mixed-Mode Scattering Parameter Measurements,"IEEE Trans. Microwave Theory Tech., vol. 47, No. 1, pp , January 1999 Vahe Adamian, B. Cole, "VNA-Based System Tests Differential Components," Microwaves and RF, March 2, pp R. A. Speciale, "A Generalization of the TSD Network-Analyzer Calibration Procedure, Covering n-port Scattering-Parameters Measurements, Affected by Leakage Errors," IEEE Trans. Microwave Theory Tech., vol. 25, No. 12, pp , December 1977 J. V. Butler, D. K. Rytting, M. F. Iskander, R. D. Pollard, and M. V. Bossche, "16-term Error Model and Calibration Procedure for On-Wafer Network Analysis Measurements," IEEE Trans. Microwave Theory Tech., vol. 39, No. 12, pp , December 1991 G. F. Engen, "Calibration the Six-Port Reflectometer by Means of Sliding Terminations," IEEE Trans. Microwave Theory Tech., vol. 26, No. 12, pp , December 1978 K. Hoffmann and Z. Skvor, "A Novel Vector Network Analyzer," IEEE Trans. Microwave Theory Tech., vol. 46, No. 12, pp , December 1998 Rautio J. C., "Techniques for Correcting Scaterring Parameters Data of an Imperfectly Terminated Multiport when Measured with a Two Port Network Analyzer", IEEE Trans. on MTT, vol. MTT-31, No.5, May 1983, pp

There is a twenty db improvement in the reflection measurements when the port match errors are removed.

There is a twenty db improvement in the reflection measurements when the port match errors are removed. ABSTRACT Many improvements have occurred in microwave error correction techniques the past few years. The various error sources which degrade calibration accuracy is better understood. Standards have been