Título/s: | Incomplete 2-port vector network analyzer calibration methods |
Autor/es: | Henze, Alejandro; Tempone, Nicolás; Monasterios, Guillermo; Silva, Hernando |
Institución: | INTI-Electrónica e Informática. Laboratorio Metrología RF & Microondas. Buenos Aires, AR |
Editor: | INTI-Electrónica e Informática |
Palabras clave: | Calibración; Redes eléctricas; Analizadores; Vectores; Análisis vectorial; Errores; Mediciones; Simulación |
Idioma: | spa |
Fecha: | 2014 |
Ver+/- Incomplete 2-Port Vector Network Analyzer
Calibration Methods A. Henze 1, N. Tempone 2, G. Monasterios 3, H. Silva 4 RF Metrology Laboratory – Instituto Nacional de Tecnología Industrial (INTI) Buenos Aires, Argentina 1 ahenze@inti.gov.ar 2 ntempone@inti.gob.ar 3 guillem@inti.gov.ar 4 hsilva@inti.gov.ar Abstract— Different types of incomplete 2-port vector network analyzer (VNA) calibration methods are explained. All of them are particular cases of the 12- term error model and a comparison, including advantages and disadvantages, between them and a Full 2-Port method, such as TOSM, is made. Resumen— En el presente informe se explican los distintos tipos de calibración incompleta de un VNA de 2 puertos. Todos ellos son casos particulares del modelo de 12 términos de error, y se realiza una comparación, incluyendo ventajas y desventajas, entre ellos respecto a un método Full 2-Port como el método TOSM. I. INTRODUCTION When calibrating a 2-Port VNA, Full 2-Port calibration is usually employed [1]. There are different types of methods depending on the error model to be considered. The most common calibration method used for coaxial systems is TOSM (also known as SOLT) which uses the 12- term error model [2]. However, this method requires an 8- step procedure to get both ports calibrated. When is not necessary to measure all four scattering parameters (i.e. S11, S12, S21 and S22) of the Device Under Test (DUT) or uncertainties are not necessary to be as small as possible, alternative calibration methods may be employed. Advantages and disadvantages must be previously considered in order to determine which one will be the best option for each particular case. II. TOSM CALIBRATION Before measuring any DUT S-parameters, both VNA’s ports must be first calibrated in order to calculate system errors. Most common employed method is TOSM. It consists in calculating 6 forward (F) and 6 reverse (R) error terms as shown in figures 1 and 2. Fig. 1 Forward 12-term error model flow chart where forward error terms are e00 : Directivity (F) e11 : Port-1 Source Match (F) e10e01 : Reflection Tracking (F) e10e32 : Transmission Tracking (F) e30 : Leakage (Crosstalk)(F) e22 : Port-2 Load Match (F) Fig. 2 Reverse 12-term error model flow chart where reverse error terms are e′33 : Directivity (R) e′11 : Port-1 Load Match (R) e′23e′32 : Reflection Tracking (R) e′23e′01 : Transmission Tracking (R) e′03 : Leakage (Crosstalk) (R) e′22 : Port-2 Source Match (R) Solving measured S-parameters from figures 1 and 2 [2] ( ) S S eeSeSe eSee e a b =S ∆+−− ∆−⋅ += 221122221111 22110110 00 0 0 11M 1 (1) SeeSeSe See e a b =S ∆+−− ⋅ += 221122221111 213210 30 0 3 21M 1 (2) ( ) S S eeSeSe eSee e a b =S ∆+−− ∆−⋅ += ′ ′ 221122221111 11223223 33 3 3 22M ''''1 ''' ' (3) SeeSeSe See e a b =S ∆+−− ⋅ += ′ ′ 221122221111 120123 03 3 0 12M ''''1 '' ' (4) where SxxM: Measured, i.e. uncorrected, S-parameters Sxx: Corrected S-parameters 21122211 SSSS=S −∆ (5) A. VNA Calibration Calibration procedure consists in measuring 7 different reference standards (2 Opens, 2 Shorts, 2 Matches and a Thru) with known reflection and/or transmission values from a TOSM calibration kit. In this paper reference standards are considered to have ideal values as follows 1=ΓOPEN (6) 1−=ΓSHORT (7) 0=ΓMATCH (8) = 01 10 THRUS (9) To perform a complete 2-Port calibration, an 8-step procedure must be done as follows Step 1: Connect Open1 to Port 1 Step 2: Connect Short1 to Port 1 Step 3: Connect Match1 to Port 1 Step 4: Connect Open2 to Port 2 Step 5: Connect Short2 to Port 2 Step 6: Connect Match2 to Port 2 Step 7: Connect Match1 Port 1 / Match2 Port 2 Step 8: Connect Thru between Port 1 and Port 2 1) Port 1 Calibration: Making steps 1 to 3, an OSM calibration [2] to Port 1 is performed and the following forward error terms are calculated from (1) ( )11100 matchS=e M (10) )()( 2)()( 111M111M 00111M111M 11 shortSopenS eshortSopenS =e − ⋅−+ (11) [ ] [ ] )()( )()(2 111M111M 00111M00111M 0110 shortSopenS eshortSeopenS =ee − −⋅−⋅− (12) TABLE I PORT 1 CALIBRATION SUMMARY Reference Error to be corrected Description Open1 Short1 e11 Source Match (F) e10e01 Reflection Tracking (F) Match1 e00 Directivity (F) 2) Port 2 Calibration: Making steps 4 to 6, an OSM calibration to Port 2 is performed and the following reverse error terms are calculated from (3) ( )22233´ matchS=e M (13) )()( ´2)()( ´ 222M222M 33222M222M 11 shortSopenS eshortSopenS =e − ⋅−+ (14) [ ] [ ] )()( ´)(´)(2 ´´ 222M222M 33222M33222M 3223 shortSopenS eshortSeopenS =ee − −⋅−⋅− (15) TABLE II PORT 2 CALIBRATION SUMMARY Reference Error to be corrected Description Open2 Short2 e′11 Source Match (R) e′23e′32 Reflection Tracking (R) Match2 e′33 Directivity (R) 3) Isolation Ports Calibration: Step 7 is optionally made only when very low transmission parameters must be measured. In most cases this error term is neglected. ( )2,12130 matchS=e M (16) ( )1,21203 matchS=e M′ (17) TABLE III ISOLATION PORTS CALIBRATION SUMMARY Reference Error to be corrected Description Match1 Match2 e30 Crosstalk (F) e’03 Crosstalk (R) 4) Calibration between Ports: When making step 8 both Load Match and Transmission Tracking error terms are calculated from (1), (2), (3) and (4) as follows eeThruS eThruS =e ∆−⋅ − 1111M 0011M 22 )( )( (18) [ ] )1()( 221130213210 eeeThruS=ee M −⋅− (19) eThruS eThruS =e ′∆− ′ − ′ )( )( 22M 3322M 11 (20) [ ] )1()( 113303123223 eeeThruS=ee M ′′−⋅′−′′ (21) where 10011100. eeee=e −∆ (22) 32232233 ´´´.´´ eeee=e −∆ (23) TABLE IV CALIBRATION BETWEEN PORTS SUMMARY Reference Error to be corrected Description Thru e22 Load Match (F) e’11 Load Match (R) e10e32 Transmission Tracking (F) e’23e’01 Transmission Tracking (R) Equations (10) to (21) represent the 12 error terms to be calculated. B. DUT S-Parameters Measurement
Solving equations (1) to (4), corrected S-parameters of the DUT can be expressed as follows [1]−[4] ( ) D AAeeAA =S 12212222221111 1 ⋅⋅−′⋅+⋅ (24) ( )[ ] D eeAA =S 2222222121 1 −′⋅+⋅ (25) ( ) D AAeeAA =S 12211111112222 1 ⋅⋅′−⋅+⋅ (26) ( )[ ] D eeAA =S 1111111212 1 ′−⋅+⋅ (27) where 0110 0011 11 ee eS =N M − (28) 0123 0312 12 ee eS =N M ′′ ′ − (29) 3210 3021 21 ee eS =N M − (30) 3223 3322 22 ee eS =N M ′′ ′ − (31) ( ) ( ) 1122122122221111 11 eeAAeAeA=D ′⋅⋅⋅−′⋅+⋅⋅+ (32) where Nxx are normalized S-parameters [4]. C. Full 2-Port: Advantages and Disadvantages 1) Advantages: Provides low uncertainties as all 12 error terms are calculated and all four DUT S-parameters are measured. 2) Disadvantages: Needs an 8-step procedure calibration. It is always necessary to measure all four DUT S- parameters even if only one is needed to be corrected. III. INCOMPLETE 2-PORT VNA CALIBRATION In the past, VNAs had only a transmission/reflection (T/R) test set. This allowed only forward parameters to be measured, since Port 1 acted as a source and Port 2 as a load. Then, calibration methods used were: • Transmission Response (TR) • 1-Port + Normalization (1-P+N) • Enhanced Response(ER) • One-Path 2-Port (1-P 2-P) Nowadays, most VNAs have a full S-parameter test set. This allows the source to be switched to both ports, hence it is able to measure all four S-parameters and a TOSM, i.e. complete, calibration can be done. However, when it is not necessary (or convenient for some reason) to measure all four DUT S-parameters or, uncertainties are not necessary to be as small as possible, above mentioned incomplete calibration methods can be used [5]. All of them are partial calibrations based on TOSM method described in section II. To simplify mathematical expressions, crosstalk error terms will be considered null valued for all cases 030 =e (33) 003 =e′ (34) IV. TRANSMISSION RESPONSE It is the simplest 2-Port calibration method and is used when only S21 (or S12) parameter is of interest. A Thru reference element is connected between ports for the calibration, so only transmission tracking error term is partially calculated. This causes the highest uncertainties in transmission S-parameter measurements. A. VNA Calibration (between Ports) From (2) and (33): ( ) ( ) ( ) ( )ThrueeThruSeThruSe ThruSee =S S∆+−− ⋅ 221122221111 213210 21M 1 (35) Applying (9) in (30) 2211 321021M 1 1 ee ee=S − ⋅ (36) As neither e11 nor e22 are calculated, the correction term related to them is considered null valued. 02211 =ee (37) Replacing (37) in (36) 21M3210 S=ee (38) Similar considerations are applied for the reverse transmission tracking term 12M2301 S=ee ′′ (39) B. DUT S21 (or S12) Measurement As only S21 parameter is measured and e10e32 error term is calculated, equation (25) is reduced to 3210 21 21 )( ee DUTS =S M (40) Similar considerations can be applied for S12 0123 12M 12 '' )( ee DUTS =S (41) C. Transmission Response: Advantages and Disadvantages
1) Advantages: Very fast one-step calibration procedure. Only S21 needs to be measured in order to get its corrected value, so a good option for unidirectional devices. 2) Disadvantages: Only for transmission (S21 or S12) parameters. As Transmission Tracking error term is not calculated correctly, this method is not very accurate with lossy DUTs. On the other hand, it is recommended only for insertable devices as in practice this method always considers ideal Thru values as in (9). V. 1-PORT + NORMALIZATION This method performs a 1-Port calibration (at Port 1 or Port 2) and, separately, a transmission response. This is usually employed when only forward parameters (S11 and S21) or reverse parameters (S22 and S12) are required. A. VNA Calibration 1) Port 1 (or Port 2) Calibration: Procedure is applied in the same manner as in Section II A.1 (or section II A.2). 2) Calibration between Ports: Procedure is applied in the same manner as in Section IV A. B. DUT Forward (or Reverse) Parameters Measurement As DUT reverse parameters are not measured, e22 and all reverse error terms are not calculated, hence all correction terms related to them in (24) and (25) are considered null valued. S11 can be expressed as follows eeDUTS eDUTS =S ∆−⋅ − 1111M 0011M 11 )( )( (42) As OSM and transmission normalization calibrations are performed separately, S21 corrected value remains the same as in section IV B. 3210 21 21 )( ee DUTS =S M (43) Similar considerations are applied for reverse parameters eeDUTS eDUTS =S ′∆−′⋅ ′ − 2222M 3322M 22 )( )( (44) 0123 12 12 )( ee DUTS =S M ′′ (45) C. 1-Port + Normalization: Advantages and Disadvantages 1) Advantages: Corrects directivity, reflection tracking and source match of Port 1 (or Port 2). 2) Disadvantages: Similar as in Transmission Response method. VI. ENHANCED RESPONSE It is an improvement of the 1-P+N method for measuring Forward (or Reverse) S-parameters. It needs the same four steps as before to calibrate the VNA but, in this case, it also calculates Load Match error term. This allows Transmission Tracking error term to be correctly calculated. A. VNA Calibration 1) Port 1 (or Port 2) Calibration: Procedure is applied in the same manner as in Section II A.1 (or section II A.2). 2) Calibration between Ports: Procedure is applied in the same manner as in Section II A.4. B. DUT Forward (or Reverse) Parameters Measurement Although e22 is calculated in this case, DUT reverse parameters are not measured and none of the reverse error terms is calculated. Hence, all correction terms related to them in (24) and (25) are considered null valued and S11 and S21 can be derived as follows eeDUTS eDUTS =S ∆−⋅ − 1111M 0011M 11 )( )( (46) ∆− ⋅ eDUTSe ee ee DUTS =S )( )( 11M11 1001 3210 21M 21 (47) Similar considerations are applied for reverse parameters eeDUTS eDUTS =S M ′∆−′⋅ ′ − 2222M 3322 22 )( )( (48) ′∆−′ ′′ ⋅ ′′ eDUTSe ee ee DUTS =S )( )( 22M22 3223 0123 12M 12 (49) C. Enhanced Response: Advantages and Disadvantages 1) Advantages: Calculates Transmission Tracking error term correctly. 2) Disadvantages: As only Forward (or Reverse) S- parameters are measured, Load Match value can not be used for correcting DUT S-parameters. VII. ONE-PATH 2-PORT Originally named One-Path Full 2-Port, was introduced to T/R VNAs in order to measure all four S-parameters. However, DUT must be manually reversed to measure Reverse S-parameters . At present most VNAs have this calibration option, but special care must be taken as some manufactures consider ER method as 1-P 2-P. A. VNA Calibration
This method considers Forward and Reverse models the same as follows 3300 e=e ′ (50) 2211 e=e ′ (51) 32230110 ee=ee ′′ (52) 23013210 ee=ee ′′ (53) 1122 e=e ′ (54) 0330 e=e ′ (55) Hence, it needs the same four steps as in the previous methods to calibrate the VNA and only 6 forward error terms are needed to be calculated using (10), (11), (12), (16), (18) and (19). B. DUT Parameters Measurement When measuring DUT device, forward parameters are measured first, and then DUT is connected backwards and reverse parameters are measured. This allows equations (24) to (27) to be used with no correction terms null valued. C. One Path 2-Port: Advantages and Disadvantages 1) Advantages: All four DUT S-parameters can be measured. As Forward and Reverse error terms have same values, only a four-step procedure is needed to calibrate the VNA. 2) Disadvantages: Not recommended for VNAs using any combination of coaxial sexed port connectors due to the necessity of adapters. A series of single sweep and DUT manually change procedure must be performed in order to get all four S-parameters. In practice, uncertainties may be higher that Full 2-Port due to connector mechanical repeatability or cable flexibility. VIII. SIMULATIONS A series of comparisons between incomplete calibrations methods respect to TOSM were carried out. S11 and S21 measurements were simulated and maximal deviation results are shown in figures 3 to 6. A. S11 Deviation Results Different maximal deviations of |S11| for 1-P+N and ER methods respect to TOSM are shown in figure 3. As in both incomplete methods, S11 has the same value (see equations (42) and (46)), such deviations respect to TOSM are the same. These deviations depend on Port 2 Load Match, i.e. e22 value, and DUT´s attenuation, i.e. S21 value. For example, if the DUT consists of a 6-dB attenuator and |e22| = 0.1, then maximal deviation respect to TOSM method will be 0.026. If now the DUT consists of a coaxial cable with nominal 0 dB attenuation value, and |e22| remains in 0.1, then maximal deviation respect to TOSM method arises to 0.100. Fig. 3 |S11| maximal deviation for 1-Port + Normalization and Enhanced Response with respect to TOSM method. B. S21 Deviation Results Different maximal deviations of |S21| for TR and ER methods respect to TOSM are shown in figures 4 and 5 respectively for a DUT having a nominal attenuation value of 0 dB. Fig. 4 |S21|dB maximal deviation for Transmission Response with respect to TOSM method when measuring a S21 value of 0 dB. Fig. 5 |S21|dB maximal deviation for Enhanced Response with respect to TOSM method when measuring a S21 value between 0 dB and 6 dB. For example, if DUT´s parameters |S11| = |S22| = 0.1, and
VNA´s error terms |e11| = |e22| = 0.1, then maximal deviation respect to TOSM method will be 0.17 dB for TR method and 0.09 dB for ER method. According to figures 5 and 6, if now the same DUT has an attenuation value of 6 dB and all other values remain the same, then maximal deviation respect to TOSM method arises to 0.24 dB for TR method and remains in 0.09 dB for ER method. Fig. 6 |S21|dB maximal deviation for Transmission Response with respect to TOSM method when measuring a S21 value of -6 dB. IX. CONCLUSIONS Different types of incomplete 2-Port VNA calibrations methods are explained in this paper. Each one of them has its own advantages and disadvantages respect to a complete 2-Port method as TOSM. In practice, if VNA´s error terms and/or DUT´s mismatches are quite low, there will be no significant deviation between incomplete and complete calibration methods when measuring S11 or S21. On the contrary, if VNA´s source and load match error term values are considerable and also DUT is lossy, then incomplete methods are not suitable due to the significant deviations they may have. REFERENCES [1] AN 1287-3, “Applying error correction for VNAs”, 2nd. Ed., Santa Clara, CA: Agilent Tech., 2002. [2] D. Rytting, “Network analyzer error models and calibration methods”, Palo Alto, CA, Hewlett Packard Inc., 1998. [3] B. Hall, “VNA error models: Comments on EURAMET/cg-2/v.01”, ANAMET Report 051, Measurement Standards Laboratory of New Zealand Lower Hutt, New Zealand, 2010. [4] J. Dunsmore, “Handbook of microwave component measurement”, Agilent Tech., John Wiley & Sons, Ltd., UK, 2012. [5] M. Hiebel, “Fundamentals of vector network analysis”, Rohde & Schwarz GmbH & Co. KG, 5th Ed., 2011. [6] G. Wübbeler, Clemens Elster, Thomas Reichel and Rolf Judaschke, “Determination of the complex residual error parameters of a calibrated one-port vector network analyzer”, IEEE Transactions, Vol. 58, No. 9, 2009. [7] AN 1287-11, “Specifying calibration standards and kits for Agilent vector network analyzers”, Agilent Tech., 2011. Ver+/- | |
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